Physics-informed ConvNet: Learning Physical Field from a Shallow Neural Network

TL;DR

This paper introduces a shallow physics-informed convolutional neural network (PICN) that incorporates physical laws into its structure, aiming to improve modeling of multi-physical systems with limited data and noise.

Contribution

The paper proposes a novel shallow CNN framework, PICN, that embeds physical laws directly into the network structure, differing from traditional deep PINNs.

Findings

PICN effectively solves nonlinear physical operator equations.

PICN recovers physical information from noisy data.

PICN shows potential in approximating multi-frequency physical fields.

Abstract

Big-data-based artificial intelligence (AI) supports profound evolution in almost all of science and technology. However, modeling and forecasting multi-physical systems remain a challenge due to unavoidable data scarcity and noise. Improving the generalization ability of neural networks by "teaching" domain knowledge and developing a new generation of models combined with the physical laws have become promising areas of machine learning research. Different from "deep" fully-connected neural networks embedded with physical information (PINN), a novel shallow framework named physics-informed convolutional network (PICN) is recommended from a CNN perspective, in which the physical field is generated by a deconvolution layer and a single convolution layer. The difference fields forming the physical operator are constructed using the pre-trained shallow convolution layer. An efficient linear interpolation network calculates the loss function involving boundary conditions and the physical constraints in irregular geometry domains. The effectiveness of the current development is illustrated through some numerical cases involving the solving (and estimation) of nonlinear physical operator equations and recovering physical information from noisy observations. Its potential advantage in approximating physical fields with multi-frequency components indicates that PICN may become an alternative neural network solver in physics-informed machine learning.