Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Opening the Black-Box: Symbolic Regression with Kolmogorov-Arnold Networks for Energy Applications

Nataly R. Panczyk, Omer F. Erdem, Majdi I. Radaideh

TL;DR

This work addresses the need for interpretable and explainable AI in safety-critical energy applications by evaluating Kolmogorov Arnold Networks (KAN) against traditional Feedforward Neural Networks (FNN) across eight nuclear-energy datasets. It combines a theoretical justification for KANs with a practical benchmarking pipeline that includes symbolic equation conversion and Kernel SHAP-based explainability. The study finds that KANs can match or exceed FNN performance when the output space is constrained, while providing perfectly interpretable symbolic models and physics-consistent feature relationships that SHAP can corroborate. This suggests KANs as a viable, more transparent alternative for high-stakes engineering problems, with implications for regulatory trust and real-time decision support; future work will expand to uncertainty quantification and broader domains.

Abstract

While most modern machine learning methods offer speed and accuracy, few promise interpretability or explainability -- two key features necessary for highly sensitive industries, like medicine, finance, and engineering. Using eight datasets representative of one especially sensitive industry, nuclear power, this work compares a traditional feedforward neural network (FNN) to a Kolmogorov-Arnold Network (KAN). We consider not only model performance and accuracy, but also interpretability through model architecture and explainability through a post-hoc SHAP analysis. In terms of accuracy, we find KANs and FNNs comparable across all datasets, when output dimensionality is limited. KANs, which transform into symbolic equations after training, yield perfectly interpretable models while FNNs remain black-boxes. Finally, using the post-hoc explainability results from Kernel SHAP, we find that KANs learn real, physical relations from experimental data, while FNNs simply produce statistically accurate results. Overall, this analysis finds KANs a promising alternative to traditional machine learning methods, particularly in applications requiring both accuracy and comprehensibility.

Opening the Black-Box: Symbolic Regression with Kolmogorov-Arnold Networks for Energy Applications

TL;DR

This work addresses the need for interpretable and explainable AI in safety-critical energy applications by evaluating Kolmogorov Arnold Networks (KAN) against traditional Feedforward Neural Networks (FNN) across eight nuclear-energy datasets. It combines a theoretical justification for KANs with a practical benchmarking pipeline that includes symbolic equation conversion and Kernel SHAP-based explainability. The study finds that KANs can match or exceed FNN performance when the output space is constrained, while providing perfectly interpretable symbolic models and physics-consistent feature relationships that SHAP can corroborate. This suggests KANs as a viable, more transparent alternative for high-stakes engineering problems, with implications for regulatory trust and real-time decision support; future work will expand to uncertainty quantification and broader domains.

Abstract

While most modern machine learning methods offer speed and accuracy, few promise interpretability or explainability -- two key features necessary for highly sensitive industries, like medicine, finance, and engineering. Using eight datasets representative of one especially sensitive industry, nuclear power, this work compares a traditional feedforward neural network (FNN) to a Kolmogorov-Arnold Network (KAN). We consider not only model performance and accuracy, but also interpretability through model architecture and explainability through a post-hoc SHAP analysis. In terms of accuracy, we find KANs and FNNs comparable across all datasets, when output dimensionality is limited. KANs, which transform into symbolic equations after training, yield perfectly interpretable models while FNNs remain black-boxes. Finally, using the post-hoc explainability results from Kernel SHAP, we find that KANs learn real, physical relations from experimental data, while FNNs simply produce statistically accurate results. Overall, this analysis finds KANs a promising alternative to traditional machine learning methods, particularly in applications requiring both accuracy and comprehensibility.

Paper Structure

This paper contains 38 sections, 21 equations, 11 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Literature Review and Research Gaps
  3. Novelty
  4. Theory
  5. Kolmogorov Arnold Networks
  6. Explainability vs. Interpretability
  7. SHapley Additive exPlanations (SHAP)
  8. Data
  9. Critical Heat Flux Dataset
  10. Materials and Fuel Performance Dataset
  11. Light Water Reactor Dataset
  12. Heat Conduction Dataset
  13. Microreactor Dataset
  14. Power Control Dataset
  15. Nuclear Safety Dataset
  16. ...and 23 more sections

Figures (11)

  • Figure 1: Top-view schematic of the MIT research reactor core used in the Power Control (PC) dataset as shown in radaideh_neorl_2023
  • Figure 2: Feature importance ranking via SHAP for all outputs for both models of the light water reactor (LWR) dataset.
  • Figure 3: Feature importance ranking via SHAP for all outputs for both symbolic KAN and FNN models of the heat conduction (HEAT) dataset.
  • Figure 4: Feature importance ranking via SHAP for all outputs for both symbolic KAN and FNN models of the critical heat flux (CHF) dataset.
  • Figure 5: Feature importance ranking via SHAP for all outputs for both models of the Microreactor dataset.
  • ...and 6 more figures