Physics guided machine learning using simplified theories

TL;DR

This paper presents a modular physics-guided machine learning framework that integrates simplified theories into deep learning models to enhance generalizability and accuracy in physical science applications.

Contribution

It introduces a novel architecture that incorporates features from simplified theories at intermediate layers to improve predictive performance.

Findings

Enhanced accuracy in airfoil aerodynamic predictions.

Improved generalizability to unseen configurations.

Effective integration of simplified theories into deep learning models.

Abstract

Recent applications of machine learning, in particular deep learning, motivate the need to address the generalizability of the statistical inference approaches in physical sciences. In this letter, we introduce a modular physics guided machine learning framework to improve the accuracy of such data-driven predictive engines. The chief idea in our approach is to augment the knowledge of the simplified theories with the underlying learning process. To emphasise on their physical importance, our architecture consists of adding certain features at intermediate layers rather than in the input layer. To demonstrate our approach, we select a canonical airfoil aerodynamic problem with the enhancement of the potential flow theory. We include features obtained by a panel method that can be computed efficiently for an unseen configuration in our training procedure. By addressing the generalizability concerns, our results suggest that the proposed feature enhancement approach can be effectively used in many scientific machine learning applications, especially for the systems where we can use a theoretical, empirical, or simplified model to guide the learning module.