171 citations · 200 across the 10 of their papers we have counts for
5 papers · 1 filter
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…