Meshless physics-informed deep learning method for three-dimensional solid mechanics
arXiv:2012.01547 · doi:10.1002/nme.6828
Abstract
Deep learning and the collocation method are merged and used to solve partial differential equations describing structures' deformation. We have considered different types of materials: linear elasticity, hyperelasticity (neo-Hookean) with large deformation, and von Mises plasticity with isotropic and kinematic hardening. The performance of this deep collocation method (DCM) depends on the architecture of the neural network and the corresponding hyperparameters. The presented DCM is meshfree and avoids any spatial discretization, which is usually needed for the finite element method (FEM). We show that the DCM can capture the response qualitatively and quantitatively, without the need for any data generation using other numerical methods such as the FEM. Data generation usually is the main bottleneck in most data-driven models. The deep learning model is trained to learn the model's parameters yielding accurate approximate solutions. Once the model is properly trained, solutions can be obtained almost instantly at any point in the domain, given its spatial coordinates. Therefore, the deep collocation method is potentially a promising standalone technique to solve partial differential equations involved in the deformation of materials and structural systems as well as other physical phenomena.
References in corpus (14)
- Adam: A Method for Stochastic Optimization
- PyTorch: An Imperative Style, High-Performance Deep Learning Library
- Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
- DGM: A deep learning algorithm for solving partial differential equations
- An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications
- Solving high-dimensional partial differential equations using deep learning
- Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
- Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks
- Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport
- Flow over an espresso cup: Inferring 3D velocity and pressure fields from tomographic background oriented schlieren videos via physics-informed neural networks
- Prediction and optimization of mechanical properties of composites using convolutional neural networks
- Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity
- Topology optimization of 2D structures with nonlinearities using deep learning
- Physics-informed Neural Networks for Solving Nonlinear Diffusivity and Biot's equations