The work presented in this paper aims at developing a novel meshless parameter estimation framework for a system of partial differential equations (PDEs) using artificial neural network (ANN) approximations. The PDE models to be treated consist of linear and nonlinear PDEs, with Dirichlet and Neumann boundary conditions, considering both regular and irregular boundaries. This paper focuses on testing the applicability of neural networks for estimating the process model parameters while simultaneously computing the model predictions of the state variables in the system of PDEs representing the process. The capability of the proposed methodology is demonstrated with five numerical problems, showing that the ANN-based approach is very efficient by providing accurate solutions in reasonable computing times.

本文提出的工作旨在利用人工神经网络（ANN）近似为偏微分方程（PDE）系统开发一种新颖的无网格参数估计框架。要处理的PDE模型由线性和非线性PDE组成，具有Dirichlet和Neumann边界条件，同时考虑了规则边界和不规则边界。本文着重于测试神经网络在估计过程模型参数的适用性的同时，在代表过程的PDE系统中计算状态变量的模型预测。通过五个数值问题证明了所提出方法的能力，表明基于ANN的方法通过在合理的计算时间内提供准确的解决方案非常有效。