北京雁栖湖应用数学研究院

张晓明

左佳蓉

2026年06月05日 15:00 至 16:00

A3-1-301

Zoom 204 323 0165 (BIMSA)

This report mainly introduces the core content of Section 3.1, “Representation Model Modifications,” from the review paper From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning. Physics-informed machine learning methods generally consist of three components: a representation model used to approximate the solution of the governing equation, governing equations used to describe the underlying physical laws, and an optimization process used to train the model. Among these components, the representation model directly determines the network’s ability to express complex physical fields, boundary conditions, and multiscale features. Therefore, it is an important entry point for improving the performance of PINNs. Section 3.1 of the paper systematically reviews recent improvement strategies at the level of representation models, including input and output transformations, feature expansions, hard constraint embedding, MLP architecture improvements, the application of Kolmogorov-Arnold networks in PIML, residual connections, and model decomposition methods.