Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics
arXiv:2307.02494 · doi:10.1007/s00521-024-10132-2
Abstract
Machine Learning methods belong to the group of most up-to-date approaches for solving partial differential equations. The current work investigates two classes, Neural FEM and Neural Operator Methods, for the use in elastostatics by means of numerical experiments. The Neural Operator methods require expensive training but then allow for solving multiple boundary value problems with the same Machine Learning model. Main differences between the two classes are the computational effort and accuracy. Especially the accuracy requires more research for practical applications.
References in corpus (14)
- DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
- DGM: A deep learning algorithm for solving partial differential equations
- Fourier Neural Operator for Parametric Partial Differential Equations
- Data-driven computational mechanics
- Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification
- Simulator-free Solution of High-Dimensional Stochastic Elliptic Partial Differential Equations using Deep Neural Networks
- Physics-Informed Neural Operator for Learning Partial Differential Equations
- Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems
- A Deep Neural Network Surrogate for High-Dimensional Random Partial Differential Equations
- Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets
- Model-Parallel Fourier Neural Operators as Learned Surrogates for Large-Scale Parametric PDEs
- On the use of graph neural networks and shape-function-based gradient computation in the deep energy method
- Physics-Informed Deep Neural Operator Networks
- Competitive Physics Informed Networks