Learning Generalized Diffusions using an Energetic Variational Approach

TL;DR

This paper introduces a framework for learning physical laws of dissipative systems from data by leveraging energy-dissipation principles, demonstrating robustness and scalability to complex, high-dimensional systems.

Contribution

It presents a novel energetic variational approach to identify governing equations from both continuous and discrete data, enhancing robustness and applicability to complex physical systems.

Findings

Framework effectively learns dissipative laws from noisy data

Method extends easily to complex and high-dimensional systems

Numerical examples validate robustness and data impact analysis

Abstract

Extracting governing physical laws from computational or experimental data is crucial across various fields such as fluid dynamics and plasma physics. Many of those physical laws are dissipative due to fluid viscosity or plasma collisions. For such a dissipative physical system, we propose a framework to learn the corresponding laws of the systems based on their energy-dissipation laws, assuming either continuous data (probability density) or discrete data (particles) are available. Our methods offer several key advantages, including their robustness to corrupted/noisy observations, their easy extension to more complex physical systems, and the potential to address higher-dimensional systems. We validate our approaches through representative numerical examples and carefully investigate the impacts of data quantity and data property on model discovery.