用物理原则增强神经网络，精准模拟大变形下的各向异性非弹性材料
A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains
- 基于混合张量的输入表示，结合能量耗散双势函数
- 在未训练过的边界条件下仍保持高精度与稳定性
- 适合需要高保真材料建模的工程仿真与开源研究
我们提出一种用于有限应变下各向异性非弹性材料的本构建模补充方法，将神经网络与材料基本原理相结合。核心是双势函数，可一致地刻画各向异性并满足耗散不等式，无需凸性假设。神经网络采用混合弹性、非弹性与结构张量的不变量输入表示，引入输入单调神经网络以扩展可接受势函数类，并采用循环液态神经网络避免大变形下的指数映射时间积分，提升非弹性材料训练稳定性。方法在材料点与结构尺度上均进行了验证，相比无物理约束的循环模型，对未见边界值问题的变形与反力预测均表现出更高准确性与鲁棒性。神经网络与有限元实现均已开源，可通过 https://doi.org/10.5281/zenodo.17199965 获取。
原文摘要 · Abstract (English)
We propose a complement to constitutive modeling that augments neural networks with material principles to capture anisotropy and inelasticity at finite strains. The key element is a dual potential that governs dissipation, consistently incorporates anisotropy, and-unlike conventional convex formulations-satisfies the dissipation inequality without requiring convexity. Our neural network architecture employs invariant-based input representations in terms of mixed elastic, inelastic and structural tensors. It adapts Input Convex Neural Networks, and introduces Input Monotonic Neural Networks to broaden the admissible potential class. To bypass exponential-map time integration in the finite strain regime and stabilize the training of inelastic materials, we employ recurrent Liquid Neural Networks. The approach is evaluated at both material point and structural scales. We benchmark against recurrent models without physical constraints and validate predictions of deformation and reaction forces for unseen boundary value problems. In all cases, the method delivers accurate and stable performance beyond the training regime. The neural network and finite element implementations are available as open-source and are accessible to the public via https://doi.org/10.5281/zenodo.17199965.
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