A Regression-Based Collaborative Filtering Recommendation Approach to Time-Stepping Multi-Solver Co-Simulation

The ever-increasing application of modeling and simulation to the development of complex engineering systems has made co-simulation indispensable to the handling of coupled multi-domain models. The mechanism for controlling communication between multiple solvers holds the key to co-simulation performance and is regarded as one of the most challenging parts in co-simulation as a lot of tradeoffs need to be made in terms of stability, accuracy, and efficiency. As such, a holistic and dynamic approach is required, which has not been addressed by this paper that has a focus on either tailored problem with a specific numerical analysis scheme or software platforms for implementing data exchange. This paper precisely aims to address this gap by developing a knowledge-based approach to streamlining the co-simulation process. Specifically, a regression-based collaborative filtering approach is developed to recommend suitable ordinary differential equation solvers for individual simulators according to the specific engineering characteristics and historical simulation data. On this basis, the theoretical analysis of the stability region and truncation error is conducted to provide guidance on controlling time stepping of individual simulators using a Jacobi communication scheme. This approach has been evaluated in several computational experiments, in which the advantages of the proposed approach are demonstrated. First, the recommendation algorithm is reliable in making suggestions on viable solvers during simulation run time, especially when only sparse historical datasets are available. Second, the time-stepping scheme noticeably improves the computational efficacy owing to it having no dependence on the initial step-size choice, which is a more eminent advantage for high-fidelity co-simulation problems.