Stacked networks improve physics-informed training: applications to neural networks and deep operator networks

TL;DR

This paper introduces a stacking framework for physics-informed neural networks that enhances training efficiency and accuracy by progressively building complex models through iterative low-fidelity to high-fidelity learning.

Contribution

It proposes a novel multifidelity stacking approach for physics-informed networks, improving training and solution accuracy for complex physical systems.

Findings

Stacking improves accuracy of physics-informed neural networks.

Reduces the size of networks needed for accurate solutions.

Effective on benchmark problems like wave and Burgers equations.

Abstract

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can be difficult or impossible to train accurately for some systems of equations. We present a novel multifidelity framework for stacking physics-informed neural networks and operator networks that facilitates training. We successively build a chain of networks, where the output at one step can act as a low-fidelity input for training the next step, gradually increasing the expressivity of the learned model. The equations imposed at each step of the iterative process can be the same or different (akin to simulated annealing). The iterative (stacking) nature of the proposed method allows us to progressively learn features of a solution that are hard to learn directly. Through benchmark problems including a nonlinear pendulum, the wave equation, and the viscous Burgers equation, we show how stacking can be used to improve the accuracy and reduce the required size of physics-informed neural networks and operator networks.