2022/11/24 by Xiaolong He, He, Xiaolong, Youngsoo Choi +7 · 1 citation
Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Lattice Boltzmann Simulation Studies #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2211.13698
openalex publication_date 2022/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A parametric adaptive greedy Latent Space Dynamics Identification (gLaSDI) framework is developed for accurate, efficient, and certified data-driven physics-informed greedy auto-encoder simulators of high-dimensional nonlinear dynamical systems. In the proposed framework, an auto-encoder and dynamics identification models are trained interactively to discover intrinsic and simple latent-space dynamics. To effectively explore the parameter space for optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed error indicator is introduced to search for optimal training samples on the fly, outperforming the conventional predefined uniform sampling. Further, an efficient k-nearest neighbor convex interpolation scheme is employed to exploit local latent-space dynamics for improved predictability. Numerical results demonstrate that the proposed method achieves 121 to 2,658x speed-up with 1 to 5% relative errors for radial advection and 2D Burgers dynamical problems.