English

Neuro-Symbolic ODE Discovery with Latent Grammar Flow

Machine Learning 2026-04-20 v1 Artificial Intelligence Computational Engineering, Finance, and Science Symbolic Computation

Abstract

Understanding natural and engineered systems often relies on symbolic formulations, such as differential equations, which provide interpretability and transferability beyond black-box models. We introduce Latent Grammar Flow (LGF), a neuro-symbolic generative framework for discovering ordinary differential equations from data. LGF embeds equations as grammar-based representations into a discrete latent space and forces semantically similar equations to be positioned closer together with a behavioural loss. Then, a discrete flow model guides the sampling process to recursively generate candidate equations that best fit the observed data. Domain knowledge and constraints, such as stability, can be either embedded into the rules or used as conditional predictors.

Keywords

Cite

@article{arxiv.2604.16232,
  title  = {Neuro-Symbolic ODE Discovery with Latent Grammar Flow},
  author = {Karin Yu and Eleni Chatzi and Georgios Kissas},
  journal= {arXiv preprint arXiv:2604.16232},
  year   = {2026}
}