Data-driven surrogate modeling 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. Surrogate models based on INCDE are subsequently trained and tested for J2 and Drucker-Prager plasticity. The surrogate models are 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：数据驱动的代理建模已成为降低多尺度模拟计算成本的一种有前景的方法。递归神经网络（RNN）是建模路径依赖行为的常用选择。然而，先前研究表明，RNN无法做出与输入应变扰动一致的预测，这可能导致在有限元模拟中产生振荡和缺乏收敛性。在本工作中，我们利用近年来涌现的神经微分方程连续建模时间序列，并展示了其在弹塑性路径依赖材料行为建模中的鲁棒性。我们开发了一种新的序列模型，称为增量式神经控制微分方程（INCDE），用于通用时变动态系统，包括路径依赖本构模型。从稳定性和收敛性角度对INCDE进行了公式化与分析。基于INCDE的代理模型随后针对J2和Drucker-Prager塑性进行训练和测试。这些代理模型被用于材料点模拟以及通过有限元方法求解的边值问题，并采用多种循环和单调加载协议，以证明所提出方法的鲁棒性、一致性和准确性。