DNN Approximation of Nonlinear Finite Element Equations
- Portland State Univ., OR (United States)
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Portland State Univ., OR (United States)
We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the trained DNN to replace the coarse nonlinear operator thus avoiding the need to visit the fine level discretization in order to evaluate the actions of the true coarse nonlinear operator. The feasibility of the studied approach is demonstrated in a two level FAS (full approximation scheme) used to solve a nonlinear diffusion-reaction PDE.
- Research Organization:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1573161
- Report Number(s):
- LLNL-TR-791918; 991070
- Country of Publication:
- United States
- Language:
- English
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