Abstract
We present a method for solving partial differential equations using artificial neural networks and an adaptive collocation strategy. In this procedure, a coarse grid of training points is used at the initial training stages, while more points are added at later stages based on the value of the residual at a larger set of evaluation points. This method increases the robustness of the neural network approximation and can result in significant computational savings, particularly when the solution is non-smooth. Numerical results are presented for benchmark problems for scalar-valued PDEs, namely Poisson and Helmholtz equations, as well as for an inverse acoustics problem.
Original language | English |
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Pages (from-to) | 345-359 |
Number of pages | 15 |
Journal | Computers, Materials and Continua |
Volume | 59 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2019 |
Keywords
- Adaptive collocation
- Artificial neural networks
- Deep learning
- Inverse problems
ASJC Scopus subject areas
- Biomaterials
- Modelling and Simulation
- Mechanics of Materials
- Computer Science Applications
- Electrical and Electronic Engineering