Related papers: Spectral Filtering of Interpolant Observables for …
This work introduces a novel approach for data-driven model reduction of time-dependent parametric partial differential equations. Using a multi-step procedure consisting of proper orthogonal decomposition, dynamic mode decomposition and…
In Data Assimilation, observations are fused with simulations to obtain an accurate estimate of the state and parameters for a given physical system. Combining data with a model, however, while accurately estimating uncertainty, is…
This paper addresses the problem of tracking in-plane waves from image sequences using periodic surface patterns. Wave-induced deformation is modeled as a spatial phase modulation of a periodic carrier. We propose ADOPT (Analytical…
With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
Spectral deferred corrections (SDC) is an iterative approach for constructing higher- order accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of…
In the past years, video communication has found its application in an increasing number of environments. Unfortunately, some of them are error-prone and the risk of block losses caused by transmission errors is ubiquitous. To reduce the…
In this paper we present a fourth-order in space and time block-structured adaptive mesh refinement algorithm for the compressible multicomponent reacting Navier-Stokes equations. The algorithm uses a finite volume approach that…
A warping operator consists of an invertible axis deformation applied either in the signal domain or in the corresponding Fourier domain. Additionally, a warping transformation is usually required to preserve the signal energy, thus…
First-order convergence in time and space is proved for a fully discrete semi-implicit finite element method for the two-dimensional Navier--Stokes equations with $L^2$ initial data in convex polygonal domains, without extra regularity…
We derive optimal filters on the sphere in the context of detecting compact objects embedded in a stochastic background process. The matched filter and the scale adaptive filter are derived on the sphere in the most general setting,…
As climate change intensifies, the shift to cleaner energy sources becomes increasingly urgent. With wind energy production set to accelerate, reliable wind probabilistic forecasts are essential to ensure its efficient use. However, since…
Complex nonlinear turbulent dynamical systems are ubiquitous in many areas. Recovering unobserved state variables is an important topic for the data assimilation of turbulent systems. In this article, an efficient continuous in time data…
Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution…
Network filtering is an important form of dimension reduction to isolate the core constituents of large and interconnected complex systems. We introduce a new technique to filter large dimensional networks arising out of dynamical behavior…
We apply a continuous data assimilation method to the Navier-Stokes-Fourier system governing the evolution of a compressible, rotating and thermally driven fluid. A rigorous proof of the tracking property is given in the asymptotic regime…
Accurate and efficient global ocean state estimation remains a grand challenge for Earth system science, hindered by the dual bottlenecks of computational scalability and degraded data fidelity in traditional data assimilation (DA) and deep…
The large underlying assumption of climate models today relies on the basis of a "confident" initial condition, a reasonably plausible snapshot of the Earth for which all future predictions depend on. However, given the inherently chaotic…
Performing highly accurate simulations of droplet systems is a challenging problem. This is primarily due to the interface dynamics which is complicated further by the addition of surfactants. This paper presents a boundary integral method…
Data assimilation, in its most comprehensive form, addresses the Bayesian inverse problem of identifying plausible state trajectories that explain noisy or incomplete observations of stochastic dynamical systems. Various approaches have…