Asymptotic-preserving neural network for the Boltzmann equation with uncertainties
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To enhance the performance of standard physics-informed neural network (PINN) for solving high-dimensional PDE problems, we adapt the asymptotic-preserving PINN to solve the multi-scale semi-conductor Boltzmann and Boltzmann-Poisson equation. We then extend to the uncertainty quantification problem and adapt the asymptotic-preserving PINN with the stochastic Galerkin framework. Numerical experiments and formal error analysis will be presented to demonstrate the efficiency and accuracy of our proposed neural network approach.
