Orthogonal projection-based regularization for efficient model augmentation

TL;DR

This paper introduces an orthogonal projection-based regularization method to improve the training and interpretability of physics-augmented deep learning models for nonlinear system identification.

Contribution

It proposes a novel regularization technique that enhances parameter learning and model accuracy in physics-informed deep learning models.

Findings

Improved model training stability and accuracy.

Enhanced interpretability of physics-based components.

Effective integration of physics priors into deep models.

Abstract

Deep-learning-based nonlinear system identification has shown the ability to produce reliable and highly accurate models in practice. However, these black-box models lack physical interpretability, and a considerable part of the learning effort is often spent on capturing already expected/known behavior of the system, that can be accurately described by first-principles laws of physics. A potential solution is to directly integrate such prior physical knowledge into the model structure, combining the strengths of physics-based modeling and deep-learning-based identification. The most common approach is to use an additive model augmentation structure, where the physics-based and the machine-learning (ML) components are connected in parallel, i.e., additively. However, such models are overparametrized, training them is challenging, potentially causing the physics-based part to lose interpretability. To overcome this challenge, this paper proposes an orthogonal projection-based regularization technique to enhance parameter learning and even model accuracy in learning-based augmentation of nonlinear baseline models.