Machine Learning–Assisted Multi-Time-Step Method for Structural Dynamics

Abstract Multi-time-step (MTS) methods enable fast, stable, and accurate simulations of multi-scale problems in structural dynamics. This is achieved by decomposing a large computer model into several subdomains and using a small time step in subdomains with high temporal gradients while integrating other subdomains with a large time step to save computational cost. Thus, compared to conventional uniform time-stepping (UTS) schemes that use a small time step for the entire problem domain, MTS methods are significantly faster. Despite the computational efficiency of existing MTS methods, they still require a three-step process: solve the subdomains independently, compute the Lagrange multipliers needed for enforcing continuity of the solution across the interface between subdomains, and finally couple all the subdomains together by updating their solutions to satisfy the continuity constraints. The key to obtaining accurate solutions with MTS methods is to compute the Lagrange multipliers accurately, which necessitates the time-consuming three-step process. To eliminate this three-step process a machine learning approach is used to obtain the Lagrange multipliers needed for coupling the various subdomains at each time step. Data collected from solutions generated using conventional MTS methods are used to train a long short-term memory (LSTM) network that predicts these Lagrange multipliers. Output from the LSTM network, along with other state information, is then used to solve all the subdomains in a single (one-step) process. The resulting algorithm is called the machine learning–assisted MTS (ML-MTS) method and it advances the global solution in a single pass while maintaining continuity of the solution across the subdomain interfaces. Two numerical examples are presented to compare the performance of the proposed ML-MTS approach to existing MTS methods in terms of accuracy and computational cost. Results show that the proposed ML-MTS method achieves additional speedup on top of the computational gains of existing MTS methods while maintaining the accuracy of the solution.