Automatically Differentiable Model Updating (ADiMU): conventional, hybrid, and neural network material model discovery including history-dependency

Abstract: We introduce the first Automatically Differentiable Model Updating (ADiMU) framework that finds any history-dependent material model from full-field displacement and global force data (global, indirect discovery) or from strain-stress data (local, direct discovery). We show that ADiMU can update conventional (physics-based), neural network (data-driven), and hybrid material models. Moreover, this framework requires no fine-tuning of hyperparameters or additional quantities beyond those inherent to the user-selected material model architecture and optimizer. The robustness and versatility of ADiMU is extensively exemplified by updating different models spanning tens to millions of parameters, in both local and global discovery settings. Relying on fully differentiable code, the algorithmic implementation leverages vectorizing maps that enable history-dependent automatic differentiation via efficient batched execution of shared computation graphs. This contribution also aims to facilitate the integration, evaluation and application of future material model architectures by openly supporting the research community. Therefore, ADiMU is released as an open-source computational tool, integrated into a carefully designed and documented software named HookeAI.