Long short-term memory networks as emulators for finite element models of nonlinear structural dynamic systems: part 1—methodology and description of application examples

Abstract To address the challenge of high computational costs associated with nonlinear time history analysis (NLTHA) of high-fidelity finite element (FE) models in design of structural systems (e.g., Performance-Based Seismic Design (PBSD)) and digital twins, data-driven machine learning (ML) surrogate models have emerged as efficient emulators. In a series of two papers, we present a tutorial and comprehensive study on the use of long short-term memory (LSTM) networks, as fast emulators for nonlinear structural dynamic systems exhibiting varying degrees of material and geometric nonlinearities. This paper, which is Part 1 of the two-part papers, introduces six structural engineering examples, ranging from academic examples to practical real-world applications, aimed at exploring both the potential and limitations of LSTM. Results indicate that while LSTM networks function effectively as surrogate models in controlled academic settings, where simplifications inherent to FE modeling assumptions prevail, they often struggle to capture the complex, nonlinear dynamics characteristic of real-world applications. To this end, this paper proposes LSTM Recursive Averaged Multi-step Sequence-to-Sequence (LSTM-RAMSS) framework to improve LSTM performance as a surrogate model. Three key improvements are made. First, we introduce a novel convolutional autoencoder (CAE)-based framework to effectively select seismic ground-motion records (i.e., input excitations), broadening the diversity and representativeness of earthquake input excitations and improving LSTM training robustness. Second, a dilation strategy is incorporated within the LSTM-RAMSS framework to capture memory across different time scales, enabling capture of nonlinear inelastic dynamic behavior over varying time durations. Finally, the LSTM-RAMSS framework is presented as a hybrid of the LSTM-NARX (Nonlinear AutoRegressive model with eXogenous input) and LSTM-Seq2Seq (Sequence-to-Sequence). The recursive architecture, inspired by the LSTM-NARX, enables the model to incorporate past predictions into future estimates, while the multi-step-ahead predictive capability, derived from the LSTM-Seq2Seq, allows accurate prediction of extended structural responses. By combining these two design principles, RAMSS enhances both the accuracy and the reliability of LSTM-based predictions for structural response time histories. In Part 2 of this two-part series, we demonstrate the efficacy of the proposed methodologies, of this Part 1, applied to FE models across the six structural engineering challenges, spanning basic benchmark “toy problems”, state-of-the-art numerical benchmark scenarios, and models validated through real-world shake table testing.