Gappy AE: A nonlinear approach for Gappy data reconstruction using auto-encoder
Year: 2024
Type: article
Abstract: We introduce a novel data reconstruction algorithm known as Gappy auto-encoder (Gappy AE) to address the limitations associated with Gappy proper orthogonal decomposition (Gappy POD), a widely used method for data reconstruction when dealing with sparse measurements or missing data. Gappy POD has inherent constraints in accurately representing solutions characterized by slowly decaying Kolmogorov N-widths, primarily due to its reliance on linear subspaces for data prediction. In contrast, Gappy AE leverages the power of nonlinear manifold representations to address data reconstruction challenges of conventional Gappy POD. It excels at real-time state prediction in scenarios where only sparsely measured data is available, filling in the gaps effectively. This capability makes Gappy AE particularly valuable, such as for digital twin and image correction applications. To demonstrate the superior data reconstruction performance of Gappy AE with sparse measurements, we provide several numerical examples, including scenarios like 2D diffusion, 2D radial advection, and 2D wave equation problems. Additionally, we assess the impact of four distinct sampling algorithms – discrete empirical interpolation method, the S-OPT algorithm, Latin hypercube sampling, and uniformly distributed sampling – on data reconstruction accuracy. Our findings conclusively show that Gappy AE outperforms Gappy POD in data reconstruction when sparse measurements are given.
Authors: Youngkyu Kim, Youngsoo Choi, Byounghyun Yoo
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,660
Funders: U.S. Department of Energy, National Research Foundation, Ministry of Education, Ministry of Trade, Industry and Energy, Korea Institute of Science and Technology, National Research Foundation of Korea, Office of Science, National Nuclear Security Administration, Korea Evaluation Institute of Industrial Technology, Advanced Scientific Computing Research, Lawrence Livermore National Laboratory
OpenAlex ID: W4394676192