论文标题
使用PINN在离散系统中发现管理方程
Discovering Governing Equations in Discrete Systems Using PINNs
论文作者
论文摘要
非线性动力学系统的稀疏识别是在动态系统社区中不断提高重要性的话题。在这里，我们在许多自由度的晶格非线性动力学系统的层面上进行探索。我们说明了适当适应物理信息神经网络（PINN）的能力，以在受物理应用程序启发的这种离散的高维系统中解决参数识别的反面问题。该方法在包括真实场现场的示例（$ ϕ^4 $和正弦戈登）以及复杂场（离散的非线性schr {Ö} dinger方程式）以及超越汉密尔顿（Hamiltonian）到耗散案例（离散的复杂的Ginzburg-Ginzburg-landau方程）中的各种示例中进行了说明。一路上讨论了该方法的成功以及该方法的某些局限性。
Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom. We illustrate the ability of a suitable adaptation of Physics-Informed Neural Networks (PINNs) to solve the inverse problem of parameter identification in such discrete, high-dimensional systems inspired by physical applications. The methodology is illustrated in a diverse array of examples including real-field ones ($ϕ^4$ and sine-Gordon), as well as complex-field (discrete nonlinear Schr{ö}dinger equation) and going beyond Hamiltonian to dissipative cases (the discrete complex Ginzburg-Landau equation). Both the successes, as well as some limitations of the method are discussed along the way.
