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.

翻译：理解自然与工程系统通常依赖于符号化表述（如微分方程），这类表述能提供超越黑箱模型的可解释性与可迁移性。我们提出潜在语法流（LGF）——一种从数据中发现常微分方程的神经符号化生成框架。LGF将方程编码为基于语法的表示，嵌入离散潜在空间，并通过行为损失函数迫使语义相似的方程在空间中更为接近。随后，离散流模型引导采样过程，递归生成最符合观测数据的候选方程。领域知识与约束条件（如稳定性）既可作为规则内嵌其中，亦可用作条件预测器。