从数据中自动发现可解释的微分方程，结合神经与符号方法。
Neuro-Symbolic ODE Discovery with Latent Grammar Flow
- 用语法结构将方程编码到离散潜空间，保持语义相似性。
- 通过离散流模型递归生成最符合数据的候选方程。
- 支持加入稳定性等先验知识，适合科学建模场景。
理解自然与工程系统常依赖符号形式，如微分方程，其具备黑箱模型所缺乏的可解释性与泛化能力。我们提出潜语法流（Latent Grammar Flow, LGF），一种神经符号生成框架，用于从数据中发现常微分方程。LGF 将方程表示为基于语法的离散潜空间结构，并通过行为损失使语义相近的方程在潜空间中更接近。随后，利用离散流模型引导采样过程，递归生成最契合观测数据的候选方程。领域知识与约束（如稳定性）可嵌入规则或作为条件预测器使用。
原文摘要 · Abstract (English)
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.
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