Automated machine learning for physics-informed convolutional neural networks

TL;DR

This paper applies AutoML techniques to optimize the architecture and loss functions of physics-informed CNNs, improving their performance in solving PDEs across various datasets.

Contribution

It introduces a novel AutoML framework with specific search spaces and a two-stage strategy for designing PICNNs tailored to different physical problems.

Findings

AutoML outperforms manual design in PICNNs

Significant performance improvements on multiple PDE datasets

Effective search spaces for loss functions and architectures

Abstract

Recent advances in deep learning for solving partial differential equations (PDEs) have introduced physics-informed neural networks (PINNs), which integrate machine learning with physical laws. Physics-informed convolutional neural networks (PICNNs) extend PINNs by leveraging CNNs for enhanced generalization and efficiency. However, current PICNNs depend on manual design, and inappropriate designs may not effectively solve PDEs. Furthermore, due to the diversity of physical problems, the ideal network architectures and loss functions vary across different PDEs. It is impractical to find the optimal PICNN architecture and loss function for each specific physical problem through extensive manual experimentation. To surmount these challenges, this paper uses automated machine learning (AutoML) to automatically and efficiently search for the loss functions and network architectures of PICNNs. We introduce novel search spaces for loss functions and network architectures and propose a two-stage search strategy. The first stage focuses on searching for factors and residual adjustment operations that influence the loss function, while the second stage aims to find the best CNN architecture. Experimental results show that our automatic searching method significantly outperforms the manually-designed model on multiple datasets.