Sobolev training of thermodynamic-informed neural networks for interpretable elasto-plasticity models with level set hardening
Sobolev training of thermodynamic-informed neural networks for interpretable elasto-plasticity models with level set hardening
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DOI：
10.1016/j.cma.2021.113695
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发表时间：
2021-04
影响因子：
7.2
通讯作者：
Nikolaos N. Vlassis;WaiChing Sun
中科院分区：
文献类型：
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作者：
Nikolaos N. Vlassis;WaiChing Sun
我们引入了一个深度学习框架，旨在训练具有可解释组件的平滑弹塑性模型，如存储的弹性能量函数、屈服面和基于一组深度神经网络预测的塑性流。通过将屈服函数重新定义为一个不断发展的水平集，我们引入了一种深度学习方法来推导控制硬化/软化机制的Hamilton-Jacobi方程的解。这个机器学习强化定律可以恢复任何经典的手工强化规则，并发现未知或难以用数学表达式表达的新机制。利用Sobolev训练来控制学习函数的导数，得到的机器学习弹塑性模型在热力学上是一致的，可解释的，同时表现出出色的学习能力。利用三维FFT求解器建立了多晶数据库，并进行了数值实验，分别验证了模型各组成部分的实现。我们的数值实验表明，与黑盒深度神经网络模型（如循环神经网络、一维卷积神经网络和多步前馈模型）相比，这种新方法提供了更鲁棒和准确的循环应力路径正演预测。
We introduce a deep learning framework designed to train smoothed elastoplasticity models with interpretable components, such as the stored elastic energy function, yield surface, and plastic flow that evolve based on a set of deep neural network predictions. By recasting the yield function as an evolving level set, we introduce a deep learning approach to deduce the solutions of the Hamilton–Jacobi equation that governs the hardening/softening mechanism. This machine learning hardening law may recover any classical hand-crafted hardening rules and discover new mechanisms that are either unbeknownst or difficult to express with mathematical expressions. Leveraging Sobolev training to gain control over the derivatives of the learned functions, the resultant machine learning elastoplasticity models are thermodynamically consistent, interpretable, while exhibiting excellent learning capacity. Using a 3D FFT solver to create a polycrystal database, numerical experiments are conducted and the implementations of each component of the models are individually verified. Our numerical experiments reveal that this new approach provides more robust and accurate forward predictions of cyclic stress paths than those obtained from black-box deep neural network models such as the recurrent neural network, the 1D convolutional neural network, and the multi-step feed-forward model.