基于神经放缩（Neural Deflation）从轨迹中数据驱动发现守恒律
Data-Driven Discovery of Conservation Laws from Trajectories via Neural Deflation
AI总结：
该研究拓展了神经放缩方法，无需已知运动方程，直接从系统轨迹数据驱动发现非线性动力系统的完整函数独立守恒律，在多个经典动力系统案例中验证了有效性，提升了方法在仅含离散快照数据场景下的实用性。
摘要：
在本文作者部分成员早前的工作中，提出了所谓的神经放缩（neural deflation）方法，用于识别非线性动力系统的一组完整的函数独立守恒律。本文在此基础上实现了重要拓展：我们不再依赖运动方程的显式已知条件，而是直接从系统轨迹出发开发该方法。这一点对于提升方法的实际应用性至关重要，适用于仅能获取系统离散快照数据的场景。我们在多个不同案例中展示了方法的结果及得到的对应守恒律数量，案例包括一维与二维简谐振子、Toda晶格、Fermi-Pasta-Ulam-Tsingou晶格以及Calogero-Moser系统。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
