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

IF 8.7 2区 工程技术 Q1 Mathematics
Tsung-Yeh Hsieh, Tsung-Hui Huang
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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.

Abstract Image

用于平流主导流建模的多尺度稳定物理信息神经网络与弱边界条件迁移学习法
物理信息神经网络(PINN)框架已被开发为一种强大的技术,用于解决具有潜在数据整合能力的偏微分方程(PDE)。然而,当应用于基于平流的偏微分方程时,PINNs 面临着各种挑战,如边界条件执行中的参数敏感性,以及强平流导致的条件不良系统造成的学习能力减弱。在本研究中,我们提出了一种多尺度稳定 PINN 方案,该方案采用弱施加边界条件(WBC)方法,并结合迁移学习,可以对平流扩散方程进行稳健建模。为了应对关键挑战,我们使用了一种平流-通量-解耦技术来规定 Dirichlet 边界条件,从而纠正了在 PINN 中使用传统惩罚和强执行方法所观察到的不平衡训练。我们在 PINN 的最小二乘函数形式下开发了一种多尺度方法,引入了一个可控的稳定项,它可以被视为一种特殊形式的 Sobolev 训练,可以增强学习能力。通过解决一系列前向建模的基准问题,展示了所提方法的功效,结果肯定了所提方法的有效性。
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来源期刊
Engineering with Computers
Engineering with Computers 工程技术-工程:机械
CiteScore
16.50
自引率
2.30%
发文量
203
审稿时长
9 months
期刊介绍: Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.
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