Neuro-Symbolic ODE Discovery with Latent Grammar Flow

2026-04-17

AI Summary

This work proposes the Latent Grammar Flow (LGF) framework to automatically discover interpretable and transferable ordinary differential equation (ODE) models from observational data. LGF uniquely integrates grammar-guided discrete latent spaces with neuro-symbolic generative modeling, employing a behavioral similarity loss to ensure that semantically related equations are proximate in the latent space. It recursively generates high-quality candidate equations via discrete normalizing flows, enabling efficient exploration of the symbolic model space. The framework naturally incorporates domain knowledge and structural constraints—such as stability—into the discovery process, facilitating the identification of physically meaningful ODEs. By jointly optimizing for interpretability and generalization, LGF significantly improves both the accuracy of equation discovery and out-of-distribution predictive performance compared to existing approaches.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Neuro-Symbolic Learning
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• ODE discovery
• symbolic regression
• neuro-symbolic
• interpretable modeling
• grammar-based representation

Innovation

• Neuro-Symbolic
• ODE Discovery
• Latent Grammar Flow
• Discrete Flow Model
• Grammar-based Representation