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The accurate reconstruction of dynamic street scenes is critical for applications in autonomous driving, augmented reality, and virtual reality. Traditional methods relying on dense point clouds and triangular meshes struggle with moving…
This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a…
Starting from first principles, we derive the fundamental equations that relate the $n$-point correlation functions in real and redshift space. Our result generalises the so-called `streaming model' to higher-order statistics: the full…
We address the problem of data augmentation in a rotating turbulence set-up, a paradigmatic challenge in geophysical applications. The goal is to reconstruct information in two-dimensional (2D) cuts of the three-dimensional flow fields,…
We study a one-dimensional gas of $N$ Brownian particles that diffuse independently, but are {\it simultaneously} reset to the origin at a constant rate $r$. The system approaches a non-equilibrium stationary state (NESS) with long-range…
In this work, an inverse problem in the fractional diffusion equation with random source is considered. The measurements used are the statistical moments of the realizations of single point data $u(x_0,t,\omega).$ We build the…
This work presents a mathematical model to enable rapid prediction of airborne contaminant transport based on scarce sensor measurements. The method is designed for applications in critical infrastructure protection (CIP), such as…
In this work, we study an inverse problem of recovering a space-time dependent diffusion coefficient in the subdiffusion model from the distributed observation, where the mathematical model involves a Djrbashian-Caputo fractional derivative…
Reconstruction of geometry based on different input modes, such as images or point clouds, has been instrumental in the development of computer aided design and computer graphics. Optimal implementations of these applications have…
This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…
Reconstruction of an object from points cloud is essential in prosthetics, medical imaging, computer vision, etc. We present an effective algorithm for an Allen--Cahn-type model of reconstruction, employing the Lagrange multiplier approach.…
In this paper, we describe a novel application of sigma-point methods to continuous-discrete filtering. In principle, the nonlinear continuous- discrete filtering problem can be solved exactly. In practice, the solution contains terms that…
Despite diffusion models' superior capabilities in modeling complex distributions, there are still non-trivial distributional discrepancies between generated and ground-truth images, which has resulted in several notable problems in image…
A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…
We solve a model of sluggish stochastic motion in which a Brownian particle diffuses with a diffusion coefficient that decays algebraically with the distance to the origin, as $|x|^{-\alpha}$. Additionally, the particle resets with a…
We propose a numerical algorithm for solving the atmospheric dispersion problem with elevated point sources and ground-level deposition. The problem is modelled by the 3D advection-diffusion equation with delta-distribution source terms, as…
Learning dynamical systems from sparse observations is critical in numerous fields, including biology, finance, and physics. Even if tackling such problems is standard in general information fusion, it remains challenging for contemporary…
For the first time, we develop in this paper the globally convergent convexification numerical method for a Coefficient Inverse Problem for the 3D Helmholtz equation for the case when the backscattering data are generated by a point source…
Reconstructing a 3D point cloud from a given conditional sketch is challenging. Existing methods often work directly in 3D space, but domain variability and difficulty in reconstructing accurate 3D structures from 2D sketches remain…
Dealing with the inverse source problem for the scalar wave equation, we have shown recently that we can reconstruct the space-time dependent source function from the measurement of the wave, collected at a single point $x$ for a large…