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Integrating Symbolic Neural Networks with Building Physics: A Study and Proposal

Xia Chen, Guoquan Lv, Xinwei Zhuang, Carlos Duarte, Stefano Schiavon, Philipp Geyer

TL;DR

This study explores the application of KAN in building physics, focusing on predictive modeling, knowledge discovery, and continuous learning, and proposes a model selection decision tree to guide practitioners in appropriate applications for building physics.

Abstract

Symbolic neural networks, such as Kolmogorov-Arnold Networks (KAN), offer a promising approach for integrating prior knowledge with data-driven methods, making them valuable for addressing inverse problems in scientific and engineering domains. This study explores the application of KAN in building physics, focusing on predictive modeling, knowledge discovery, and continuous learning. Through four case studies, we demonstrate KAN's ability to rediscover fundamental equations, approximate complex formulas, and capture time-dependent dynamics in heat transfer. While there are challenges in extrapolation and interpretability, we highlight KAN's potential to combine advanced modeling methods for knowledge augmentation, which benefits energy efficiency, system optimization, and sustainability assessments beyond the personal knowledge constraints of the modelers. Additionally, we propose a model selection decision tree to guide practitioners in appropriate applications for building physics.

Integrating Symbolic Neural Networks with Building Physics: A Study and Proposal

TL;DR

This study explores the application of KAN in building physics, focusing on predictive modeling, knowledge discovery, and continuous learning, and proposes a model selection decision tree to guide practitioners in appropriate applications for building physics.

Abstract

Symbolic neural networks, such as Kolmogorov-Arnold Networks (KAN), offer a promising approach for integrating prior knowledge with data-driven methods, making them valuable for addressing inverse problems in scientific and engineering domains. This study explores the application of KAN in building physics, focusing on predictive modeling, knowledge discovery, and continuous learning. Through four case studies, we demonstrate KAN's ability to rediscover fundamental equations, approximate complex formulas, and capture time-dependent dynamics in heat transfer. While there are challenges in extrapolation and interpretability, we highlight KAN's potential to combine advanced modeling methods for knowledge augmentation, which benefits energy efficiency, system optimization, and sustainability assessments beyond the personal knowledge constraints of the modelers. Additionally, we propose a model selection decision tree to guide practitioners in appropriate applications for building physics.

Paper Structure

This paper contains 31 sections, 23 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Introduction to Kolmogorov-Arnold Networks
  3. Application of KANs in Building Physics
  4. Description of Case Studies
  5. Case Study 1: Steady-State Heat Conduction
  6. Case Study 2: Transient Heat Conduction
  7. Case Study 3: Dynamic Heat Transfer with Periodic Boundary Conditions
  8. Case Study 4: Performance Comparison with MLPs
  9. Results and Discussion
  10. Analysis of Results
  11. Case Study 1: Steady-State Heat Conduction
  12. Case Study 2: Transient Heat Conduction
  13. Case Study 3: Dynamic Heat Transfer with Periodic Boundary Conditions
  14. Case Study 3*: Significant Improvement through Prior Knowledge Integration
  15. Case Study 4: Performance Comparison with MLPs
  16. ...and 16 more sections

Figures (5)

  • Figure 1: KAN prediction results across different case studies. Case 1: steady heat transfer in walls; Case 2: transient heat transfer in semi-infinite soil; Case 3: periodic dynamic heat transfer in walls; Case 3*: periodic dynamic heat transfer in walls with prior knowledge decomposition.
  • Figure 2: Robustness comparison against data sparseness between KAN and MLP based on the whole dataset with the availability of 100%, 50%, 25%, 10%, and 5% respectively, averaged over 10 random runs. KAN shows better accuracy and robustness against data sparseness.
  • Figure 3: Performance comparison between KAN and MLP in capturing top 25%, 10%, and 5% extreme values. KAN shows better accuracy with less underestimation of extreme values.
  • Figure 4: Decision tree for choosing between KAN and MLP in building physics applications.
  • Figure :