# Machine Learning for Inverse Problems and Data Assimilation

arXiv: https://arxiv.org/abs/2410.10523 · HTML: https://mlsanity.com/paper/2410.10523/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2024.

## Built on by (most cited first, 7 of 7)

- [Learning Probabilistic Filters with Strictly Proper Scoring Rules](https://mlsanity.com/paper/2606.26497/) (2026)
- [Amortized Filtering and Smoothing with Conditional Normalizing Flows](https://mlsanity.com/paper/2604.07169/) (2026)
- [Long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems](https://mlsanity.com/paper/2412.14318/) (2024)
- [Auto-differentiable data assimilation: Co-learning of states, dynamics, and filtering algorithms](https://mlsanity.com/paper/2603.20891/) (2026)
- [Continuous Data Assimilation with Learned Surrogate Dynamics](https://mlsanity.com/paper/2606.00480/) (2026)
- [Energy-based Transport for Amortized Bayesian Inference](https://mlsanity.com/paper/2605.15407/) (2026)
- [The interface of data assimilation and machine learning](https://mlsanity.com/paper/2610.07496/) (2026)

## Abstract (arXiv)

The aim of this book is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is primarily aimed at researchers from inverse problems and/or data assimilation who wish to see a mathematical presentation of machine learning as it pertains to their fields. As a by-product, we include a succinct mathematical treatment of various fundamental underpinning topics in machine learning, and adjacent areas of (computational) mathematics.