Machine Learning with Physics Knowledge for Prediction: A Survey

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.

Authors

• Joe Watson
• Chen Song The University of Texas at Austin
• Oliver Weeger
• Theo Gruner
• An Thai Le Intelligent Autonomous Systems Lab, Computer Science Department, Technical University of Darmstadt, Darmstadt, Germany
• Kay Hansel
• Ahmed Hendawy
• Oleg Arenz
• Will Trojak
• Miles Cranmer
• Carlo D'Eramo TU Darmstadt Hessian.ai CAIDAS, University of Würzburg
• Fabian Buelow
• Tanmay Goyal
• Jan Peters
• Martin W Hoffmann

Keywords

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