MINHAZ UDDIN 

Integrating Physics-Informed and Machine 
Learning Models for Indoor Temperature 

Prediction  

 

 

 

 

 

 

 

Vaasa 2025 

School of Technology and Innovations 
Master’s Thesis 

 Sustainable and Autonomous systems 



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UNIVERSITY OF VAASA 
School of Technology and Innovations 

Author: MINHAZ UDDIN 
Title of the thesis:  Integrating Physics-Informed and Machine Learning Models for 

Indoor Temperature Prediction. 
Degree: Master of Science in Computing Sciences 
Degree Programme: Sustainable and Autonomous Systems 
Supervisor: 
Co-supervisor 

Petri Välisuo  
Amit Shukla 

Year: 2025 Pages: 69 

ABSTRACT: Nordic buildings face increasing demands for energy efficiency and consistent indoor 
thermal comfort, creating accurate indoor temperature predictions increasingly crucial for 
intelligent HVAC control. This research addresses this challenge by proposing a hybrid prediction 
framework that combines physics-informed learning with traditional data-driven models to 
improve long-term accuracy. 
 
This study uses a multiple-source dataset consisting of building sensors and satellite-derived 
solar radiation measurements. It includes important physical variables like the inside 
temperature, the temperature of the supply air, the temperature outside, and the amount of 
solar radiation. Using this multi-source dataset, several traditional machine learning models 
were developed for comparison such as Extreme Gradient Boosting, Feedforward Neural 
Networks, Random Forest, and Long Short-Term Memory and the proposed Physics-Informed 
Neural Network model. 
 
Findings across the three forecasting horizons (short term: 1 hour, medium term: 6 hours, and 
long term: 12 hours) show that each model has the strengths at different periods-  LSTM 
performs best in short-term prediction (MAE: 0.18), XGBoost in medium term prediction (MAE: 
0.33), and the PINN achieves the most accurate (MAE: 0.29) in long-term prediction through its 
embedded physical constraints. Overall, the findings highlight the benefits of data-driven and 
physics-informed methods, and it emphasizes the potential of hybrid modelling approaches for 
supporting energy efficient, comfort oriented HVAC control in public buildings. 
 
 

KEYWORDS: Machine Learning, Physics-Informed Neural Networks,LSTM, XGBoost, FNN, 
Prediction model, Indoor Prediction, Differential equations model, Smart Buildings, Multi-
Horizon Forecasting. 



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Contents  

1 Introduction 9 

1.1 Background and Motivation 11 

1.1.1 Importance of Indoor Temperature Comfort and Energy Efficiency 11 

1.1.2 Data Driven Modeling for Indoor Temperature Prediction 12 

1.1.3 Opportunities of Physics-Guided Modeling 13 

1.2 Problem Statement and Research Questions 14 

1.2.1 Research Questions 15 

1.3 Research Objectives 16 

1.4 Scope and Limitation 17 

1.5 Thesis Structure Overview 18 

2 Literature Review 20 

2.1 Indoor Temperature Prediction and its overview 20 

2.2 Machine Learning Model for Indoor temperature modeling 21 

2.3 Physics Informed Neural Networks 21 

2.4 Physics-Informed Neural Networks for fast full-field temperature prediction 23 

2.5 Summary of Research Gaps 24 

3 Methodology 25 

3.1 Overview of Methodological Approach 25 

3.2 Data Preprocessing 26 

Handling Missing Data: 26 

Timestamp Alignment: 26 

Feature selection: 27 

Data Normalization: 27 

3.3 Dataset Characteristics and Limitations 28 

3.4 Feature Engineering 30 

3.4.1 Selection of relevant features 32 

3.4.2 Target variable creation 32 

3.4.3 Temporal Structure for Forecasting 33 



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3.5 Model Architecture 33 

3.5.1 Feedforward Neural Network 34 

3.5.2 Long Short-Term Memory 35 

3.5.3 Extreme Gradient Boosting 35 

3.5.4 Random Forest 36 

3.6 Physics-Informed Neural Network Modeling 36 

3.6.1 Governing Differential Equation 37 

3.6.2 Learning Physics Parameters 38 

3.6.3 Physics Loss Integration 39 

3.6.4 Machine Learning Model Comparison 40 

3.7 Evaluation Metrics and Performance Comparison 40 

3.7.1 Mean Absolute Error 41 

3.7.2 Root Mean Squared Error 41 

3.7.3 Coefficient of Determination 42 

4 Results and Findings 43 

4.1 FNN Architecture Search and Performance 43 

4.2 One-Hour Prediction Window 44 

4.3 Six-Hours Prediction Window 46 

4.4 Twelve-Hours Prediction Window 48 

4.5 Physics-Based ODE Model Performance 50 

4.6 Physics-Informed Neural Network Performance 52 

4.7 XGBoost Model Results 54 

4.8 Random Forest Model Performance 57 

4.9 LSTM Model Results 59 

4.10 Model Performance Table 61 

5 Conclusions 63 

6 Limitations 64 

References 66 

Appendices 69 



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Appendix 1. Github Link 69 



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Figures  
 
Figure 1  Architecture of the Feedforward Neural Network used for Indoor 

Temperature Prediction. 34 

Figure 2: Architecture of the Physics-Informed Neural Network (PINN) for indoor 

temperature prediction 40 

Figure 3 : One Hour Prediction: FNN vs Actual 45 

Figure 4: One Hour Prediction: ODE(Physics) vs Actual 45 

Figure 5: One Hour Prediction: FNN vs ODE vs PINN 45 

Figure 6: Six-Hour Forecast: FNN vs Actual 47 

Figure 7: Six-Hour Forecast: ODE vs Actual 47 

Figure 8: Six-Hour Forecast: FNN vs ODE vs PINN 47 

Figure 9: Twelve-Hour Prediction: FNN vs Actual 48 

Figure 10: Twelve-Hour Forecast: ODE vs Actual 49 

Figure 11:Twelve-Hour Forecast: FNN vs ODE vs PINN 49 

Figure 12: Physics Parameter Learning 50 

Figure 13: Physics Parameter Loss Over Epochs 51 

Figure 14: PINN Data Loss Over Epochs 52 

Figure 15:PINN Physics Loss Over Epochs 53 

Figure 16: Data Loss+ Physics Loss Over Epochs 53 

Figure 17: XGBoost One-Hour: Prediction vs Actual 55 

Figure 18 : XGBoost Six-Hour: Prediction vs Actual 55 

Figure 19: XGBoost Twelve-Hour : Prediction vs Actual 56 

Figure 20: One-Hour Forecast: Random Forest vs Actual 57 

Figure 21: Six-Hour Forecast: Random Forest vs Actual 58 

Figure 22:Twelve-Hour Prediction: Random Forest vs Actual 58 

Figure 23:One-Hour LSTM Prediction vs Actual 60 

Figure 24: Six-Hour Prediction Plot 60 

Figure 25: Twelve-Hour LSTM Prediction Plot 61 

 



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Tables 
 
Table 1 : Summary Statistics of Input Variables and Justifying the Use of RobustScaler

 31 

Table 2: FNN Architecture Search Parameters Used in This Study 43 

Table 3 :Top 20 FNN Architectures Based on Validation MAE 44 

Table 4:Performance Metrics for the One Hour Prediction (FNN vs PINN) 46 

Table 5:Performance Metrics for the Six Hour Prediction (FNN Vs PINN) 48 

Table 6: Performance Metrics for the Twelve Hour Prediction (FNN Vs PINN) 50 

Table 7: Physics Learnable Perameters Value 51 

Table 8: PINN Architecture Parameter Used In This Study 52 

Table 9: PINNs Learnable Parameters Value 54 

Table 10: XGBoost Architecture Parameters Used In This Study 54 

Table 11: XGBoost Prediction Performance 56 

Table 12: Random Forest Parameters Used in This Study 57 

Table 13: Random Forest Prediction Performance 59 

Table 14: LSTM Architecture Parameters Used In This Study 59 

Table 15:Combined Model Performance Table 62 

 
 



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Abbreviations 

CFD Computational Fluid Dynamics 

CNN Convolutional Neural Network 

CO₂  Carbon Dioxide 

EU European Union 

FNN Feedforward Neural Network 

HVAC Heating, Ventilation, and Air Conditioning 

IoT Internet of Things 

LSTM Long Short-Term Memory 

ML Machine Learning 

MLP Multi-Layer Perceptron 

MAE Mean Absolute Error 

ODE Ordinary Differential Equation 

PINNs Physics-Informed Neural Networks 

RF Random Forest (Regressor) 

ReLU Rectified Linear Unit 

RMSE Root Mean Squared Error 

R² Coefficient of Determination (R-squared) 

SVM Support Vector Machine 

XGBoost Extreme Gradient Boosting 

  



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1 Introduction 

The accumulation of greenhouse gases, mainly CO₂, is one of the main causes of climate 

change and global temperature increase. This means that we need to be more focused 

on considerable emission reductions. In response, the European Union has set targets to 

minimize emissions by 55% by 2030 and to achieve climate neutrality by 2050 (Loffa et 

al., 2025). In Nordic countries, heating homes mostly uses a lot of energy and reason is  

long winters and cold weather. Which makes it necessary to keep the indoor 

temperature constantly controlled. An accurate real-time model for predicting indoor 

temperature distribution is essential for both energy efficiency and thermal comfort (Ma 

et al., 2021; Park et al., 2021), particularly when a workplaces or localized zones requires 

controlling (Sun et al., 2020). As building became progressively digitized, there is an 

opportunity to use sensor-based data and advanced algorithms to develop predictive 

models that can forecast temperature changes and optimize heating, ventilation, and 

control central or non-central air conditioning operations. 

 

Conventional modeling approaches, such as physics-based simulations that use 

thermodynamic principles, are often limited by their complexity, high computational 

cost, and dependence on precise building specifications (Lu et al., 2020). In recent times, 

data-driven methods, mainly machine learning (ML) models, have gained more attention 

due to their ability to model nonlinear relationships from sensor data without having 

complete physical knowledge (Amasyali & El-Gohary, 2018). 

 

Among various ML methodologies, deep learning models such as Feedforward Neural 

Networks (FNN), Long Short-Term Memory networks (LSTM), and Extreme Gradient 

Boosting (XGBoost) have been utilized with different levels of efficacy for predicting 

indoor environment characteristics (Li et al., 2025; Li et al., 2020; Norouzi et al., 2023) . 

However, a major limitation of purely data-driven models is their lack of physical 

interpretability and their inability to generalize under novel conditions. As a result, 

physics-informed neural networks (PINNs) have emerged. These help to make sure that 



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model predictions are within the limits of what science says is possible. They normally 

do this by adding physics rules and laws directly into the loss function during training 

period (Raissi et al., 2019). The most interesting part of PINNs is that it ensures that 

model predictions not only fit observed data but also obey critical physical principles. 

 

According to Nordic climate where temperature fluctuations are significant, it is essential 

to accurately predict indoor temperature to maintain thermal comfort and reduce 

unnecessary heating energy use. Reliable prediction models support the proactive 

control of Heating, Ventilation, and Air Conditioning (HVAC) systems, and it prevents energy 

waste by ensuring comfortable indoor conditions for occupants. In the context of indoor 

temperature prediction, combining the physics ordinary differential equation (ODE) with 

ML models has shown promise in enhancing prediction accuracy while maintaining 

physical accuracy also (Hannula et al., 2025; Häkkinen, n.d.). This is a hybrid approach 

that aims to create a bridge between theoretical and data-driven modeling. It enables 

significant improvements to HVAC control strategies. Additionally, Internet of things 

(IoT)-enabled sensors and smart buildings have made huge amounts of sensor data 

available, which allows for more accurate and detailed modeling structure. According to 

the researcher (Miller et al., 2018), these datasets are kind of an ideal foundation for 

creating intelligent control systems that can dynamically react to user behavior, internal 

thermal loads, and other external variables. By using this data in hybrid modeling 

frameworks, it is possible to predict indoor temperature trends across various time 

periods and implement measures to prevent any issues. 

 

This thesis investigates the importance of PINNs for indoor temperature prediction in 

public buildings, while comparing their performance with traditional ML models. The 

goal is to develop a reliable and generalizable model that can support the energy-

efficient operation of buildings under any real-world conditions. 

 

 

 



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1.1 Background and Motivation 

1.1.1 Importance of Indoor Temperature Comfort and Energy Efficiency  

Especially in the Nordic region, indoor thermal comfort maintenance and maintaining 

energy efficiency are one of the main pillars in modern building operations. One of the 

main reasons behind it is the long winter season in Nordic contries, which makes 

consistent heating demand. As it is known, thermal comfort has major impacts on 

human health, cognitive performance, and productivity(Luo et al., 2023). Improper 

maintenance in indoor conditions can provide discomfort, as a result, it can reduce 

concentration, increase fatigue, and affect long-term health(Du et al., 2023). In research 

it is found that in the EU, its buildings are responsible for about 40% of the total energy 

consumption and 36% of CO2 emissions, where space heating being is being found the 

primary energy consumption (Economidou et al., 2020). As a result, international and 

regional energy policies such as the EU green deal are focused on retrofitting and 

operational optimization of existing buildings and it is hope to meet climate neutrality 

goals by 2050 (Loffa et al., 2025). 

 

Predictive modeling, like indoor temperature prediction or comfort level prediction, 

becomes an important part of a smart building control system. By predicting indoor 

temperature changes, operations of HVAC systems can be adjusted carefully, 

unnecessary energy use can be reduced, and thermal discomfort can be avoided also. 

The success of this kind of model depends on its ability to process complex relationships 

in the data and adapt to dynamic scenarios (Amasyali & El-Gohary, 2018). 

 

Importantly, these predictive models can be improved and provide more accurate results 

by aligning them with physical law. As  researchers (Hannula et al., 2025; Häkkinen, n.d.) 

demonstrated, that the models which mainly integrate physics-based constraints with 

ML, such as PINNs which has a chance that it can perform better in real-world 



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applications by ensuring physical consistency and improving generalization under 

variable conditions. 

 

Hence, optimizing the indoor temperature is not just always about comfort, it is also 

important for reducing operational costs, achieving efficient energy goals and making 

perfect contribution to broader climate change mitigation. 

 

1.1.2 Data Driven Modeling for Indoor Temperature Prediction  

Data-driven approaches, especially ML models, which have shown significant 

improvement and promised results in indoor temperature forecasting because it can 

understand and it has the ability to learn complex, nonlinear patterns from sensor data. 

Indoor temperature predictions and its changes is mostly done with ML models like 

XGBoost, LSTM, Convolutional Neural Network with Long Short-Term Memory (CNN-

LSTM), and Multi-layer Perception (MLP) (Hannula et al., 2025;  Li et al., 2020; Häkkinen, 

n.d.). Although, all these individual data-driven models face several challenges that 

constrain the accuracy, robustness, and generalization. 

 

One significant challenge is dependence on better-quality representative training data. 

In the case of most building environments, sensor placement, calibration errors, and 

data gaps give noisy data and sometimes an incomplete dataset. This has negative effects 

on model training and reduce the prediction reliability also (Amasyali & El-Gohary, 2018; 

Miller et al., 2018). Moreover, these ML models are sensitive to changes in external 

environmental conditions such as weather changes, occupancy, humidity, and there is a 

chance that it can perform well in training environments but struggle when it will be 

deployed in an environment that is much different from their training data or unseen 

condition (Yan et al., 2015). 

 

Another limitation is the “black box” nature of most ML models. Though this kind of 

model can provide accurate predictions in under some controlled scenarios, but it 

generally fails to explain how these kinds of predictions are made. It is therefore difficult 



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to ensure that the model always works, Which would be a needed for safety-critical for 

HVAC control application type situations (Li et al., 2025). Traditional ML models generally 

require large quantities of labelled data for training, which may not always be possible 

and feasible in many buildings, especially older buildings. As sensor installation is not 

feasible on those buildings, or it will be much more costly. 

 

To address these limitations, recent research proposes that integrating physics domain 

knowledge with ML, such as PINNs, which mainly aims to embed thermodynamic 

principles into learning processes and uses that knowledge to train the model. So that 

the trained model is expected to predict more accurately. These kind of hybrid 

approaches can improve prediction accuracy and provide more sustainable solutions in 

intelligent building systems (Hannula et al., 2025; Raissi et al., 2019; Amasyali & El-

Gohary, 2018).  

 

 

1.1.3 Opportunities of Physics-Guided Modeling 

Physics-Informed modelling, offers some promising direction for the improvement of 

indoor temperament prediction in buildings. By introducing and integrating physics laws 

directly into the learning process of a model, it can overcome many weaknesses found 

in purely data-driven methods (Amasyali & El-Gohary, 2018; Raissi et al., 2019). 

 

One of the main benefits of physics-informed approaches is their ability to use the 

thermodynamic principle for training the model or use it for physics learning. For 

example, while forecasting indoor temperature, the heat transfer equation based on 

Fourier law of heat conduction can be added, or the energy balance principle can also 

be integrated as a part of the physics function. This mainly allows the model not only to 

learn from available data but also helps to know physics behaviour as it is leading to 

more stable and realistic predictions (Hannula et al., 2025; Häkkinen, n.d.). 

 



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Another important opportunity is improved data efficiency. ML models mainly require 

large datasets to generalize well, which might not be always possible and feasible. 

However, this kind of assumption is not true, mainly in practical environments where 

limited amount of data is available. PINNs models can achieve better performance even 

with a small dataset, as it provides additional structure which can be provided into ML 

models and guide the learning process. This makes it a perfect fit for applications using 

historical or sensor data (Zhao et al., 2021). 

 

Moreover, the hybrid design of PINN models provides sufficient flexibility to integrate 

ML architectures such as LSTM and FNN, which also has the ability of learning complex 

and nonlinear relationship patterns . This balance is especially useful for smart HVAC 

systems because trust in predictions is crucial for automated decision-making (Jaffal, 

2023).  

 

Recent research also shows that PINN models perform more accurately under some 

extreme and changing conditions. For instance, there is one research that explain that 

PINNs can provide better prediction accuracy in colder periods compared to standard 

LSTM model, mainly due to their alignment with thermodynamic behavior in the 

extrapolation scenario (Hannula et al., 2025; Häkkinen, n.d.). 

 

In summary, integrating physics laws and their knowledge into ML creates opportunities 

to improve robustness, accuracy, and reliability in indoor temperature forecasting. This 

makes physics-guided modeling particularly gorgeous and sustainable for smart building 

control strategies. 

 

1.2 Problem Statement and Research Questions 

The increasing demand for energy efficiency and indoor thermal comfort in different 

buildings of Nordic countries has given more priority in the development of accurate and 

reliable indoor temperature prediction models. While in traditional models and their 

learning shows promising results in complex modeling and thermal behavior, which 



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mainly uses sensor and some environmental data (Amasyali & El-Gohary, 2018; Jaffal, 

2023). However, physics-informed models need more detailed input parameters. They 

are also kind of more computationally intensive (Zhao et al., 2021). As limited research 

has been conducted comparing PINNs with traditional models like LSTM, XGBoost, and 

FNN on building sensor datasets, this study aims to fill that gap by evaluating their 

performance using multi-source input data. 

 

Indoor temperature can be predicted using combination of real time and historical data 

from various sources. These sources include building sensor data such as current indoor 

temperature, districts heating water temperature, humidity, and CO₂ levels, HVAC 

system inputs such as supply air temperature, return air temperature, air flow rate, 

district heating water incoming and outgoing temperature. Satellite based data like 

surface temperature and solar radiation can also add and support more environmental 

context to it. 

 

Predicting indoor temperature is important because thermal systems can have some 

time delays means that by the time a change in temperature occurred and detected by 

a controller the comfortness of may already compromised. So predictive models enable 

a proactive suggestion to HVAC control system which allows the system to have some 

idea of future conditions such as sudden drop in outdoor temperature then it will adjust 

heating or cooling before any discomfort happens. So, this is not only improves thermal 

comfort but also optimize energy by avoiding over heating or under heating the indoor. 

 

Therefore, in this thesis, both data-driven models and physics equation-based learning 

approach are used by developing a hybrid model for indoor temperature forecasting. 

 

1.2.1 Research Questions 

• How accurately indoor temperature can be predicted using ML models and which 

model is the most suitable? 



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• How PINNs can improve the accuracy of indoor temperature prediction com-

pared to traditional data driven models? 

• Can multi-horizon prediction improve the reliability of indoor temperature pre-

dictions for HVAC control in smart buildings? 

 

1.3 Research Objectives 

The primary objective of this thesis is to develop a prediction model that integrates 

physical knowledge in a form of ODE using outdoor temperature, solar radiation, 

ventilation and other data to model heat transfer. This approach enables the prediction 

of air temperature based on the range of features, added with a physics-consistent and 

generalizable indoor temperature prediction model for residential and public buildings. 

This research aims to bridge the gap between traditional ML models and physics-based 

learning and its approaches. PINNs can be used to connect domain knowledge to the 

learning process., we can achieve more accurate results. The study shows the 

effectiveness of this hybrid approach in comparison to baseline models such as LSTM, 

XGBoost, and FNN. The objectives of the study are articulated below:- 

 

Objective 1: To develop and evaluate traditional machine learning models (LSTM, 

XGboost, FNN, Random forest) 

This study aims to create a model using indoor sensor data, satellite based solar radiation 

input and other environmental parameters for indoor temperature prediction and 

evaluating the ML performance. 

 

Objective 2: To construct a physics-informed neural network  

To construct a model by embedding thermodynamic principles into it and provide loss 

functions like physics loss and data loss to guide the model's Learning process towards 

physically consistent predictions. 

 

Objective 3: To compare the predictive accuracy, generalization ability, and physical 

consistency  



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Compare the models like XGboost, LSTM, Random forest which are traditional models, 

and the PINNs model across multiple forecasting horizons and check which one is 

working more efficiently for prediction.  

 

1.4 Scope and Limitation 

This study aims to predict indoor temperatures in both residential and non-residential 

buildings in Nordic climate zones. Where heating plays an important role in overall 

energy consumption. The scope is defined by the use of real-world sensor data and 

historical data from systems. The models are trained and tested using data collected 

from smart buildings equipped with sensors from Finland (Nordic Zone). 

The core of this study lies in the comparative evaluation of traditional ML models such 

as (FNN, LSTM, XGBoost) and PINN model which is also a combination of FNN model 

with combination of physics loss and data loss. The PINN is constructed by integrating a 

simplified thermodynamic ODE which represent indoor thermal dynamics and guiding 

the learning process toward physically meaningful predictions. 

 

However, this study has several limitations: 

• Simplified physics representation: The thermal behavior of buildings is influ-

enced by multiple interacting factors such as solar gains, outdoor temperature, 

humidity, and indoor air temperature. The physics equation used in this thesis 

captures only this subset of dynamics. 

• Building-specific modeling: The models are developed using data from a limited 

number of buildings. Therefore, generalization to buildings with different struc-

tures, insulation properties or usage patterns may be limited without retraining 

or adaptation. 

• Data quality and missing values: Although with lots of preprocessing efforts 

missing or noisy sensor data can introduce an uncertainty in both data-driven 

and PINN models. 

 



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In spite of these limitations, the results teach us important things about the good and 

bad parts of using hybrid learning for smart building energy prediction and contribute to 

the emerging body of research on physics based learning in the built environment. 

 

1.5 Thesis Structure Overview 

Chapter 1: Introduction 

This chapter introduces the motivation behind the study. It also outlines the research 

problem. The chapter identifies the existing research gap. It also presents the objectives 

and scope of the work. It also provides information about indoor temperature prediction 

and explains why combining physics-informed learning with ML models is important for 

improving energy efficiency in smart buildings. 

 

Chapter 2: Literature Review 

This chapter reviews the existing structure of research related to indoor temperature 

prediction, energy-efficient building operation, and data-driven modeling techniques, 

like: FNN, LSTM, and XGBoost. It also discusses PINNs model as well. The chapter also 

highlights the limitations of purely data-driven methods and the opportunities 

presented by hybrid modeling approaches. 

 

Chapter 3: Methodology  

In this chapter, it mainly describes the data sources, feature engineering, and 

preprocessing steps. Details of the development of baseline ML models and the physics-

informed model. Also explains the physics-guided modeling components and governing 

equations and how they are integrated, and defines the evaluation metrics used for 

compare model performance. 

 

Chapter 4: Results and Findings 

In this chapter, it presents the experimental results for all models and prediction horizons. 

The performance is compared based on MAE, RMSE, and R², and also the prediction 

behavior is shown using a time-series plots. The chapter highlights three major findings. 



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1) LSTM performs best in short-term 1 hour predictions. 

2) XGBoost performs competitively for 6 hour forecasts. 

3) PINN model provides the more stable prediction for 12 by integrating physical 

constraints. 

 

Additionally, the chapter also analyzes error behavior, model limitations, and cases 

where models struggle to find sudden temperature fluctuations. 

 

Chapter 5: Conclusions 

This chapter summarizes the significant scientific contributions and insights obtained 

through the comparative evaluation. It explains how hybrid physics-informed 

approaches improve the stability and PINN model accuracy of long-term predictions. 

 

Chapter 6: Limitations 

This chapter highlights key limitations in both the practical and methodological aspects. 

These limitations include sensor uncertainty, sensor placement, sudden temperature 

spikes, and limited ground-truth reliability. The chapter also suggests directions for 

future research, including comfort-based prediction, and advanced PINN frameworks. 



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2 Literature Review 

This chapter mainly identifies the existing research that has been done on prediction 

using data-driven and physics-informed ML models. The review highlights main themes 

such as conventional thermodynamic modeling, the rise of ML approaches like FNN, 

XGBoost, LSTM, and the recent emergence of PINNS. The key purpose of this review is 

to build a theoretical foundation that will guide through the hybrid modeling approach 

that is adopted in this thesis. This kind of theoretical foundation mainly supports the 

development of physically consistent, scalable, and interpretable predictive models that 

can be used for real-world building data and environmental data for predicting indoor 

climate control optimization. 

 

2.1 Indoor Temperature Prediction and its overview 

Indoor temperature prediction plays an important role in an efficient energy control 

system, like an HVAC system.  Accurate prediction supports real-time decision making 

and demand side management. This is important mainly in buildings where maintaining 

thermal comfort is critical (Ma et al., 2021). Traditional physics-based simulations using 

EnergyPlus or Modelica are based on the principles of thermodynamics. Despite this, 

their deployment is often hampered by the need for detailed building metadata, long 

computational runtimes, and scalability issues(Luo et al., 2023; Miller et al., 2018). 

 

In recent years data driven ML models such as LSTM, XGBoost, CNN can solve complex 

and nonlinear issues from historical sensor data which enables more accurate prediction 

without deep knowledge of building physics. Although this model may not perform well 

or have lack of interpretability in unseen scenarios  (Häkkinen, n.d.; Hannula et al., 2025). 

So for this reason physics informed approaches is introduced as it can combine both ML  

with the structure of physics laws by integrating equations like furrier equation, energy 

balance equations improve its robustness (Zhao et al., 2021; Hannula et al., 2025; 

Häkkinen, n.d.). 

 



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2.2 Machine Learning Model for Indoor temperature modeling 

Particularly in ML, data-driven ML models were able to gain more popularity for indoor 

temperature prediction as it has the ability to learn complex, nonlinear relationships 

from sensor data without requiring any detailed physics knowledge of building. The 

increasing availability of IoT based sensor data such as indoor temperature, outdoor 

condition, ventilation settings and solar radiation has further boosted the use of these 

methods in smart buildings (Amasyali & El-Gohary, 2018). Models such as FNN, Random 

Forests (RF), Support Vector Machines (SVM), and XGBoost have been widely used for 

indoor temperature forecasting (Amasyali & El-Gohary, 2018). FNNs and XGBoost are 

particularly suited for capturing nonlinearities and short-term dynamics, but they have 

one issue such as a lack of long-term temporal dependencies. To overcome this, LSTM 

architectures have been added in recent studies (Li et al., 2020). As of now, LSTMs can 

learn temporal dependencies more effectively, especially in hourly or sub-hourly 

building sensor  datasets. 

 

However, purely data-driven models tend to act as black box modeling. Their 

performance deteriorates when exposed to out-of-distribution inputs or sensor drifts, 

limiting their reliability for building automation systems (Loffa et al., 2025; Luo et al., 

2023). Studies have shown that it often fail to generalize under changes in occupant 

behavior, external weather, or system faults (Muroni et al., 2019) 

 

2.3 Physics Informed Neural Networks 

Physics-Informed Neural Networks were mainly introduced as a hybrid modeling 

approach to address the shortcomings of ML models (Raissi et al., 2019). In PINNs, 

domain knowledge is embedded into the neural network training by incorporating a 

physics-based residual into the loss function. This gives a chance to the model to remain 

grounded in physical principles even when the data is sparse or noisy. 

 



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In the building energy modeling context, several studies have explored PINNs and 

physics-based learning. For instance, Ma et al. applied a physics-constrained deep 

learning model for indoor temperature forecasting and reporting improved 

generalization and consistency over standard LSTM (Ma et al., 2021). Hannula et al. 

developed a PINN using a simplified energy balance differential equation. Which 

demonstrates that it can outperform a regular LSTM in terms of Root Mean Squared 

Error (RMSE) and interpretability (Hannula et al., 2025). Similarly, Wang et al. extended 

this idea by integrating PINNs with sensor fusion techniques for better spatiotemporal 

temperature prediction(Wang et al., 2025). 

 

A recent comparative study by titled Physics-Informed vs. Deep Learning Indoor 

Temperature, the authors (Loffa et al., 2025) mainly identifies the limitations of 

traditional ML and deep learning models, such as LSTM. The main reason for this 

modeling is forecasting indoor temperature under data-scarce or non-ideal conditions. 

It is recognized that data-driven models often act as black boxes with limited physical 

clarity. So, the authors propose a PINN framework that interconnects governing 

thermodynamic principles directly into its learning process. This approach emphasizes 

the integration of a residual-based loss function derived from the parameters of 

simplified ODEs. Two weeks to two years of data was used for prediction model training 

and for the evaluation of their performance with varying data volume. The dataset 

comprises simulated data that is generated using output from an Energy Plus simulation. 

For this research, Turin (Italy), Munich (Germany), Copenhagen (Denmark), and Madrid 

(Spain). These cities represent a diverse range of climates with hot summers and cold 

winters. Their findings show that the PINN models consistently outperform LSTM models 

in small data scenarios across multiple cities. In that research, with two weeks of training 

data, PINN achieved a lower mean absolute error (MAE) of 0.40 °c in Turin compared to 

LSTM, which is 0.56 °C. In the case of Munich, the PINNs also outperformed the LSTM 

across all periods, with the most stable performance, MAE of 0.15 °C (PINN) and 0.49 °C 

for (LSTM). Even in more complex environments like Madrid, the PINN maintains an error 



23 

 

   

 

below 2°C in all cases. The research highlights that incorporating physics laws into 

training enables PINNS to generalize better and provide reliable predictions. 

 

2.4 Physics-Informed Neural Networks for fast full-field temperature 

prediction 

Accurately predicting indoor temperature is little challenging as it normally follows two 

approaches like physics-based models and data- driven based model. To overcome the 

limitations of both model (Jing et al., 2023) introduced a physics-informed framework of 

neural networks for predicting full field indoor temperatures. Their method combines 

CFD simulations, Physics laws, and sparse sensor data into a unified learning system. The 

framework has three components: 

• A surrogate model that is trained on CFD data and ruled by energy conservation 

equations, 

• A model that adjusts the surrogate model output using a small set of real sensor 

measurements through transfer learning. 

• A recovery model that integrates both to produce fast and accurate temperature 

prediction across time series. 

 

The authors tested these methods in a simulated room environment with changing air 

velocity and heat sources. With four observation points, the models performed well 

according to the author (RMSE = 0.777 °C, R² = 0.999 at 600s). With more sensors (24 

points), accuracy improved further (RMSE = 0.425 °C). 

 

Although the training phase required significant CFD work and sensor data and once 

trained PINN enables real time accurate predictions for that environment. However, it 

has a limitation that it is not ideal for small building zones with complex heat sources 

due to modeling limitations. 

 

 



24 

 

   

 

2.5 Summary of Research Gaps 

Existing studies (Jing et al., 2023; Loffa et al., 2025) and lots of other research mainly 

train and validate their frameworks on a simulated building or a limited set of climate 

zones. Their ability to generalize across the real sensor data of a building with data-

driven model, physics-informed models and diverse weather patterns make a 

comparison between the models performance evaluation has remained in a gap. While 

many significant progresses have been made but gaps remain in model transferability, 

performance variation under noisy or non-noisy data, and integration with real-world 

HVAC control logic remains gap. Most current works evaluate models on isolated 

buildings without generalizing across zones with simulated data or varying weather 

scenarios or considering human comfort. Moreover, there are some works done with 

PINNs model, but there is less research done about the performance of PINNs model 

considering to others models, so we can say it is still in experimental stages. 

 

 



25 

 

   

 

3 Methodology 

This chapter outlines the methodology for the development, training, and evaluation of 

ML models and hybrid physics-informed models for indoor temperature prediction. This 

research aims to provide a transparent and consistent process from data collection to 

model evaluation. Mainly, the workflow includes data preprocessing, model design, 

training strategy, performance evaluation, and then making a comparison between 

traditional ML models and physics-informed models. One of the main focuses of this 

research is the integration of physics-based constraints using the ODE of indoor heat 

transfer to enhance the model concept and physics consistency. 

 

3.1 Overview of Methodological Approach 

The methodology that is followed in this thesis is a combination of both data-driven and 

physics-informed techniques to forecast indoor temperature with accuracy and 

consistency. Some key components of this methodology are: 

• Collecting and preprocessing building sensor data and satellite based solar radi-

ation observation data at 5-minute intervals. 

• Feature engineering and identifying meaningful input variables. 

• Model development using traditional models: FNN, XGBoost, and LSTM. 

• Development of a hybrid PINN model, which is integrated with physics laws via 

ODEs. 

• Multi-horizon or multi-interval prediction to evaluate short and long-term pre-

dicting efficiency. 

• Evaluation of performance using performance metrics, including MAE and RMSE. 

Each model was trained with historical data from a selected public building. The dataset 

includes sensor measurements and satellite solar radiation inputs, which allows models 

to capture both internal and external influences while measuring indoor temperature 

changes. The PINN model is mainly designed to integrate a physics-based residual term 

and find the physics loss by comparing with the predicted data. So, this ensures the 

model maintains physical plausibility even if there is noisy data in the scenarios. 



26 

 

   

 

3.2 Data Preprocessing 

In this research, before training any ML or physics-informed models, one of the main 

critical steps is to preprocess the raw data and ensure usability, consistency, and quality. 

In this research, indoor temperature prediction relies on multiple data sources, including 

sensor-based data from buildings and external environmental data such as satellite 

based solar radiation parameters. These datasets vary in terms of sampling frequency. 

So, some preprocessing operations were required to process the data. 

 

Handling Missing Data:  

It is known that in the real world, sensor data often has missing and corrupted values 

due to some transmission errors, sensor faults, or downtime. The dataset used for this 

research also has some time intervals with missing values, and there was no continuation 

of values, so this cause time alignment issues, which are addressed by applying spline 

interpolation at a fixed  5-minute interval. This spline interpolation approach generates 

smooth curves with existing data points and also estimates missing values with better 

accuracy than other linear methods. So, this interpolated dataset mainly ensures 

uniform time intervals and fills gaps in the data sequence. 

 

Timestamp Alignment:  

The telemetry data from sensors sometimes included different time zones and formats. 

As for this research, satellite data is also used, so for all timestamps, it was converted to 

a uniform format, though sensors were established in Pietarsaari, Jakobstad, Finland, 

and we have downloaded satellite data from other sources, so it was localized to the 

desired time zone UTC+2 for Finland. So, this step mainly ensures consistency when 

merging datasets from different sources. 

 



27 

 

   

 

Feature selection:  

The dataset includes many variables, but for this research, it was found that only a subset 

was relevant for temperature prediction modeling. So, the selected features included: 

• Indoor temperature (Target variable) 

• Supply Air Temperature 

• Outdoor temperature 

• Satellite-based solar radiation values 

  

Data Normalization: 

For bringing all features to the same scale and avoiding any dominance by any single 

variable, the Robust scaler from scikit learn was used. Without normalization variables 

like radiation, outdoor temperature, and supply air, return air temperature would appear 

on different numerical scales. This can cause models, mainly neural network models, to 

give more weight to features with large values simply because of their scale. For ML tasks, 

two popular scaling methods are: MinMax scaler and Standard scaler. 

 

MinMax Scaler: It mainly scales values to a fixed range, typically [0,1]. This scaler method 

is simple, and it works well when the data is clean. But it is very sensitive to any outliers. 

A single extreme value can stretch the range, and there is a chance to distort all other 

values. 

 

Standard Scaler: It mainly transforms data using the mean and standard deviation. So it 

centers the data around zero with unit variance. However, it also sometimes struggles 

when outliers are present because the mean and standard deviation are easily 

influenced by extreme values. It is already known that in environmental and building 

telemetry datasets, outliers are almost unavoidable. So sudden sensor spikes, sensor 

drops can happen, and it is normal system behavior. 

 



28 

 

   

 

Because of this, we mainly chose the Robust Scaler method. This method is designed to 

reduce the effect of outliers. Instead of using the mean and standard deviation, it uses 

the median and the interquartile range (IQR), which is more stable when unusual values 

appear. 

The scaling formula is:  

 

 
𝑋𝑠𝑐𝑎𝑙𝑒𝑑 =

𝑋  −  𝑚𝑒𝑑𝑖𝑎𝑛(𝑋)

𝐼𝑄𝑅(𝑋)
 

 

(1) 

 

So, by using this way, even if a sensor suddenly reports an unrealistic peak, the scaling 

process stays stable and meaningful. 

 

Overall, Robust Scaler ensured that all the features were on a similar scale without any 

sudden anomalies or distortions in the learning process, which leads to more reliable 

gradient updates and better model convergence. 

 

3.3 Dataset Characteristics and Limitations 

The dataset used in this research mainly a collection of indoor temperature, outdoor 

temperature, supply air temperature, and satellite-based radiation values which is 

collected from a public building of Pietarsaari, Jakobstad, Finland. This dataset mainly 

covers the time between November 12, 2024, and January 7, 2025. Although, this 

dataset is important for developing and testing indoor temperature prediction models, 

it is also very important to understand its limitations to the proper assessment of model 

performance. 

 

At first It is important to note that the exact placement of sensors inside the building is 

unknown. Indoor temperature sensors can be located near windows, doors, and 

ventilation outlets. This kind of situation can influence in the recorded of temperature 

readings. As there is an absence of detailed sensor documentation, it is tough to assess 

the accuracy of the measurements across the entire indoor environment.  



29 

 

   

 

 

Second, while data exploration several sudden spikes and abnormal jumps were 

observed in the indoor temperature readings. These types of sudden spikes which are 

mainly anomalies may be caused by multiple factors, such as: 

• Errors in sensor calibration  

• Temporary heating or cooling system adjustments issue, 

• Window or door opening events, 

• Data transmission related issue, 

• Rare environmental disturbances. 

 

Since indoor temperature normally changes slowly over short period of time, but if there 

is any sudden changes that may indicate sensor noise or operational errors. Although 

interpolation and smoothing techniques were applied but still such anomalies may affect 

model accuracy. 

 

Furthermore, the dataset has only one indoor temperature sensor, which makes it 

difficult to perform any cross-validation between multiple sensors. Having several indoor 

sensors at different locations would allow us to identify if there is any faulty readings, 

spatial averaging, or multizone modeling. The single sensor makes fault detection 

challenging and it increases dependence on preprocessing methods to ensure data 

quality. 

 

Finally, the short duration of the dataset, however, limits the models exposure to longer 

seasonal variations like extreme cold conditions, or unusual summer conditions, and 

different operational states of the HVAC system. Although the dataset is sufficient for 

testing the feasibility of short-term forecasting and physics-informed learning, the long-

term thermal behavior of the building may not be fully captured by it. 



30 

 

   

 

3.4 Feature Engineering  

Feature engineering is a process of selecting and creating useful input variables that help 

ML models to produce better predictions. In this research, it plays an important role in 

improving the accuracy of indoor temperature forecasting models. 

 

From the original telemetry building dataset from Pietarsaari, Jakobstad, Finland. We 

have selected some key variables such as indoor temperature (Tin), Outdoor 

temperature (Tout), Supply air temperature, and satellite-based solar radiation. It is 

found that these are the important factors that normally affect the temperature of a 

building. However, it is important to clarify that these features were selected from the 

available sensor data and not necessarily based on a full ranking of importance. 

Therefore, it is more correct to say that these variables are assumed to be some of the 

most important. 

 

Additionally, the dataset for this building was missing two critical variables information 

such as central heating water temperature and district heating flow and both of which 

are critical variables in understanding heat delivery and energy consumption. So, 

without these variables it is difficult to directly calculate heating energy or differentiate 

between internal and external heating influences. 

 

To make the model easy to understand and the heating and cooling effect better, we 

created a new feature called ventilation temperature difference (ΔT).  It is calculated as 

Tsupply – Tindoor.  This ΔT refers to the temperature difference between the supply air 

temperature and the indoor air temperature There is also another temperature 

difference, which is important difference between the indoor temperature  and the 

outdoor temperature. Another important feature is that we have used step by step 

recursive forecasting and It uses the last timestep's data (temperature at time t) to 

predict temperature at time t+1 and then it uses the predicted value at t+1 as part of the 

input to forecast t+2 kind of one-step-ahead predictions. 

 



31 

 

   

 

Before training the models, we scaled all the features using RobustScaler from 

preprocessing library of SKLearn toolbox . This mainly helps to normalize the data and 

makes the training more stable, especially if there are any unusual spikes or outliers in 

the dataset. We chose Robust Scaler specifically because it is less influenced by outliers 

compared to other scalers like MinMax Scaler or Standard Scaler. So instead of using 

mean and standard deviation, Robust scaler uses median and interquartile range. It is 

found that it is more reliable when the dataset contains some extreme values. In our 

research case, it is sudden temperature change or sensor spikes, which are common in 

building telemetry data.   

 

Variable Mean Median Std. Dev Min Max 

Indoor Temperature (°C) 22.15 22.27 2.30 13.26 28.02 

Supply Temperature (°C) 34.65 33.65 7.31 20.48 123.36 

Outdoor Temperature (°C) -1.78 -1.45 4.55 -14.99 9.23 

Satellite Radiation 4.40 0.00 11.24 0 108.91 

Table 1 : Summary Statistics of Input Variables and Justifying the Use of RobustScaler 

 

So here the table includes the mean, median, standard deviation, minimum, and 

maximum values for each feature. and satellite radiation and supply air temperature 

variables show a large difference between their minimum and maximum values with 

standard deviations of 11.24 and 7.31 respectively. it is a indication presence of 

significant outliers which can negatively impact model performance if not handled 

properly. Similarly for the indoor temperature the range is from 13.26 to 28.02, which as 

we discussed earlier about sudden spikes and it supposed to be more stable within short 

timeframes. So, this observation justify that instead of using StandardScaler or 

MinMaxScaler, we applied RobustScaler which uses the median and interquartile range 

and is less sensitive to outliers. 

 



32 

 

   

 

Overall, this feature engineering process helps us to prepare a more meaningful dataset 

which mainly supports both ML and PINN models for predicting indoor temperature 

more accurately. 

 

3.4.1 Selection of relevant features 

Based on the literature review and domain knowledge, a few variables were selected as 

we discussed in the previous section. In this section, we will discuss a little about those 

features as they were used for indoor temperature prediction: 

Supply Air temperature: It shows the amount of heat air entering the space, and it has 

a direct impact on the indoor temperature. 

Outdoor temperature: It captures the external weather impact on indoor thermal 

conditions, especially as the research is done in Nordic climates. 

Solar radiation: It is used as a proxy for solar gain. High solar radiation typically lead to 

increased indoor temperatures, particularly in buildings with large windows or poor 

insulation. 

 

Although central heating water temperature data would have been an important feature 

for modeling the indoor temperature mainly for estimating heat transfer through 

radiators. But unfortunately, it was not available for each room or zone in our dataset. 

So, it could not be included in this research. 

 

3.4.2 Target variable creation 

In this research, the outcome variable is indoor temperature. Therefore, the model is 

trained to predict future temperatures. Instead of limiting the model for a single step or 

short-term prediction, the models were designed to estimate indoor temperature at, at 

1-hour, 6-hours, and 12-hours intervals ahead. 

 

This research approach mainly allows for both short-term control optimization and 

medium-term planning. These are essential in case of HVAC operations effectiveness and 



33 

 

   

 

energy management. This forecasting research can be treated as a regression problem, 

where the model results are a single continuous temperature value corresponding to a 

specific prediction horizon. 

 

3.4.3 Temporal Structure for Forecasting 

In this research, several experiments were conducted, and in the final version of the 

experiments, the forecasting approach was simplified to use only the most recent 

observation (last step) instead of a 30-minute or 60-minute loopback window. This 

decision was made based on performance evaluation and model interpretability. 

 

Each input to the model consists of the latest available values of indoor temperature at 

time t. For predicting the indoor temperature at future time steps t+60, t+360, or t+720 

minutes. This one-step input structure reduces computational complexity while still 

retaining meaningful prediction. Moreover, it aligned with operational use cases where 

real-time decisions are made based on the last sensor readings. Despite the absence of 

any temporal sequence in the modelling, this formulation sequence allows for effective 

learning for any immediate impact on indoor thermal conditions. 

 

Long term sensor history was not assumed to be very meaningful in this research as in 

this context, that since outside weather and indoor conditions are are often non-

stationary. So, relying on long sequences could lead to overfitting patterns and therefore 

it can be said that time series prediction can merely utilize some regular usage patterns, 

but not otherwise be very useful. 

 

3.5 Model Architecture 

In this research to evaluate the performance of different forecasting strategies for indoor 

temperature prediction, several ML models were developed and trained in this research 

experiment. The selected models mainly represent a combination of traditional 

regression techniques, neural networks, and PINNs. All models were trained using the 



34 

 

   

 

same preprocessed dataset and temporal sequence to ensure comparability between all 

the models. 

 

3.5.1 Feedforward Neural Network  

The FNN model was mainly implemented using PyTorch, where multiple fully connected 

layers were explored with ReLU activations. Here three key variables: supply air 

temperature, outdoor temperature, and satellite radiation value were taken as a input. 

And in the model, an exhaustive search over single, double, and triple-layer 

configurations was performed. In each layer, a search was performed varying the 

number of neurons from 1 to 10 per layer. Leading to almost 1110 architecture 

combinations being checked to identify the most optimal architecture of neural 

networks which is layers of 8, 9, and 6 neurons respectively. Then the final output layer 

contains a single neuron which is the predicted indoor temperature value for the next 

time step. Each model was trained to minimize the MSE between the predicted and 

actual indoor temperature values. Finally, the best performing architecture was selected 

based on validation performance using early stopping with a certain patience value. 

 

Figure 1  Architecture of the Feedforward Neural Network used for Indoor Temperature 
Prediction. 

 



35 

 

   

 

 

3.5.2 Long Short-Term Memory  

LSTM networks are a specialized neural network architecture designed for time-series 

prediction. They can retain information from previous time steps through internal 

memory cells. In this research, The model architecture used in this study consisted of an 

input layer, two stacked LSTM layers (with 64 and 32 units), followed by two dense layers 

for final regression output. Unlike FNN models, LSTM models need sequences of multiple 

time steps. In this research, each training example was constructed from 12 previous 

time steps of data to predict the temperature at the next five-minute interval. The input 

features included supply air temperature, outdoor temperature, satellite-derived 

radiation, and indoor temperature. For data splitting, the LSTM model followed the same 

timestamp-based separation used for all other models. The final 288 samples (one day) 

was reserved as the test set, while all other samples used for the training set. The input 

sequences were scaled using RobustScaler, which is consistent with the preprocessing 

that was applied to the other ML models. The model was trained using the Adam 

optimizer and a mean squared error (MSE) loss function. To prevent overfitting, early 

stopping was applied, and the network was trained for up to ten epochs with a batch 

size of 32. 

 

3.5.3 Extreme Gradient Boosting  

XGBoost model is a robust ensemble learning method, which is based on gradient 

boosted decision trees, and it was used for its effectiveness in handling structured 

tabular data. In this research, the model was mainly trained using reg:squarederror as 

the objective function, which corresponds to the standard squared error loss used for 

continuous regression tasks. The reason for using reg:squarederror is that indoor 

temperature forecasting is a continuous regression problem. The square error loss 

penalizes larger mistakes more strongly than smaller ones. L2 and L1 regularization work 

as a penalty to reduce the impact of overly large leaf weights in the boosted trees. This 

loss function penalizes larger prediction errors more strongly, making it ideal for indoor 



36 

 

   

 

temperature forecasting, where minimal deviation from the actual temperature is crucial. 

Furthermore, the model incorporates L1 and L2 regularization to prevent model 

overfitting by penalizing overly complex tree structures. 

 

The model uses the most recent available sensor readings to make predictions. These 

readings include supply air temperature, outdoor temperature, satellite solar radiation, 

and the previous indoor temperature value (t-1). These features together represent the 

thermal factors that influence indoor temperature behavior. XGBoost then learns 

nonlinear relationships based on these inputs and predicts the next indoor temperature 

value. This forms the basis for forecasting at 1-hour, 6-hours, and 12-hours horizons in 

this thesis. 

 

3.5.4 Random Forest  

The RF regressor modeling includes a classical ensemble baseline. So it was trained with 

500 decision trees, a maximum depth of 15, and bootstrap sampling, with node splits 

controlled by min samples split = 5, min samples leaf = 2. In the implementation of 

modelling, the same data split was done as it was implemented for other models. This 

approach provided a useful and meaningful comparison against more complex neural 

and hybrid models. The hyperparameters for the RF model were chosen through a 

combination of best-practice defaults, and the characteristics of the dataset. 

 

All these models were evaluated under a multiple-horizon forecasting setup, so each 

model predicts the indoor temperature at 1-hour, 6-hours, and 12-hours intervals using 

the latest available indoor temperature and other features as an input. 

 

3.6 Physics-Informed Neural Network Modeling 

In conventional ML models, it can capture patterns from data. It often lacks physical 

interpretability, and there is a chance that it may produce unrealistic predictions when 

extrapolated beyond training conditions. For this limitation, A PINN approach was 



37 

 

   

 

integrated into the research. This method combines data-driven learning with known 

physics laws, mainly a simplified equation for indoor temperature dynamics. The Fourier 

law of heat transfer explains how an individual object's temperature changes over time 

when exposed to an environment with a different temperature. 

Fourier law of heat transfer definition: The rate of change of temperature of an objects 

temperature is directly proportion to the difference between its temperature and the 

surrounding ambient temperature.  

Mathematical Form: 

 𝑑𝑇

𝑑𝑡
=   − k(T − 𝑇𝑎𝑚𝑏𝑖𝑒𝑛𝑡) 

(2) 

 

Where: 

• T: Temperature of the object (indoor temperature) 

• 𝑇𝑎𝑚𝑏𝑖𝑒𝑛𝑡: Surrounding or environmental temperature (outdoor temperature) 

• k: A positive constant depending on the system (thermal conductance) 

• 
𝑑𝑇

𝑑𝑡
: Rate of temperature change 

 

3.6.1 Governing Differential Equation 

This research adapts the governing equation used in (Hannula et al., 2025; Häkkinen, 

n.d.). In our research, the equation is reinterpreted to model air-based systems by 

replacing the supply water temperature with supply air temperature. The rest of the 

structure remains consistent, maintaining the balance between internal heat gains, 

losses, and solar radiation. 

The equation is formulated as follows: 

 

 𝑑𝑇

𝑑𝑡
=  θ0   · (𝑇𝑠𝑢𝑝𝑝𝑙𝑦𝑎𝑖𝑟

− 𝑇𝑖𝑛 ) + 𝜃1 · (𝑇𝑖𝑛 − 𝑇𝑜𝑢𝑡 ) + 𝜃2 · 𝛷 

 

(3) 

 

Where: 

• 𝑇in: indoor temperature 



38 

 

   

 

• 𝑇supplyair: supply air temperature 

• 𝑇out: outdoor temperature 

• Φ: solar radiation  

• θ0, θ1, θ2 : learnable parameters representing heat transfer rates from respective 

sources 

 

The term θ1(𝑇𝑖𝑛 − 𝑇𝑜𝑢𝑡)  directly represents Fourier Law of Cooling. which represent 

that indoor temperature will decrease if it is warmer than outdoors, and the rate 

depends on θ₁. The ODE and the approach was adopted in (Hannula et al., 2025; 

Häkkinen, n.d.). Which successfully integrated physical laws into learning indoor 

temperature patterns. 

 

3.6.2 Learning Physics Parameters 

In the equation, there are three parameters θ0, θ1, θ2  and all of these were learned 

directly from the data using gradient descent. Here, the time derivative 
𝑑𝑇𝑖𝑛

𝑑𝑡
   was 

approximated using first-order finite difference (Euler’s Method), which is calculated as: 

 

 Tin(𝑡 + 1 ) − 𝑇𝑖𝑛(𝑡)

Δ𝑡
 

 

(4) 

 

Where: 

• 𝑇𝑖𝑛 =  Indoor temperature at a specific moment in time 

• 𝑇𝑖𝑛 (𝑡 + 1)= Indoor temperature at the next step. 

• 𝑇𝑖𝑛 (𝑡)= Indoor temperature at the current time step 

• Δ𝑡= The time difference between two consecutive measurements. 

 

A loss function which was then defined to minimize the mean squared error between 

the left-hand side of the derivative and the right hand side of the equation. So, after a 



39 

 

   

 

few iterations, these three learnable parameters provided a physically meaningful 

simulation of indoor temperature evolution. 

 

3.6.3 Physics Loss Integration 

For incorporating the physical knowledge into the neural network model a composite 

loss function was defined: 

 

 ℒ𝑡𝑜𝑡𝑎𝑙 = 𝜆data . ℒ𝑑𝑎𝑡𝑎 +  𝜆physics .  ℒ𝑝ℎ𝑦𝑠𝑖𝑐𝑠 

 

(5) 

Where: 

• ℒdata: Standard MSE loss between predicted and sensor indoor temperature 

• ℒphysics: MSE between model dynamics and the differential equation 

• λdata, λphysics : Weighting factors balancing the contribution of data and physics 

terms. 

 

In this research, λdata = 1,   and λphysics = 0.003  were selected while code 

implementation based on experiment which will maintain an appropriate balance 

between data fitting and physical realism. 

 

 



40 

 

   

 

 

Figure 2: Architecture of the Physics-Informed Neural Network (PINN) for indoor temperature 
prediction 

 

3.6.4 Machine Learning Model Comparison 

In this research, both traditional and data driven ML model was developed and using 

learnable theta parameters and the Euler method a forward simulation also conducted 

for prediction temperature evolution. This simulated result was compared with the 

actual measurements and other ML models like FNN, LSTM, XGBoost. So, it can evaluate 

how well the physics model aligned with other observed dynamics. 

So, the PINN model not only provide almost competitive accuracy but also it ensures 

that the predictions obeyed fundamental thermodynamic principles. This total process 

mainly enhanced the model robustness particularly in some cases where data was sparse. 

 

3.7 Evaluation Metrics and Performance Comparison 

For assessing the predictive accuracy and generalization capabilities of developed ML 

models, a commonly used regression evaluation metric was employed. These metrics 



41 

 

   

 

mainly provided the  insights into both absolute error and overall goodness of fit 

between the predicted and actual indoor temperature values. 

 

3.7.1 Mean Absolute Error  

The MAE is a statistical metric which is mainly used to measure the average magnitude 

of the errors between predicted and observed values. It is defined by: 

 

 
𝑀𝐴𝐸 =  

1

𝑛
∑|𝑦𝑡𝑟𝑢𝑒 − 𝑦𝑝𝑟𝑒𝑑|

𝑛

𝑖=1

  
 

(6) 

 

Here, 𝑦𝑡𝑟𝑢𝑒 is actual indoor temperature and 𝑦𝑝𝑟𝑒𝑑 is predicted temperature, and n is 

the number of samples. MAE gives an intuitive measure of model accuracy in degree 

Celsius. This is the reason that it is suitable for thermal comfort temperature evaluation. 

 

3.7.2 Root Mean Squared Error  

The RMSE mainly penalizes larger error more than MAE due to the squaring operation, 

as it offers more sensitive evaluation metric when larger deviation are more critical. It is 

defined as: 

 

 

 

𝑅𝑀𝑆𝐸 = √
1

𝑛
∑(𝑦𝑡𝑟𝑢𝑒 − 𝑦𝑝𝑟𝑒𝑑)2

𝑛

𝑖=1

 

 

 

(7) 

 

RMSE is particularly useful as when there is large deviation from true values are less 

tolerable. Here, 𝑦𝑡𝑟𝑢𝑒  is the actual indoor temperature and 𝑦𝑝𝑟𝑒𝑑  is the predicted 

temperature. 



42 

 

   

 

3.7.3 Coefficient of Determination 

The coefficient of determination ( 𝑅2 ) score evaluates how well the predictions 

approximate with the actual values. It mainly represent the proportion of variance in 

target variable which is predictable from the input features. It is defined as: 

 

 
𝑅2 = 1 −

∑ (𝑦𝑡𝑟𝑢𝑒 − 𝑦𝑝𝑟𝑒𝑑)2𝑛
𝑖=1

∑ (𝑦𝑡𝑟𝑢𝑒 − 𝑦
ˉ

𝑝𝑟𝑒𝑑)2𝑛
𝑖=1

 

 

(8) 

 

Here,  𝑦
ˉ
 is the mean of actual target values. So, 𝑅2 score is close to 1 indicates a strong 

agreement between the prediction and the ground truth. 



43 

 

   

 

4 Results and Findings 

This chapter presents the experimental results. These results are from the 

implementation and evaluation of three different modeling strategies. These strategies 

are for indoor temperature prediction. FNN, ODE model based on physics, and PINN. All 

models were trained and tested using a dataset containing 16,089 samples collected at 

five-minute intervals between November 12, 2024, and January 7, 2025. Of these 

samples, 15,801 were used for training and 288 for testing. All models used the same 

input variables: supply air temperature, outdoor temperature, and solar radiation, and 

here indoor air temperature was the target variable. The forecasting task was performed 

for 1-hour, 6-hours, and 12-hours horizons. 

 

4.1 FNN Architecture Search and Performance 

An large scale architecture search was conducted across 1,110 different FNN 

architectures. The search varied the number of hidden layers (from 1 to 3) and the 

number of neurons per layer (from 1 to 10) while using the rectified linear unit (ReLU) 

activation function. The goal was to identify the optimal configuration based on the 

validation performance metrics of MAE, RMSE, and R² score. 

 

Parameter Value 

Hidden layers 1 to 3 layers 

Neurons per layer 1 to 10 

Total architectures tested 1,110 

Activation function ReLU 

Optimizer Adam 

Loss function MAE 

Scaler RobustScaler 

Table 2: FNN Architecture Search Parameters Used in This Study 

 



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Table 3 :Top 20 FNN Architectures Based on Validation MAE 

 

From this search, we identified the best-performing architecture as [8, 9, 6], 3-layer FNN 

with 188 trainable parameters. Its validation performance was MAE: 0.3838 °C, RMSE: 

0.6351 °C, R²: 0.6179. After being retrained on the full training dataset, the model 

achieved the following performance on the full test set test MAE: 0.7255 °C, test RMSE: 

0.9257 °C, test R²: 0.1884. While the FNN produced reasonable single-step predictions, 

its recursive multi-step forecasting stability still needed to be looked into more. 

 

4.2 One-Hour Prediction Window 

The best-performing FNN architecture was evaluated using a 1-hour one-step-ahead 

predictions corresponding forecasting window, which corresponded to 12 sequential 

five-minute prediction steps. In this setting, the model's predictions are used as inputs 

at each step, allowing error accumulation to be observed. 



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Figure 3 : One Hour Prediction: FNN vs Actual 

 

Figure 4: One Hour Prediction: ODE(Physics) vs Actual 

 

Figure 5: One Hour Prediction: FNN vs ODE vs PINN 



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Model MAE (°C) RMSE (°C) R² 

FNN 1.24 1.31 –1 

PINN 0.52 0.57 –1 

Table 4:Performance Metrics for the One Hour Prediction (FNN vs PINN) 

Here, the results clearly show the limitations of a purely data-driven model when used 

for recursive multi-step prediction. 

The FNN shows a rapid increase in errors over the short 1-hour period. This results in a 

high MAE and a negative R² value, which indicates that the model's performance is worse 

than a simple mean baseline. This behaviour is expected because recursive forecasting 

increases small deviations in single-step predictions, specifically when the model lacks 

explicit knowledge of the underlying thermal dynamics. However, the physics-based ODE 

model achieves the best short-term accuracy, Since the ODE model is based on the 

physical structure of heat transfer, it remains stable over recursive predictions and avoids 

the drift observed in the FNN. But in the case of PINNs, it performs substantially better 

than the FNN and approaches the accuracy of the ODE. Its ability to combine data-driven 

learning with the equation prevents instability and maintains stable forecasting 

behaviour. Although the PINN is slightly less accurate than the pure ODE model in the 

short term, it has the advantage of learning from data while maintaining physical 

constraints, which is beneficial in the long term. 

 

4.3 Six-Hours Prediction Window 

To evaluate model stability over a longer forecasting horizon, the FNN, ODE, and PINN 

models were tested over a 6-hour period. 



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Figure 6: Six-Hours Forecast: FNN vs Actual 

 

Figure 7: Six-Hours Forecast: ODE vs Actual 

 

Figure 8: Six-Hours Forecast: FNN vs ODE vs PINN 



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Model MAE (°C) RMSE (°C) R² 

FNN 0.60 0.62 –1 

PINN 0.36 0.34 0.34 

Table 5:Performance Metrics for the Six Hours Prediction (FNN Vs PINN) 

Here, the results show a clear shift in model performance compared to the one-hours 

window. So according to these results, the FNN performs slightly better with reduced 

MAE and root mean squared error. But the negative R² value shows that the model still 

fails to generalize the underlying physical behaviour. For ODE model, the performance 

of the model decreases over longer horizons. Here, PINNs achieves the best performance 

on the 6-hour window with positive R², indicating meaningful predictability. 

 

4.4 Twelve-Hours Prediction Window 

The final evaluation scenario examines the models behavior over a 12-hours period. 

 

Figure 9: Twelve-Hours Prediction: FNN vs Actual 

 



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Figure 10: Twelve-Hours Forecast: ODE vs Actual 

 

 

Figure 11:Twelve-Hours Forecast: FNN vs ODE vs PINN 

 

 

 

 

 



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Model MAE (°C) RMSE (°C) R² 

FNN 0.47 0.68 –0.29 

PINN 0.29 0.51 0.63 

Table 6: Performance Metrics for the Twelve Hours Prediction (FNN Vs PINN) 

 

In this, 12-hours analysis clearly shows differences in model stability. The FNN model 

continues to accumulate recursive errors, resulting in divergence and negative R² values. 

The ODE model remains stable and PINNs gives the most accurate and consistent long-

term predictions. It has the lowest MAE and RMSE, and it is the only one with a strongly 

positive R². These results confirm that integrating physics conditions results in far 

superior long-term prediction performance compared to purely data-driven or physics-

based models. 

 

4.5 Physics-Based ODE Model Performance 

The physics-based ODE model is easy to understand because it is based on Fourier law 

of heat conduction. It uses a simple equation that shows how indoor temperature  

changes with supply air temperature, outdoor temperature, and solar radiation.

 

Figure 12: Physics Parameter Learning 



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Figure 13: Physics Parameter Loss Over Epochs 

 

Parameter Value 

(θ0) (supply air effect) 0.0019 

(θ1) (outdoor influence) –0.0011 

(θ2) (solar influence) 0.00005 

Table 7: Physics Learnable Perameters Value 

These values match the expected thermal behaviour. As we know Supply air has a 

warming effect, the outdoor temperature contributes to cooling, and solar radiation 

provides a small, positive heat gain. In ODE model, it produces smooth and physically 

meaningful predictions and maintains stability during long-horizon prediction. However, 

in the models it cannot fully capture rapid variations and there is reason that in the 

dataset we have sudden outliers which is not possible for physics-based equation to 



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identify as our input features does not contain that relevant information. Still, it provides 

a reliable physical baseline and is an essential component for the PINN framework. 

 

4.6 Physics-Informed Neural Network Performance 

The PINN combines learned differential equation-based physics with a FNN architecture. 

This hybrid modeling approach allows the PINN to learn complex nonlinear patterns 

from the dataset while maintaining physical consistency. 

 

Parameter Value 

Input variables Tsup, Tout, Φ, Tin 

Physics equation dT/dt = θ₀(Tsup−Tin) + θ₁(Tin−Tout) + θ₂Φ 

Learnable parameters θ₀, θ₁, θ₂, C 

Network architecture [8, 9, 6] 

Loss function Data loss + Physics loss 

Optimizer Adam 

Table 8: PINN Architecture Parameter Used In This Study 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Figure 14: PINN Data Loss Over Epochs 



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Figure 15:PINN Physics Loss Over Epochs 

 

Figure 16: Data Loss+ Physics Loss Over Epochs 

 

 



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Parameter PINN Value ODE Value 

(θ0) (supply air) 0.0018 0.0019 

(θ0) (outdoor) –0.0010 –0.0011 

(θ0) (solar) 0.000038 0.000050 

Table 9: PINNs Learnable Parameters Value 

In this table, PINN and ODE values are together to check model successfully maintains 

the physical structure or not. Here, PINNs parameters closely matches the ODE results. 

In short, PINN model performs better than the FNN and ODE models in all testing 

scenarios. This close alignment between the differential equation parameters and the 

PINN-learned values further confirms the model accuracy also. 

 

4.7 XGBoost Model Results 

XGBoost model was tested using the same input features as the other models. It was 

trained on one-step-ahead prediction and evaluated for 1-hour, 6-hours, and 12-hours 

prediction window. This arrangement allows for direct comparison with other models. 

However this parameters are selected based on trial and error not based on any 

optimization 

Parameter Value 

Input features Supply air, Outdoor temp, Solar radiation, Indoor temp 

n_estimators 500 

max_depth 4 

learning_rate 0.05 

subsample 0.8  

reg_lambda (L2) 1.0 

reg_alpha (L1) 0.1 

Objective reg:squarederror (MSE) 

Scaler RobustScaler 

Table 10: XGBoost Architecture Parameters Used In This Study 

 



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One-Hour Model Graph: 

 

Figure 17: XGBoost One-Hour: Prediction vs Actual 

 

 

Six-Hours Model Graph: 

 

Figure 18 : XGBoost Six-Hours: Prediction vs Actual 

 



56 

 

   

 

 

Figure 19: XGBoost Twelve-Hour : Prediction vs Actual 

 

Forecast Horizon MAE (°C) RMSE (°C) R² 

1-Hour  0.20 0.23 –1 

6-Hours 0.33 0.52 0.45 

12-Hours  0.31 0.50 0.46 

Table 11: XGBoost Prediction Performance 

XGBoost shows strong short-term predictive accuracy, It achieved the lowest 1-hour MAE 

among all models. Although, Performance gradually declines with longer prediction 

results. But still, XGBoost remains stable in MAE across 6 and 12 hours prediction 

windows and outperforms the FNN 

 

 

 

 



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4.8 Random Forest Model Performance 

The RF regressor model was evaluated over three prediction time frames: 1- hour, 6- 

hours and 12 hours. 

The model was trained using 15,801 and 5-minute samples and using same input 

features. and the hyperparameters were selected based on trial and error. 

 

Parameter Value 

Input features Supply air, Outdoor temp, Solar radiation, Indoor temp 

Number of trees 500 

Max depth 15 

Min samples split 5 

Min samples leaf 2 

Max features sqrt 

Bootstrap True 

Loss metric MSE (via internal splitting) 

Scaler RobustScaler 

Random seed 42 

Table 12: Random Forest Parameters Used in This Study 

 

One-Hour Model Graph: 

 

Figure 20: One-Hour Forecast: Random Forest vs Actual 

 



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Six-Hours Model Graph: 

 

Figure 21: Six-Hour Forecast: Random Forest vs Actual 

 

Twelve- Hours Model Graph: 

 

 

Figure 22:Twelve-Hours Prediction: Random Forest vs Actual 

 

 



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Horizon MAE (°C) RMSE (°C) R² 

1-Hour 0.22 0.27 −1 

6-Hours 0.33 0.51 0.48 

12-Hours 0.31 0.51 0.45 

Table 13: Random Forest Performance Prediction 

RF model shows strong short-term predictive performance among all the three horizons, 

achieving the lowest MAE of 0.221 °C in the 1-hour window. However, still for one hour 

horizon it shows highly unstable R² value. And across the 6-hours and 12-hour horizons 

RF model maintained consistent accuracy, achieving MAE values of 0.332 °C and 0.316 °C . 

 

4.9 LSTM Model Results 

The LSTM network was performed for three forecast horizons: 1-hour, 6-hours, and 12-

hours. 

 

Parameter Value 

Input features Supply air, Outdoor temp, Satellite value, Indoor temp 

Sequence length 12 timesteps (1 hour) 

Prediction horizon 1 step ahead (5 min), recursive 

Architecture LSTM(64) -> LSTM(32) -> Dense(16) -> Dense(1) 

Activation functions LSTM: tanh, Dense: ReLU 

Optimizer Adam (lr = 0.001) 

Loss function MSE 

Batch size 32 

Epochs 10 (early stopping) 

Scaler RobustScaler 

Table 14: LSTM Architecture Parameters Used In This Study 

 

 

 

 

 



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One-Hour Model Graph: 

 

Figure 23:One-Hour LSTM Prediction vs Actual 

 

Six-Hours Model Graph: 

 

Figure 24: Six-Hour Prediction Plot 

 

 



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Twelve-Hours Model Graph:  

 

 

Figure 25: Twelve-Hour LSTM Prediction Plot 

 

Horizon MAE (°C) RMSE (°C) R² 

1-Hour 0.18 0.26 −0.30 

6-Hours 0.34 0.52 0.47 

12-Hours 0.31 0.47 0.53 

Table 15: LSTM Performance Prediction 

4.10 Model Performance Table 

Model Name Hours MAE (°C) RMSE (°C) R² 

FNN 

1h 1.24 1.31 -1 

6h 0.60 0.62 -1 

12h 0.47 0.68 -0.29 

PINN 

1h 0.52 0.57 -1 

6h 0.36 0.34 0.34 

12h 0.29 0.51 0.63 



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XGBoost 

1h 0.20 0.23 -1 

6h 0.33 0.52 0.45 

12h 0.31 0.50 0.46 

Random Forest 

1h 0.22 0.27 -1 

6h 0.33 0.51 0.48 

12h 0.31 0.51 0.45 

LSTM 

1h 0.18 0.26 -0.30 

6h 0.34 0.52 0.47 

12h 0.31 0.47 0.53 

 

Table 16: Combined Model Performance Table 

 

From the 12-hours prediction result, PINNs has the best performance, and it 

outperforms XGBoost by 6.4%, RF by 7.6%, LSTM by 8.1%, the FNN by 39.0% in terms of 

MAE. 

 

From the 6-hours prediction result, XGBoost performed best, improving MAE by 4.3% 

over LSTM, 8.0% over the PINN, 45.1% over the FNN baseline. And it is performing nearly 

identically to RF. 

 

From the 1-hour prediction result, LSTM achieved the lowest error, performing 9.9% 

better than XGBoost, 15.4% better than RF, 64.4% better than the PINN, and 84.9% 

better than the FNN model. 



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5 Conclusions 

This thesis explored data-driven, physics-based, and hybrid physics-informed techniques 

for predicting indoor temperatures using building sensor and satellite data. Three 

categories of models were examined: ML models such as (FNN, RF, XGBoost, and LSTM), 

a ODE model, and the proposed PINN model, which incorporates the building’s thermal 

dynamics directly into the learning process. 

 

The results across the three forecasting horizons (1-hour, 6-hours, and 12-hours) show 

that no single model is universally optimal. Rather, performance depends on the 

prediction horizon and model structure. LSTM achieved the lowest error in the one-hour 

prediction, demonstrating the strength of sequence-based learning when dependencies 

are temporal. XGBoost performed best at the six-hours horizon, showing the 

effectiveness of tree-based models for medium-range forecasting. For the 12-hours 

prediction horizon, the physics-informed neural network outperformed all other models. 

It proves that Integrating physical constraints improved stability over longer periods. 

 

Overall, this study indicates that integrating physical knowledge with data-driven 

learning can produce more precise and physically consistent forecasts, especially for 

longer prediction windows. 

 



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6 Limitations  

Although in this research shows the potential of hybrid data-physics methods for indoor 

temperature prediction, but some limitations should be acknowledged. 

 

First, The analysis was done using data from a single building and limited winter season 

period data. It is important to know that indoor temperature behavioural patterns is 

influenced by seasonal patterns, solar radiations, occupancy, ventilation, and heating 

strategies. It is possible that these conditions may vary across buildings. In this case 

missing sensor location information makes it impossible to assess what factors were 

cause of sudden changes. As sensor placement plays an important role in indoor 

environmental monitoring, and the lack of this information introduces uncertainty into 

both the training and evaluation of the models. 

 

Second, in the dataset for indoor temperature data there are some sudden spikes. So it 

is recommended to install multiple sensors for reading. These sudden fluctuations can 

be sensor noise, calibration drift, or environmental disturbances. Since indoor 

temperature acts as the ground truth for this research model training and validation, 

such spikes reduce the reliability of performance metrics. So, In future additional sensors 

or redundant sensing could help smooth these anomalies and provide a more stable 

ground-truth reference. 

 

Third, this dataset includes data from several more buildings but due to missing 

metadata and necessary sensors most of them are not feasible for research. As multiple 

buildings exist in the broader dataset, a significant portion of the buildings in the dataset 

lack critical variables. These variables include supply/return temperature, flow rate, 

humidity, and air ventilation. Many of the buildings also contain extensive amounts of 

irrelevant sensor data. 

 



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Finally, the indoor temperature is used as a ground truth contains sudden spikes not 

explained by the independent variables, making the prediction inaccurate. These models 

may perform better with proper ground truth data because then we can evaluate 

perfectly with the ground truth. Such improvements would better support for modelling 

and enable more robust research on prediction models. 



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Appendices 

Appendix 1. Github Link 

https://github.com/uddinminhaz/Integrating-Physics-Informed-and-Machine-Learning-

Models-for-Indoor-Temperature-Prediction-  

https://github.com/uddinminhaz/Integrating-Physics-Informed-and-Machine-Learning-Models-for-Indoor-Temperature-Prediction-
https://github.com/uddinminhaz/Integrating-Physics-Informed-and-Machine-Learning-Models-for-Indoor-Temperature-Prediction-