Certified data-driven physics-informed greedy auto-encoder simulator

• URL: http://arxiv.org/abs/2211.13698v1
• Date: Thu, 24 Nov 2022 16:22:51 GMT
• Title: Certified data-driven physics-informed greedy auto-encoder simulator
• Authors: Xiaolong He, Youngsoo Choi, William D. Fries, Jonathan L. Belof, Jiun-Shyan Chen
• Abstract summary: An auto-encoder and dynamics identification models are trained interactively to discover intrinsic and simple latent-space dynamics. An adaptive greedy sampling algorithm integrated with a physics-informed error indicator is introduced to search for optimal training samples on the fly. Numerical results demonstrate that the proposed method achieves parametric 121 to 2,658x speed-up with 1 to 5% relative errors for radial advection and 2D Burgers dynamical problems.
• Score: 0.5249805590164902
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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