Neuro-Symbolic ODE Discovery with Latent Grammar Flow
arXiv:2604.16232
The paper presents Latent Grammar Flow, a neuro‑symbolic generative framework that embeds differential equations as grammar‑based tokens in a discrete latent space and uses a discrete flow model with a behavioural loss to discover ordinary differential equations from data, while allowing domain constraints to be incorporated.
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.
Accepted to the Structured Probabilistic Inference & Generative Modeling Workshop at ICML 2026 in Seoul, South Korea