arXiv:2006.02619physics.comp-ph
Integrating Machine Learning with Physics-Based Modeling
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Abstract
Machine learning is poised as a very powerful tool that can drastically improve our ability to carry out scientific research. However, many issues need to be addressed before this becomes a reality. This article focuses on one particular issue of broad interest: How can we integrate machine learning with physics-based modeling to develop new interpretable and truly reliable physical models? After introducing the general guidelines, we discuss the two most important issues for developing machine learning-based physical models: Imposing physical constraints and obtaining optimal datasets. We also provide a simple and intuitive explanation for the fundamental reasons behind the success of modern machine learning, as well as an introduction to the concurrent machine learning framework needed for integrating machine learning with physics-based modeling. Molecular dynamics and moment closure of kinetic equations are used as examples to illustrate the main issues discussed. We end with a general discussion on where this integration will lead us to, and where the new frontier will be after machine learning is successfully integrated into scientific modeling.
These methods are really interesting for high-dimensional PDE (like HJB), but there's a ton of skepticism about the applicability of NN models for solving the more common PDE that arise in physical sciences and engineering. The tests are rarely equivalent, in that standard PDE…
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