Exact Dirichlet boundary multi-resolution hash encoding solver for structures

Abstract

Designed to address computationally expensive scientific problems, physics-informed neural networks (PINNs) have primarily focused on solving issues involving relatively simple geometric shapes. Drawing inspiration from exact Dirichlet boundary PINN and neural representation field, this study first develops a multi-resolution hash encoding solver (MHS) as another pure physics-driven alternative. Compared to vanilla PINN, MHS achieves a 1000-time increase in computational speed for the 2D plane stress case. When compared to finite element method (FEM) software with graphic processing unit (GPU) acceleration, MHS can achieve a five-time speedup for the plane case and a two-time speedup for the 3D two-span three-story frame case. The general performance of optimized hyperparameters in automated machine learning MHS (AMHS) is evaluated by transferring AMHS to solve another hyper-elasticity rubber cube problem. For a hyper-elasticity cube, the AMHS model can approach solutions with comparable accuracy to FEM results, while the developed parallel MHS delivers at least 100 times in acceleration parametric analysis, compared to FEM commercial software (GPU-accelerated).