Physics and equality constrained artificial neural networks: Application to forward and inverse problems with multi-fidelity data fusion
Physics and equality constrained artificial neural networks: Application to forward and inverse problems with multi-fidelity data fusion
复制标题
DOI：
10.1016/j.jcp.2022.111301
复制
发表时间：
2022-05-20
影响因子：
4.1
通讯作者：
Senocak, Inanc
中科院分区：
文献类型：
--
作者：
Basir, Shamsulhaq;Senocak, Inanc
物理信息神经网络(PINN)被提出用于学习偏微分方程组(PDE)的解。在PINN中，感兴趣的偏微分方程的残差形式及其边界条件被集中到一个复合目标函数中，作为软惩罚。在这里，我们表明，这种具体的制定目标函数的方式是Pinn方法应用于不同类型的偏微分方程组时严重限制的来源。为了解决这些局限性，我们提出了一个基于约束优化问题的通用框架，其中我们使用增广拉格朗日方法(ALM)来约束具有边界条件的偏微分方程组的解和任何可用的高保真数据。我们的方法擅长于多保真数据融合的正反问题。我们通过将我们的物理和等式约束的深度学习框架应用于几个涉及多维偏微分方程组的正反问题，展示了它的有效性和多功能性。与最先进的物理信息神经网络相比，我们的框架在精度水平上实现了数量级的提高。(C)2022 Elsevier Inc.保留所有权利。
Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, the residual form of the PDE of interest and its boundary conditions are lumped into a composite objective function as soft penalties. Here, we show that this specific way of formulating the objective function is the source of severe limitations in the PINN approach when applied to different kinds of PDEs. To address these limitations, we propose a versatile framework based on a constrained optimization problem formulation, where we use the augmented Lagrangian method (ALM) to constrain the solution of a PDE with its boundary conditions and any high-fidelity data that may be available. Our approach is adept at forward and inverse problems with multi-fidelity data fusion. We demonstrate the efficacy and versatility of our physics-and equality-constrained deep-learning framework by applying it to several forward and inverse problems involving multi-dimensional PDEs. Our framework achieves orders of magnitude improvements in accuracy levels in comparison with state-of-the-art physics-informed neural networks. (C) 2022 Elsevier Inc. All rights reserved.