171 citations · 200 across the 10 of their papers we have counts for
6 papers · 1 filter
Regularized Reduced Order Lippman-Schwinger-Lanczos Method for Inverse Scattering Problems in the Frequency Domain
Justin Baker, Elena Cherkaev, Vladimir Druskin +2
Inverse scattering has a broad applicability in quantum mechanics, remote sensing, geophysical, and medical imaging. This paper presents a robust direct reduced order model (ROM) m…
Solving inverse scattering problems via reduced-order model embedding procedures
Jörn Zimmerling, Vladimir Druskin, Murthy Guddati +2
We present a reduced-order model (ROM) methodology for inverse scattering problems in which the reduced-order models are data-driven, i.e. they are constructed directly from data g…
A generalized expansion method for computing Laplace-Beltrami eigenfunctions on manifolds
Jackson C. Turner, Elena Cherkaev, Dong Wang
Eigendecomposition of the Laplace-Beltrami operator is instrumental for a variety of applications from physics to data science. We develop a numerical method of computation of the…
A two-stage method for reconstruction of parameters in diffusion equations
Xuesong Bai, Elena Cherkaev, Dong Wang
Parameter reconstruction for diffusion equations has a wide range of applications. In this paper, we proposed a two-stage scheme to efficiently solve conductivity reconstruction pr…
Proximal Implicit ODE Solvers for Accelerating Learning Neural ODEs
Justin Baker, Hedi Xia, Yiwei Wang +7
Learning neural ODEs often requires solving very stiff ODE systems, primarily using explicit adaptive step size ODE solvers. These solvers are computationally expensive, requiring…
Model reduction for fractional elliptic problems using Kato's formula
Huy Dinh, Harbir Antil, Yanlai Chen +2
We propose a novel numerical algorithm utilizing model reduction for computing solutions to stationary partial differential equations involving the spectral fractional Laplacian. O…