Machine Learning with Physics Knowledge for Prediction: A Survey

2024-08-19

arXiv.org

AI Summary

Enhancing predictive and forecasting performance of physics-informed machine learning (PI-ML) for partial differential equation (PDE)-based modeling remains challenging due to heterogeneous physical knowledge integration strategies. Method: We systematically survey and unify over 120 physics-integrated ML methods, proposing a novel dual-path paradigm: “architecture embedding” (e.g., physics-constrained loss functions, structured neural operators, physics-guided data augmentation) and “data-as-knowledge” (e.g., multi-task learning, meta-learning, in-context learning, symbolic regression–assisted modeling), thereby decoupling physical knowledge injection mechanisms for the first time. Contribution/Results: We establish a theoretical framework covering seven transferable inductive biases; standardize interfaces across five mainstream open-source PI-ML libraries; release the first industry-oriented PI-ML tool landscape; and provide deployable practice guidelines for six domains—energy, climate science, fluid dynamics, materials science, biophysics, and geophysics.

Technology Category

• Machine Learning: Hardware-aware ML
• Computer Vision: Low Level & Physics-based Vision
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: ML for personalized search and recommendations

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.

Problem

• Combining machine learning with physics knowledge for prediction
• Focus on partial differential equations in predictive models
• Incorporating physics knowledge via architecture and data-driven methods

Innovation

• Incorporating physics knowledge via architectural design
• Using data-driven methods for physics-informed learning
• Applying multi-task and meta-learning techniques