GINN-KAN: Interpretability pipelining with applications in Physics Informed Neural Networks
This addresses the interpretability challenge in neural networks for scientific applications, particularly in physics, though it appears incremental as it builds on existing GINN and KAN models.
The paper tackles the problem of neural network interpretability by introducing GINN-KAN, a novel interpretable neural network that synthesizes advantages from GINN and KAN models, and demonstrates its application in Physics-Informed Neural Networks (PINNs). Results show GINN-KAN outperforms both GINN and KAN on Feynman symbolic regression benchmarks and surpasses black-box networks in PINNs when tested on 15 different partial differential equations.
Neural networks are powerful function approximators, yet their ``black-box" nature often renders them opaque and difficult to interpret. While many post-hoc explanation methods exist, they typically fail to capture the underlying reasoning processes of the networks. A truly interpretable neural network would be trained similarly to conventional models using techniques such as backpropagation, but additionally provide insights into the learned input-output relationships. In this work, we introduce the concept of interpretability pipelineing, to incorporate multiple interpretability techniques to outperform each individual technique. To this end, we first evaluate several architectures that promise such interpretability, with a particular focus on two recent models selected for their potential to incorporate interpretability into standard neural network architectures while still leveraging backpropagation: the Growing Interpretable Neural Network (GINN) and Kolmogorov Arnold Networks (KAN). We analyze the limitations and strengths of each and introduce a novel interpretable neural network GINN-KAN that synthesizes the advantages of both models. When tested on the Feynman symbolic regression benchmark datasets, GINN-KAN outperforms both GINN and KAN. To highlight the capabilities and the generalizability of this approach, we position GINN-KAN as an alternative to conventional black-box networks in Physics-Informed Neural Networks (PINNs). We expect this to have far-reaching implications in the application of deep learning pipelines in the natural sciences. Our experiments with this interpretable PINN on 15 different partial differential equations demonstrate that GINN-KAN augmented PINNs outperform PINNs with black-box networks in solving differential equations and surpass the capabilities of both GINN and KAN.