Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains difficult to deal with high-dimensional applications and extrapolative generalization. This paper introduces deep learning techniques under the data-driven framework to address these fundamental issues in nonlinear materials modeling. To this end, an autoencoder neural network architecture is introduced to learn the underlying low-dimensional representation (embedding) of the given material database. The offline trained autoencoder and the discovered embedding space are then incorporated in the online data-driven computation such that the search of optimal material state from database can be performed on a low-dimensional space, aiming to enhance the robustness and predictability with projected material data. To ensure numerical stability and representative constitutive manifold, a convexity-preserving interpolation scheme tailored to the proposed autoencoder-based data-driven solver is proposed for constructing the material state. In this study, the applicability of the proposed approach is demonstrated by modeling nonlinear biological tissues. A parametric study on data noise, data size and sparsity, training initialization, and model architectures, is also conducted to examine the robustness and convergence property of the proposed approach.

物理约束数据驱动计算是一种新兴的计算范式，它允许直接基于材料数据库模拟复杂材料，并绕过经典的本构模型构建。然而，仍然难以处理高维应用和外推泛化。本文介绍了数据驱动框架下的深度学习技术，以解决非线性材料建模中的这些基本问题。为此，引入了自动编码器神经网络架构来学习给定材料数据库的底层低维表示（嵌入）。然后将离线训练的自动编码器和发现的嵌入空间合并到在线数据驱动计算中，以便可以在低维空间上执行从数据库中搜索最佳材料状态，旨在增强投影材料数据的鲁棒性和可预测性. 为了确保数值稳定性和代表性本构流形，提出了一种针对所提出的基于自动编码器的数据驱动求解器量身定制的凸性保持插值方案，用于构建材料状态。在本研究中，通过对非线性生物组织进行建模，证明了所提出方法的适用性。关于数据噪声、数据大小和稀疏性、训练初始化和模型架构的参数研究，