Related papers: An Iterative Direct Sampling Method for Reconstruc…
Problems with localized nonhomogeneous material properties arise frequently in many applications and are a well-known source of difficulty in numerical simulations. In certain applications (including additive manufacturing), the physics of…
The paper is concerned with locally stabilized space-time IgA approximations to initial boundary value problems of the parabolic type. Originally, similar schemes (but weighted with a global mesh parameter) was presented and studied by U.…
We develop an efficient and convergent numerical method for solving the inverse problem of determining the potential of nonlinear hyperbolic equations from lateral Cauchy data. In our numerical method we construct a sequence of linear…
We consider an inverse boundary value problem for a model time-harmonic equation of acoustic tomography of moving fluid with variable current velocity, sound speed, density and absorption. In the present article it is assumed that at fixed…
We study homogenization for fully nonlinear uniformly parabolic equations in stationary ergodic spatio-temporal media from the qualitative and quantitative perspective. We show that under suitable hypotheses, solutions to fully nonlinear…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
This paper is concerned with the inverse acoustic scattering problems of reconstructing time-dependent multiple point sources and sources on a curve $L$ of the form $\lambda(t)\tau(x)\delta_L(x)$. A direct sampling method with a novel…
We present a new method to obtain spatio-temporal information from aggregated data of stationary traffic detectors, the ``adaptive smoothing method''. In essential, a nonlinear spatio-temporal lowpass filter is applied to the input detector…
This paper discusses the adaptive sampling problem in a nonholonomic mobile robotic sensor network for efficiently monitoring a spatial field. It is proposed to employ Gaussian process to model a spatial phenomenon and predict it at…
This work is concerned with the iterative regularization of a non-smooth nonlinear ill-posed problem where the forward mapping is merely directionally but not G\^ateaux differentiable. Using a Bouligand subderivative of the forward mapping,…
We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the…
The paper considers the problem to estimate non-causal graphical models whose edges encode smoothing relations among the variables. We propose a new covariance extension problem and show that the solution minimizing the transportation…
We present a deep, bidirectional, recurrent framework for cleaning noisy and incomplete motion capture data. It exploits temporal coherence and joint correlations to infer adaptive filters for each joint in each frame. A single model can be…
We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…
We present a novel method for image anomaly detection, where algorithms that use samples drawn from some distribution of "normal" data, aim to detect out-of-distribution (abnormal) samples. Our approach includes a combination of encoder and…
Novel experimental modalities acquire spatially resolved velocity measurements for steady state and transient flows which are of interest for engineering and biological applications. One of the drawbacks of such high resolution velocity…
This paper is concerned with the problem of inverse scattering of time-harmonic acoustic plane waves by a two-layered medium with a locally rough interface in 2D. A direct imaging method is proposed to reconstruct the locally rough…
This paper is concerned with adaptive mesh refinement strategies for the spatial discretization of parabolic problems with dynamic boundary conditions. This includes the characterization of inf-sup stable discretization schemes for a…
We present a space-time multiscale method for a parabolic model problem with an underlying coefficient that may be highly oscillatory with respect to both the spatial and the temporal variables. The method is based on the framework of the…
A common problem in physics is to fit regression data by a parametric class of functions, and to decide whether a certain functional form allows for a good fit of the data. Common goodness of fit methods are based on the calculation of the…