Molecular dynamics inferred transfer learning models for finite‐strain hyperelasticity of monoclinic crystals: Sobolev training and validations against physical constraints
Molecular dynamics inferred transfer learning models for finite‐strain hyperelasticity of monoclinic crystals: Sobolev training and validations against physical constraints
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DOI：
10.1002/nme.6992
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发表时间：
2022-04
影响因子：
2.9
通讯作者：
Nikolaos N. Vlassis;Puhan Zhao;R. Ma;Tommy Sewell;WaiChing Sun
中科院分区：
文献类型：
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作者：
Nikolaos N. Vlassis;Puhan Zhao;R. Ma;Tommy Sewell;WaiChing Sun
我们提出了一个机器学习框架来训练和验证神经网络，以预测单斜晶系有机分子晶体β$$\β$$-HMX在几何非线性区域的各向异性弹性响应。过滤分子动力学(MD)模拟数据库被用来训练具有Soblev范数的神经网络，该范数使用应力测量和参考构型来推导弹性存储自由能泛函。为了提高源自学习存储自由能的弹性切线预测的精度，使用转移学习技术从数据中引入附加的切线约束，同时将模型正确性的必要条件(例如，强椭圆度、晶体对称性)作为附加的物理约束引入或合并到验证测试中。对神经网络的评估基于(1)它们再现MD预测的底线本构响应的精度，(2)通过详细检查其稳定性和唯一性来测量模型的稳健性，以及(3)关于有限变形区域中的力学原理的预测响应的容许性。我们比较了不同索博列夫约束下神经网络的训练效率，并针对β$$\BETA$$-HMX的MD基准评估了模型的准确性和稳健性。
We present a machine learning framework to train and validate neural networks to predict the anisotropic elastic response of a monoclinic organic molecular crystal known as β$$ \beta $$ ‐HMX in the geometrical nonlinear regime. A filtered molecular dynamic (MD) simulations database is used to train neural networks with a Sobolev norm that uses the stress measure and a reference configuration to deduce the elastic stored free energy functional. To improve the accuracy of the elasticity tangent predictions originating from the learned stored free energy, a transfer learning technique is used to introduce additional tangential constraints from the data while necessary conditions (e.g., strong ellipticity, crystallographic symmetry) for the correctness of the model are either introduced as additional physical constraints or incorporated in the validation tests. Assessment of the neural networks is based on (1) the accuracy with which they reproduce the bottom‐line constitutive responses predicted by MD, (2) the robustness of the models measured by detailed examination of their stability and uniqueness, and (3) the admissibility of the predicted responses with respect to mechanics principles in the finite‐deformation regime. We compare the training efficiency of the neural networks under different Sobolev constraints and assess the accuracy and robustness of the models against MD benchmarks for β$$ \beta $$ ‐HMX.