Deep Material Network (DMN) has recently emerged as a data-driven surrogate model for heterogeneous materials. Given a particular microstructural morphology, the effective linear and nonlinear behaviors can be successfully approximated by such physics-based neural-network like architecture. In this work, a novel parametric DMN architecture is proposed for multiscale materials with a varying microstructure characterized by several parameters. A Physics-Informed Neural Network (PINN) is used to account for the dependence of DMN fitting parameters on the microstructural ones. Micromechanical constraints are prescribed both on the network architecture and on the output of this PINN. The proposed PINN-DMN architecture is also recast in a multiphysics setting, where physical properties other than the mechanical ones can also be predicted. In the numerical simulations conducted on three parametric microstructures, PINN-DMN demonstrates satisfying interpolative and extrapolative generalization capabilities when morphology varies. The effective multiphysics behaviors of such parametric multiscale materials can thus be predicted and encoded by PINN-DMN with high accuracy and efficiency.

翻译：深度材料网络（Deep Material Network, DMN）近期作为一种面向非均质材料的数据驱动代理模型崭露头角。对于特定的微观结构形态，该基于物理的类神经网络架构能够有效逼近其线性和非线性行为。本研究针对具有由多个参数描述的可变微观结构的多尺度材料，提出了一种新型参数化DMN架构。通过物理信息神经网络（Physics-Informed Neural Network, PINN）来刻画DMN拟合参数对微观结构参数的依赖性。在PINN的网络架构及其输出端均施加了微观力学约束。此外，所提出的PINN-DMN架构还被推广至多物理场环境，能够预测除力学属性外的其他物理属性。在对三种参数化微观结构进行的数值模拟中，PINN-DMN在形态变化时展现出令人满意的插值与外推泛化能力。因此，该参数化多尺度材料的有效多物理场行为可通过PINN-DMN实现高精度与高效率的预测与编码。