Variational Onsager Neural Networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs
Variational Onsager Neural Networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs
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DOI：
10.1016/j.jmps.2022.104856
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发表时间：
2022-04-04
影响因子：
5.3
通讯作者：
Reina, Celia
中科院分区：
文献类型：
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作者：
Huang, Shenglin;He, Zequn;Reina, Celia
我们提出了一种基于Onsager变分原理的非平衡演化方程的学习策略，它允许我们用两个势来写这样的偏微分方程：自由能和耗散势。具体来说，这两个潜在的学习宏观观测量的时空测量通过建议的神经网络架构，强烈执行热力学第二定律的满意度。该方法适用于三个不同的物理过程，旨在突出所提出的方法的鲁棒性和通用性。这些包括：（i）卷曲螺旋蛋白质的相变，其特征在于非凸自由能密度;（ii）三维粘弹性固体的一维动态响应，其利用变分公式作为获得降阶模型的工具;以及（iii）线性和非线性扩散模型，其特征在于缺乏自由能和耗散势的唯一性。这些说明性的例子展示了通过其变分作用密度（即，函数），通过利用力学和多物理问题固有的热力学结构。
We propose a thermodynamics-based learning strategy for non-equilibrium evolution equations based on Onsager's variational principle, which allows us to write such PDEs in terms of two potentials: the free energy and the dissipation potential. Specifically, these two potentials are learned from spatio-temporal measurements of macroscopic observables via proposed neural network architectures that strongly enforce the satisfaction of the second law of thermodynamics. The method is applied to three distinct physical processes aimed at highlighting the robustness and versatility of the proposed approach. These include (i) the phase transformation of a coiled-coil protein, characterized by a non-convex free-energy density; (ii) the onedimensional dynamic response of a three-dimensional viscoelastic solid, which leverages the variational formulation as a tool for obtaining reduced order models; and (iii) linear and nonlinear diffusion models, characterized by a lack of uniqueness of the free energy and dissipation potentials. These illustrative examples showcase the possibility of learning partial differential equations through their variational action density (i.e., a function instead), by leveraging the thermodynamic structure intrinsic to mechanical and multiphysics problems.