24 citations · 77 across the 14 of their papers we have counts for
18 papers
Identifying the body force from partial observations of a 2D incompressible velocity field
Aseel Farhat, Adam Larios, Vincent R. Martinez +1
Using limited observations of the velocity field of the two-dimensional Navier-Stokes equations, we successfully reconstruct the steady body force that drives the flow. The number…
The short memory limit for long time statistics in a stochastic Coleman-Gurtin model of heat conduction
Nathan E. Glatt-Holtz, Vincent R. Martinez, Hung D. Nguyen
We consider a class of semi-linear differential Volterra equations with polynomial-type potentials that incorporates the effects of memory while being subjected to random perturbat…
On the reconstruction of unknown driving forces from low-mode observations in the 2D Navier-Stokes Equations
Vincent R. Martinez
This article is concerned with the problem of determining an unknown source of non-potential, external time-dependent perturbations of an incompressible fluid from large-scale obse…
Convergence Analysis of a Viscosity Parameter Recovery Algorithm for the 2D Navier-Stokes Equations
Vincent R. Martinez
In this paper, the convergence of an algorithm for recovering the unknown kinematic viscosity of a two-dimensional incompressible, viscous fluid is studied. The algorithm of intere…
Dynamically learning the parameters of a chaotic system using partial observations
Elizabeth Carlson, Joshua Hudson, Adam Larios +3
Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assum…
Mesh-Free Interpolant Observables for Continuous Data Assimilation
Animikh Biswas, Kenneth R. Brown, Vincent R. Martinez
This paper considers a nudging-based scheme for data assimilation for the two-dimensional (2D) Navier-Stokes equations (NSE) with periodic boundary conditions and studies the synch…