数据驱动的守恒定律的发现，从轨迹通过神经紧缩

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-04 DOI:10.1016/j.cnsns.2024.108563

Shaoxuan Chen, Panayotis G. Kevrekidis, Hong-Kun Zhang, Wei Zhu

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引用次数: 0

摘要

在本作者W. Zhu等人（2023）的早期工作中，引入了所谓的神经紧缩方法来识别非线性动力系统的一套完整的功能独立守恒定律。在此，我们将这一建议向前推进了重要一步。我们没有使用潜在运动方程的显式知识，而是直接从系统轨迹开发方法。这对于在仅反映系统离散快照的数据可用的情况下增强该方法的实际实施至关重要。我们展示了该方法的结果以及在各种例子中获得的相关守恒定律的数量，包括1D和2D谐振子，Toda晶格，Fermi-Pasta-Ulam-Tsingou晶格和Calogero-Moser系统。

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Data-driven discovery of conservation laws from trajectories via neural deflation

In an earlier work by a subset of the present authors W. Zhu et al. (2023), 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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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.