Neuro-Symbolic ODE Discovery with Latent Grammar Flow
Provides a novel method for symbolic ODE discovery that balances interpretability and accuracy, but is domain-specific to dynamical systems.
LGF discovers symbolic ODEs from data using grammar-based latent representations and a discrete flow model, outperforming baselines on synthetic and real-world systems.
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.