A general deep learning framework for history-dependent response prediction based on UA-Seq2Seq model

A general deep learning framework based on the Unrolled Attention Sequence-to-Sequence (UA-Seq2Seq) model is developed to address the history-dependent response prediction problem. First, the particular traits of the history-dependent response prediction problem are analyzed, which motivate the incorporation of the unrolled gated recurrent unit (GRU) structure and the attention mechanism into the classical Seq2Seq model in natural language processing. In the UA-Seq2Seq model, the Seq2Seq skeleton frees the restrictions on both the input and target mechanical variables. Meanwhile, the novel unrolled GRU structure conforms to the general process of mechanical simulation and manages to establish the gated links with the historical states, which is further boosted by the powerful attention mechanism dedicated to retrieving the super-long-term memory information. To quickly and informatively validate the UA-Seq2Seq model, a numerical experiment based on the cyclic stress–strain response of low-yield-point steel is conducted, whose constitutive behavior depends highly on the loading history. All the training and testing configurations in the numerical experiment are specified, including a novel data normalization method – named nonlinear reference-value scaling – tailored for mechanical variables. The results verify the effectiveness of the UA-Seq2Seq model to reproduce the history-dependent hysteresis loops and confirm its capability to capture the long-term memory effect. Furthermore, a parametric analysis is carried out to demonstrate the necessity of the unrolled structure and the attention mechanism as well as the advantage of selecting the L1 loss metric, following which a qualitative mechanical interpretation of the UA-Seq2Seq model is provided to aid in the intuitive comprehension. Finally, three feasible applications and extensions of the developed framework are introduced conceptually: integration with finite element analysis, outline analysis, and transfer learning to other similar tasks. Therefore, the proposed deep learning framework is able to cover a wide range of scenarios concerning the mechanical history-dependent response simulation in practice, which facilitates its universal employment in the academic research and engineering design.