Data-driven surrogate modeling or metamodeling has emerged as a promising approach for reducing computational expenses of multiscale simulations. Recurrent Neural Network (RNN) is a common choice for modeling of path-dependent behavior. However, previous studies have shown that RNNs fail to make predictions that are consistent with perturbation in the input strain, leading to potential oscillations and lack of convergence when implemented within finite element simulations. In this work, we leverage neural differential equations which have recently emerged to model time series in a continuous manner and show their robustness in modeling elasto-plastic path-dependent material behavior. We develop a new sequential model called Incremental Neural Controlled Differential Equation (INCDE) for general time-variant dynamical systems, including path-dependent constitutive models. INCDE is formulated and analyzed in terms of stability and convergence. A surrogate model based on INCDE is subsequently trained and tested for J2 plasticity. The surrogate model is implemented for material point simulations and boundary value problems solved using the finite element method with various cyclic and monotonic loading protocols to demonstrate the robustness, consistency and accuracy of the proposed approach.

翻译：数据驱动代理建模或元建模已成为降低多尺度模拟计算成本的有效方法。递归神经网络是建模路径依赖行为的常见选择，但先前研究表明，递归神经网络无法在输入应变扰动下保持预测一致性，导致在有限元模拟中可能出现振荡和收敛性问题。本研究利用近期兴起的神经微分方程对时间序列进行连续建模，并展示了其在弹塑性路径依赖材料行为建模中的鲁棒性。我们提出了一种名为增量式神经控制微分方程的新型序列模型，适用于一般时变动力系统（包括路径依赖本构模型）。本文从稳定性和收敛性角度对增量式神经控制微分方程进行了公式推导与分析，随后基于该模型训练并测试了J2塑性代理模型。通过将代理模型应用于材料点模拟及有限元方法求解的边值问题，并采用多种循环与单调加载协议，验证了所提方法的鲁棒性、一致性与准确性。