A physics-informed operator regression framework for extracting data-driven continuum models

TL;DR

This paper introduces a physics-informed neural operator framework that learns continuum models from molecular simulation data, capturing complex physics with generalization to unseen system parameters.

Contribution

It proposes a neural network-based operator regression method that encodes physical laws and symmetries, improving data-driven continuum model discovery.

Findings

Effective in modeling local and nonlocal diffusion processes

Successfully generalizes to unseen system characteristics

Incorporates physical biases like symmetry and conservation

Abstract

The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate and robust. We present here a framework for discovering continuum models from high fidelity molecular simulation data. Our approach applies a neural network parameterization of governing physics in modal space, allowing a characterization of differential operators while providing structure which may be used to impose biases related to symmetry, isotropy, and conservation form. We demonstrate the effectiveness of our framework for a variety of physics, including local and nonlocal diffusion processes and single and multiphase flows. For the flow physics we demonstrate this approach leads to a learned operator that generalizes to system characteristics not included in the training sets, such as variable particle sizes, densities, and concentration.