Control of Partial Differential Equations via Physics-Informed Neural Networks
该文用物理信息神经网络求解偏微分方程的可控性问题，推导了状态和控制的泛化误差估计，为神经网络在此领域的应用提供了理论依据，并通过三种PDE的数值模拟验证了方法性能。
Abstract This paper addresses the numerical resolution of controllability problems for partial differential equations (PDEs) by using physics-informed neural networks. Error estimates for the generalization error for both state and control are derived from classical observability inequalities and energy estimates for the considered PDE. These error bounds, that apply to any exact controllable linear system of PDEs and in any dimension, provide a rigorous justification for the use of neural networks in this field. Preliminary numerical simulation results for three different types of PDEs are carried out to illustrate the performance of the proposed methodology.