In plain words: It turns equations into grammar-based codes, placing equations that behave alike close together, then generates new candidates step by step to fit the data. The goal is finding readable differential equations from measurements, with rules like stability built in.
Abstract · Neuro-Symbolic ODE Discovery with Latent Grammar Flow
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.
Karin Yu, Eleni Chatzi, Georgios Kissas
arXiv:2604.16232 · cs.LG, cs.AI, cs.CE, cs.SC · submitted Apr 17, 2026 · updated Jul 13, 2026
abstract · pdf · html · Accepted to the Structured Probabilistic Inference & Generative Modeling Workshop at ICML 2026 in Seoul, South Korea