A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
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DOI：
10.1016/j.cma.2021.113741
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发表时间：
2021-03-12
影响因子：
7.2
通讯作者：
Juanes, Ruben
中科院分区：
文献类型：
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作者：
Haghighat, Ehsan;Raissi, Maziar;Juanes, Ruben
我们提出了一类深度学习的应用，称为物理信息神经网络（PINN），在固体力学反演和替代建模。我们解释了如何将动量平衡和本构关系到PINN，并详细探讨了应用到线性弹性，并说明其扩展到非线性问题，通过一个例子，展示冯米塞斯弹塑性。虽然常见的PINN算法基于训练一个深度神经网络（DNN），但我们提出了一个多网络模型，可以更准确地表示字段变量。为了验证模型，我们测试的框架上生成的分析和数值参考解决方案的合成数据。我们研究了PINN模型的收敛性，并表明等几何分析（伊加）的结果与经典的低阶有限元法（FEM）相比，具有上级精度和收敛特性。我们还展示了迁移学习框架的适用性，并在网络重新训练过程中发现了大大加速的收敛。最后，我们发现，尊重物理导致改进的鲁棒性：当只训练了几个参数，我们发现PINN模型可以准确地预测解决方案的范围广泛的新参数的网络，从而指出了一个重要的应用，这个框架的灵敏度分析和代理建模。(C)2021爱思唯尔有限公司版权所有。
We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to inversion and surrogate modeling in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN, and explore in detail the application to linear elasticity, and illustrate its extension to nonlinear problems through an example that showcases von Mises elastoplasticity. While common PINN algorithms are based on training one deep neural network (DNN), we propose a multi-network model that results in more accurate representation of the field variables. To validate the model, we test the framework on synthetic data generated from analytical and numerical reference solutions. We study convergence of the PINN model, and show that Isogeometric Analysis (IGA) results in superior accuracy and convergence characteristics compared with classic low-order Finite Element Method (FEM). We also show the applicability of the framework for transfer learning, and find vastly accelerated convergence during network re-training. Finally, we find that honoring the physics leads to improved robustness: when trained only on a few parameters, we find that the PINN model can accurately predict the solution for a wide range of parameters new to the network-thus pointing to an important application of this framework to sensitivity analysis and surrogate modeling. (C) 2021 Elsevier B.V. All rights reserved.