A Hard-Constraint Wide-Body Physics-Informed Neural Network Model for Solving Multiple Cases in Forward Problems for Partial Differential Equations

• DOI: 10.3390/app14010189
• Publication Date: 2023-12-26T03:59:09Z
• Authors: Simin Chen; Zhixiang Liu; Wenbo Zhang; Jinkun Yang
• Keywords: Technology; QH301-705.5; T; Physics; QC1-999; phase transition dynamics; Engineering (General). Civil engineering (General); 01 natural sciences; physics-informed neural networks; Chemistry; numerical modeling; TA1-2040; Biology (General); 0101 mathematics; PDEs; QD1-999; hard constraint

In the fields of physics and engineering, it is crucial to understand phase transition dynamics. This field involves fundamental partial differential equations (PDEs) such as Allen–Cahn, Burgers, two-dimensional (2D) wave equations. alloys, evolution interface described by Allen–Cahn equation. Vibrational phenomena during transitions are modeled using Burgers 2D The combination these gives comprehensive information about dynamic behavior a transition. Numerical modeling methods finite difference method (FDM), volume (FVM) element (FEM) often applied solve problems that involve many (PDEs). However, physical can lead computational complexity, increasing costs dramatically. Physics-informed neural networks (PINNs), new network algorithms, integrate law constraints with algorithms (PDEs), providing way PDEs in addition traditional numerical methods. this paper, hard-constraint wide-body PINN (HWPINN) model based on proposed. improves effectiveness approximation adding structure part architecture. A hard constraint used physically driven instead practice constituting residual boundary or initial conditions. high accuracy HWPINN for solving verified through experiments. One-dimensional (1D) one-dimensional equation cases set up properties inferred from experimental data. solution predicted compared FDM evaluating error shows great potential PDE forward problem provides approach PDEs.