Neuro-Symbolic ODE Discovery with Latent Grammar Flow

TL;DR

The paper introduces Latent Grammar Flow, a neuro-symbolic framework that discovers differential equations from data by embedding symbolic representations into a latent space and guiding their generation with a flow model.

Contribution

It presents a novel generative approach combining grammar-based symbolic representations with neural flow models for ODE discovery.

Findings

Successfully generates equations fitting observed data.

Incorporates domain constraints like stability into the discovery process.

Provides a flexible framework for interpretable differential equation modeling.

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.