Machine Learning with Physics Knowledge for Prediction: A Survey

TL;DR

This survey reviews methods combining machine learning with physics knowledge, especially PDEs, highlighting architectural and data-driven approaches, applications, and open-source tools for enhanced predictive modeling in science and industry.

Contribution

It provides a comprehensive overview of physics-informed machine learning methods, categorizing approaches and discussing their industrial applications and open-source resources.

Findings

Physics-informed methods improve predictions with limited data.

Architectural and data-driven approaches offer complementary benefits.

Open-source tools facilitate wider adoption of physics-informed ML.

Abstract

This survey examines the broad suite of methods and models for combining machine learning with physics knowledge for prediction and forecast, with a focus on partial differential equations. These methods have attracted significant interest due to their potential impact on advancing scientific research and industrial practices by improving predictive models with small- or large-scale datasets and expressive predictive models with useful inductive biases. The survey has two parts. The first considers incorporating physics knowledge on an architectural level through objective functions, structured predictive models, and data augmentation. The second considers data as physics knowledge, which motivates looking at multi-task, meta, and contextual learning as an alternative approach to incorporating physics knowledge in a data-driven fashion. Finally, we also provide an industrial perspective on the application of these methods and a survey of the open-source ecosystem for physics-informed machine learning.