从轨迹数据中自动发现非线性系统的守恒律，无需已知方程。
Data-Driven Discovery of Conservation Laws from Trajectories via Neural Deflation
- 基于系统轨迹而非方程，用神经去噪方法寻找守恒量。
- 在多个经典系统中成功识别出完整守恒律集合。
- 适合缺乏动力学方程但有观测数据的物理建模场景。
在先前工作中，部分作者提出了神经去噪方法，用于识别非线性动力系统中一组完整的函数独立守恒律。本文在此基础上实现重要扩展：不再依赖系统的运动方程，而是直接从系统轨迹数据中推导守恒律。这一改进对实际应用至关重要，尤其适用于仅有离散快照数据而无显式方程的场景。我们在多种系统中验证了该方法的有效性，包括一维和二维谐振子、Toda格子、Fermi-Pasta-Ulam-Tsingou格子以及Calogero-Moser系统，均成功获得了相应的守恒律数量。
原文摘要 · Abstract (English)
In an earlier work by a subset of the present authors, the method of the so-called neural deflation was introduced towards identifying a complete set of functionally independent conservation laws of a nonlinear dynamical system. Here, we extend by a significant step this proposal. Instead of using the explicit knowledge of the underlying equations of motion, we develop the method directly from system trajectories. This is crucial towards enhancing the practical implementation of the method in scenarios where solely data reflecting discrete snapshots of the system are available. We showcase the results of the method and the number of associated conservation laws obtained in a diverse range of examples including 1D and 2D harmonic oscillators, the Toda lattice, the Fermi-Pasta-Ulam-Tsingou lattice and the Calogero-Moser system.
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