# Machine Learning with Physics Knowledge for Prediction: A Survey

arXiv: https://arxiv.org/abs/2408.09840 · HTML: https://mlsanity.com/paper/2408.09840/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2024.

## Built on by (most cited first, 6 of 6)

- [Context-Aware Deep Lagrangian Networks for Model Predictive Control](https://mlsanity.com/paper/2506.15249/) (2025)
- [Accelerating Conjugate Gradient Solvers for Homogenization Problems with Unitary Neural Operators](https://mlsanity.com/paper/2508.02681/) (2025)
- [Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes](https://mlsanity.com/paper/2511.05330/) (2025)
- [Navigating Ethical AI Challenges in the Industrial Sector: Balancing Innovation and Responsibility](https://mlsanity.com/paper/2601.09351/) (2026)
- [Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equations](https://mlsanity.com/paper/2605.06246/) (2026)
- [Physics-informed Conditional Normalizing Flows for Angles-only Cislunar Orbit Determination](https://mlsanity.com/paper/2606.30936/) (2026)

## Abstract (arXiv)

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.