# Deep Learning based discovery of Integrable Systems

arXiv: https://arxiv.org/abs/2503.10469 · HTML: https://mlsanity.com/paper/2503.10469/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 61 references that are in the map.
- First posted on arXiv 13 Mar 2025.

## Builds on (most cited first, 17 of 17)

- [Agent Laboratory: Using LLM Agents as Research Assistants](https://mlsanity.com/paper/2501.04227/) (2025)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [ResearchAgent: Iterative Research Idea Generation over Scientific Literature with Large Language Models](https://mlsanity.com/paper/2404.07738/) (2024)
- [Robust Learning with Jacobian Regularization](https://mlsanity.com/paper/1908.02729/) (2019)
- [MLGym: A New Framework and Benchmark for Advancing AI Research Agents](https://mlsanity.com/paper/2502.14499/) (2025)
- [DISCOVERYWORLD: A Virtual Environment for Developing and Evaluating Automated Scientific Discovery Agents](https://mlsanity.com/paper/2406.06769/) (2024)
- [Minimum Width for Universal Approximation](https://mlsanity.com/paper/2006.08859/) (2020)
- [LeanAgent: Lifelong Learning for Formal Theorem Proving](https://mlsanity.com/paper/2410.06209/) (2024)
- [Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks](https://mlsanity.com/paper/2003.04299/) (2020)
- [Machine-learning hidden symmetries](https://mlsanity.com/paper/2109.09721/) (2021)
- [Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles](https://mlsanity.com/paper/2301.05638/) (2023)
- [Learning Symmetries of Classical Integrable Systems](https://mlsanity.com/paper/1906.04645/) (2019)
- [Machine Learning Lie Structures & Applications to Physics](https://mlsanity.com/paper/2011.00871/) (2020)
- [Searching for ribbons with machine learning](https://mlsanity.com/paper/2304.09304/) (2023)
- [Rigor with Machine Learning from Field Theory to the Poincar'e Conjecture](https://mlsanity.com/paper/2402.13321/) (2024)
- [The R-mAtrIx Net](https://mlsanity.com/paper/2304.07247/) (2023)
- [Classical integrability in the presence of a cosmological constant: analytic and machine learning results](https://mlsanity.com/paper/2404.18247/) (2024)

## Abstract (arXiv)

We introduce a novel machine learning based framework for discovering integrable models. Our approach first employs a synchronized ensemble of neural networks to find high-precision numerical solution to the Yang-Baxter equation within a specified class. Then, using an auxiliary system of algebraic equations, [Q_2, Q_3] = 0, and the numerical value of the Hamiltonian obtained via deep learning as a seed, we reconstruct the entire Hamiltonian family, forming an algebraic variety. We illustrate our presentation with three- and four-dimensional spin chains of difference form with local interactions. Remarkably, all discovered Hamiltonian families form rational varieties.