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Machine Learning with Physics Knowledge for Prediction: A Survey

Joe Watson; Chen Song; Oliver Weeger; Theo Gruner; An Thai Le; Kay Hansel; Ahmed Hendawy; Oleg Arenz; Will Trojak; Miles D. Cranmer; Carlo D'Eramo; Fabian Bülow; Tanmay Goyal; Jan Peters; Martin W. Hoffmann
In: Transactions on Machine Learning Research (TMLR), Vol. 2025, Pages 1-61, arXiv, 2025.

Abstract

This survey examines the broad suite of methods and models for combining machine learning with physics knowledge for prediction and forecasting, with a focus on partial differential equations. These methods have attracted significant interest because of their potential im- pact on the advancement of scientific research and industrial practices, promising improve- ments to using small- or large-scale datasets and expressive predictive models with useful inductive biases. The survey has two parts. The first considers incorporating physics knowl- edge on an architectural level through objective functions, structured predictive models, and data augmentation. The second considers data as physics knowledge, which motivates look- ing 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 perspec- tive on the application of these methods and a survey of the open-source ecosystem for physics-informed machine learning.

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