Automated machine learning exact dirichlet boundary physics-informed neural networks for solid mechanics

Abstract

While Physics-informed neural networks (PINN) have made significant progress in solving partial differential equations (PDE), conventional PINN may have convergence issues due to spectral bias, the requirement of loss balancing, and a significant number of trainable weights. Exact Dirichlet boundary condition Physics-informed Neural Networks (EPINN) was developed to solve forward problems in solid mechanics by applying tensor decomposition, approximating distance function, and the principle of least work, achieving more than 127 times speedup compared to PINN. However, the sensitivity of hyperparameters of the PINN framework is less reported. To merge the gap, this study develops the mesh-free 3D Bayesian-Optimization Tree-Structured Parzen Estimator (BO-TPE) Automated Machine Learning EPINN to solve solid mechanics problems without labelled data of the solution field. Developed based on Nvidia modulus platform, the Automated Machine Learning EPINN (AEPINN) can achieve more than 20 times speedup for 2D plane stress problems and four times speedup for 3D bracket problems compared with the EPINN architecture. Compared with conventional PINN, AEPINN model achieved more than 200 times speedup for a plane stress problem and 400 times speed up for a bracket problem. For a two-span three-story frame composed of beams, columns, and slabs, the AEPINN model can simulate the frame displacement deformations comparable to ABAQUS results with adequate accuracy and speed with GPU accelerated. Optimized hyperparameters AEPINN can approach a hyperelastic cube rubber case within 60 s compared with Abaqus results of Mooney-Rivlin constitutive law. The comparison between single-precision and double-precision training is also illustrated. The influences of hyperparameters in the adopted EPINN framework are examined accordingly.