用神经微分方程+Transformer自动发现物理系统守恒律
Automated Discovery of Conservation Laws via Hybrid Neural ODE-Transformers
- 先学连续动力学，再生成符号候选守恒量
- 在真实物理系统上比基线方法更准
- 适合想从噪声数据中挖掘物理规律的研究者
守恒律的发现是科学进步的核心。然而，从观测数据中识别这些不变量仍具挑战性。我们提出一种混合框架，自动化地从含噪轨迹数据中发现守恒量。该方法结合三部分：(1) 神经常微分方程（Neural ODE）学习系统的连续动力学模型；(2) Transformer 根据学习到的向量场生成符号候选守恒量；(3) 符号-数值验证器为候选量提供强数值证明。我们在典型物理系统上测试该框架，结果表明其显著优于直接作用于轨迹数据的基线方法。这项工作展示了解耦式‘先学习后搜索’策略在从不完美数据中发现数学原理方面的鲁棒性。
原文摘要 · Abstract (English)
The discovery of conservation laws is a cornerstone of scientific progress. However, identifying these invariants from observational data remains a significant challenge. We propose a hybrid framework to automate the discovery of conserved quantities from noisy trajectory data. Our approach integrates three components: (1) a Neural Ordinary Differential Equation (Neural ODE) that learns a continuous model of the system's dynamics, (2) a Transformer that generates symbolic candidate invariants conditioned on the learned vector field, and (3) a symbolic-numeric verifier that provides a strong numerical certificate for the validity of these candidates. We test our framework on canonical physical systems and show that it significantly outperforms baselines that operate directly on trajectory data. This work demonstrates the robustness of a decoupled learn-then-search approach for discovering mathematical principles from imperfect data.
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