Neuro-Symbolic ODE Discovery with Latent Grammar Flow

Karin Yu, Eleni Chatzi, Georgios Kissas

Keywords: Deep Generative Models, Flow, Formal Grammars, Dynamical Systems, Ordinary Differential Equations, Symbolic Regression, Equation Discovery

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.

Email Sharing: We authorize the sharing of all author emails with Program Chairs.

Data Release: We authorize the release of our submission and author names to the public in the event of acceptance.

Submission Number: 8