A multiscale stabilized physics informed neural networks with weakly imposed boundary conditions transfer learning method for modeling advection dominated flow
Journal
Engineering with Computers
Journal Volume
40
Journal Issue
5
Start Page
3353
End Page
3387
ISSN
14355663
01770667
Date Issued
2024
Author(s)
Hsieh, Tsung Yeh
Abstract
Physics informed neural network (PINN) frameworks have been developed as a powerful technique for solving partial differential equations (PDEs) with potential data integration. However, when applied to advection based PDEs, PINNs confront challenges such as parameter sensitivity in boundary condition enforcement and diminished learning capability due to an ill-conditioned system resulting from the strong advection. In this study, we present a multiscale stabilized PINN formulation with a weakly imposed boundary condition (WBC) method coupled with transfer learning that can robustly model the advection diffusion equation. To address key challenges, we use an advection-flux-decoupling technique to prescribe the Dirichlet boundary conditions, which rectifies the imbalanced training observed in PINN with conventional penalty and strong enforcement methods. A multiscale approach under the least squares functional form of PINN is developed that introduces a controllable stabilization term, which can be regarded as a special form of Sobolev training that augments the learning capacity. The efficacy of the proposed method is demonstrated through the resolution of a series of benchmark problems of forward modeling, and the outcomes affirm the potency of the methodology proposed.
Subjects
Advection Diffusion Equation
Multiscale Stabilization
Physics Informed Neural Network
Transfer Learning
Weakly Imposed Boundary Conditions
Advection
Data Integration
Heat Transfer
Learning Systems
Partial Differential Equations
Stabilization
Advection-diffusion Equation
Boundary Condition Transfer
Multiscale Stabilization
Network Frameworks
Neural-networks
Parameter Sensitivities
Physic Informed Neural Network
Transfer Learning
Transfer Learning Methods
Weakly Imposed Boundary Condition
Boundary Conditions
SDGs
Publisher
Springer Science and Business Media Deutschland GmbH
Type
journal article