Publicado 4 números por año
ISSN Imprimir: 2689-3967
ISSN En Línea: 2689-3975
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hp-VARIATIONAL PHYSICS-INFORMED NEURAL NETWORKS FOR NONLINEAR TWO-PHASE TRANSPORT IN POROUS MEDIA
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SINOPSIS
Neural networks (NN) have gained a lot attention recently in solving a wide range of computational physical problems. In this paper, we focus on solving a dynamic fluid-flow in a subsurface problem with the hp-variational physics-informed neural networks (hp-VPINNs) approach. The problem is governed by a nonlinear first-order hyperbolic partial differential equation (PDE) with initial and boundary conditions. The idea is to train a neural network representing the solution such that the underlying physical laws are honored while the constraints are satisfied. By employing the approach of hp-VPINNs, the forward problem is solved without any additional labeled data in the interior of the domain. It works for a case with the nonconvex flux functions in the PDE, where the solution contains shocks and mixed waves. In addition, we performed hp refinement analysis on the problem and show that p refinement is suitable as it resolves the discontinuity in the solution. Finally, we investigated the inverse two-phase transport problem and solved for the nonlinear constitutive relation. With using sparse measurements as prior knowledge, the nonlinear constitutive relation was calculated and a solution over the entire computational domain was obtained.
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