171 citations · 200 across the 10 of their papers we have counts for
13 papers
A hybrid CNN-adjoint optimization framework for reconstruction of viscoelastic tissue properties in magnetic resonance elastography
Anwesa Dey, Johann Rudi, Elena Cherkaev
Magnetic resonance elastography (MRE) is a noninvasive imaging modality for quantifying the viscoelastic properties of soft tissues from shear wave propagation. Recovering the comp…
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…
Two-scale cut-and-projection convergence for quasiperiodic monotone operators
Niklas Wellander, Sebastien Guenneau, Elena Cherkaev
Averaging certain class of quasiperiodic monotone operators can be simplified to the periodic homogenization setting by mapping the original quasiperiodic structure onto a periodic…
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…
Learning POD of Complex Dynamics Using Heavy-ball Neural ODEs
Justin Baker, Elena Cherkaev, Akil Narayan +1
Proper orthogonal decomposition (POD) allows reduced-order modeling of complex dynamical systems at a substantial level, while maintaining a high degree of accuracy in modeling the…
Wave-driven assembly of quasi periodic patterns of particles
Elena Cherkaev, Fernando Guevara Vasquez, China Mauck +2
We theoretically show that a superposition of plane waves causes small (compared to the wavelength) particles dispersed in a fluid to assemble in quasiperiodic two or three dimensi…
Geometric series expansion of the Neumann-Poincaré operator: application to composite materials
Elena Cherkaev, Minwoo Kim, Mikyoung Lim
The Neumann-Poincaré operator, a singular integral operator on the boundary of a domain, naturally appears when one solves a conductivity transmission problem via the boundary inte…
Homogenization of quasiperiodic structures and two-scale cut-and-projection convergence
Niklas Wellander, Sébastien Guenneau, Elena Cherkaev
Quasiperiodic arrangements of the constitutive materials in composites result in effective properties with very unusual electromagnetic and elastic properties. The paper discusses…
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…
An Isoperimetric inequality for an integral operator on flat tori
Braxton Osting, Jeremy L. Marzuola, Elena Cherkaev
We consider a class of Hilbert-Schmidt integral operators with an isotropic, stationary kernel acting on square integrable functions defined on flat tori. For any fixed kernel whic…