Structural Constraints for Physics-augmented Learning

TL;DR

This paper introduces criteria to ensure physics-augmented machine learning models accurately reflect true physics, preventing models from concealing misconceptions and ensuring physical parameters are correctly identified.

Contribution

It proposes two novel criteria for validating hybrid physics-augmented models, enhancing their integrity and interpretability.

Findings

Criteria successfully applied to a nonlinear mechanical system

Ensures black-box models cannot mimic incorrect physics

Guarantees physical parameters match standalone physics models

Abstract

When the physics is wrong, physics-informed machine learning becomes physics-misinformed machine learning. A powerful black-box model should not be able to conceal misconceived physics. We propose two criteria that can be used to assert integrity that a hybrid (physics plus black-box) model: 0) the black-box model should be unable to replicate the physical model, and 1) any best-fit hybrid model has the same physical parameter as a best-fit standalone physics model. We demonstrate them for a sample nonlinear mechanical system approximated by its small-signal linearization.