Deep material network via a quilting strategy: visualization for explainability and recursive training for improved accuracy

Recent developments integrating micromechanics and neural networks offer promising paths for rapid predictions of the response of heterogeneous materials with similar accuracy as direct numerical simulations. The deep material network is one such approaches, featuring a multi-layer network and micromechanics building blocks trained on anisotropic linear elastic properties. Once trained, the network acts as a reduced-order model, which can extrapolate the material's behavior to more general constitutive laws, including nonlinear behaviors, without the need to be retrained. However, current training methods initialize network parameters randomly, incurring inevitable training and calibration errors. Here, we introduce a way to visualize the network parameters as an analogous unit cell and use this visualization to quilt patches of shallower networks to initialize deeper networks for a recursive training strategy. The result is an improvement in the accuracy and calibration performance of the network and an intuitive visual representation of the network for better explainability.

Automated summary

Recent developments in micromechanics and neural networks have provided promising paths for accurately predicting the response of heterogeneous materials. The deep material network, with its multi-layer design and trained micromechanics building blocks, offers the ability to extrapolate material behavior to different constitutive laws without retraining. However, the random initialization of network parameters in current training methods leads to unavoidable errors. In this study, we propose a visualization technique using an analogous unit cell to initialize deeper networks and improve the accuracy and calibration performance, while also providing a more intuitive representation of the network for explainability.