167 citations · 623 across the 43 of their papers we have counts for
6 papers · 1 filter
On Bayesian Consistency for Flows Observed Through a Passive Scalar
Jeff Borggaard, Nathan E. Glatt-Holtz, Justin A. Krometis
We consider the statistical inverse problem of estimating a background fluid flow field from the partial, noisy observations of the concentration of a substance pa…
GPU-Accelerated Particle Methods for Evaluation of Sparse Observations for PDE-Constrained Inverse Problems
Jeff Borggaard, Nathan E. Glatt-Holtz, Justin A. Krometis
We consider the inverse problem of estimating parameters of a driven diffusion (e.g., the underlying fluid flow, diffusion coefficient, or source terms) from point measurements of…
Affine Poisson & Non-Poisson trace principles for
Nico Lombardi, Jie Xiao
This note discovers not only an affine non-sharp-Poisson trace inequality but also its sharp-non-Poisson version for a Sobolev function with the fractional antiderivative.
On the convergence of stationary solutions in the Smoluchowski-Kramers approximation of infinite dimensional systems
Sandra Cerrai, Nathan Glatt-Holtz
We prove the convergence, in the small mass limit, of statistically invariant states for a class of semi-linear damped wave equations, perturbed by an additive Gaussian noise, both…
The Generalized Langevin Equation with a power-law memory in a nonlinear potential well
Nathan Glatt-Holtz, David Herzog, Scott McKinley +1
The generalized Langevin equation (GLE) is a stochastic integro-differential equation that has been used to describe the velocity of microparticles in viscoelastic fluids. In this…
Invariant measures for the stochastic one-dimensional compressible Navier-Stokes equations
Michele Coti Zelati, Nathan Glatt-Holtz, Konstantina Trivisa
We investigate the long-time behavior of solutions to a stochastically forced one-dimensional Navier-Stokes system, describing the motion of a compressible viscous fluid, in the ca…