Scientific machine learning for closure models in multiscale problems: a review

TL;DR

This review discusses how scientific machine learning techniques are used to develop closure models for multiscale systems, emphasizing the integration of physics-based and data-driven methods, and highlighting recent advances and ongoing challenges.

Contribution

It provides a comprehensive overview of current ML-based closure modeling approaches, including model forms, learning objectives, and the importance of physical laws, connecting to related research fields.

Findings

Progress has been made in ML-based closure models.

Physical law adherence improves model reliability.

Challenges in generalizability and interpretability remain.

Abstract

Closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have been proposed as a way to tackle the closure problem, combining traditional (physics-based) modeling with data-driven (machine-learned) techniques, typically through enriching differential equations with neural networks. This paper reviews the different reduced model forms, distinguished by the degree to which they include known physics, and the different objectives of a priori and a posteriori learning. The importance of adhering to physical laws (such as symmetries and conservation laws) in choosing the reduced model form and choosing the learning method is discussed. The effect of spatial and temporal discretization and recent trends toward discretization-invariant models are reviewed. In addition, we make the connections between closure problems and several other research disciplines: inverse problems, Mori-Zwanzig theory, and multi-fidelity methods. In conclusion, much progress has been made with scientific machine learning approaches for solving closure problems, but many challenges remain. In particular, the generalizability and interpretability of learned models is a major issue that needs to be addressed further.