A multiscale stabilized physics informed neural networks with weakly imposed boundary conditions transfer learning method for modeling advection dominated flow

Hsieh, Tsung YehTsung YehHsiehTSUNG-HUI HUANG2025-09-242025-09-242024https://www.scopus.com/inward/record.uri?eid=2-s2.0-85192158746&doi=10.1007%2Fs00366-024-01981-5&partnerID=40&md5=b65e269b4c165db52f0a4d986d250331https://scholars.lib.ntu.edu.tw/handle/123456789/732525Physics 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.Advection Diffusion EquationMultiscale StabilizationPhysics Informed Neural NetworkTransfer LearningWeakly Imposed Boundary ConditionsAdvectionData IntegrationHeat TransferLearning SystemsPartial Differential EquationsStabilizationAdvection-diffusion EquationBoundary Condition TransferMultiscale StabilizationNetwork FrameworksNeural-networksParameter SensitivitiesPhysic Informed Neural NetworkTransfer LearningTransfer Learning MethodsWeakly Imposed Boundary ConditionBoundary Conditions[SDGs]SDG13A multiscale stabilized physics informed neural networks with weakly imposed boundary conditions transfer learning method for modeling advection dominated flowjournal article10.1007/s00366-024-01981-52-s2.0-85192158746