# Integrating Machine Learning with Physics-Based Modeling

arXiv: https://arxiv.org/abs/2006.02619 · HTML: https://mlsanity.com/paper/2006.02619/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2020.

## Built on by (most cited first, 8 of 8)

- [Polyconvex anisotropic hyperelasticity with neural networks](https://mlsanity.com/paper/2106.14623/) (2021)
- [Physics-Guided Deep Learning for Dynamical Systems: A Survey](https://mlsanity.com/paper/2107.01272/) (2021)
- [Knowledge-augmented Deep Learning and Its Applications: A Survey](https://mlsanity.com/paper/2212.00017/) (2022)
- [Deep Grey-Box Modeling With Adaptive Data-Driven Models Toward Trustworthy Estimation of Theory-Driven Models](https://mlsanity.com/paper/2210.13103/) (2022)
- [Frame-independent vector-cloud neural network for nonlocal constitutive modeling on arbitrary grids](https://mlsanity.com/paper/2103.06685/) (2021)
- [Multiway Ensemble Kalman Filter](https://mlsanity.com/paper/2112.04322/) (2021)
- [Interpretable and Scalable Graphical Models for Complex Spatio-temporal Processes](https://mlsanity.com/paper/2301.06021/) (2023)
- [Structure-preserving neural networks for the regularized entropy-based closure of the Boltzmann moment system](https://mlsanity.com/paper/2404.14312/) (2024)

## Abstract (arXiv)

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.