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This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in $\mathbb{R}^n$,…
Heat losses through the building envelope is one of the key factors in the calculation of the building energy balance. If steady-state heat conduction is observed, which is commonly used to assess the heat losses in building, there is an…
We study here the approximation by a finite-volume scheme of a heat equation forced by a Lipschitz continuous multiplicative noise in the sense of It\^o. More precisely, we consider a discretization which is semi-implicit in time and a…
Accurate reconstruction of ocean is essential for reflecting global climate dynamics and supporting marine meteorological research. Conventional methods face challenges due to sparse data, algorithmic complexity, and high computational…
Before reflow soldering of integrated electronic products, the numerical simulation of temperature control curve of reflow furnace is crucial for selecting proper parameters and improving the overall efficiency of reflow soldering process…
We prove sharp pointwise heat kernel estimates for symmetric Markov processes associated with symmetric Dirichlet forms that are local with respect to some coordinates and nonlocal with respect to the remaining coordinates. The main theorem…
In this work we analyze a convex-programming method for estimating superpositions of point sources or spikes from nonuniform samples of their convolution with a known kernel. We consider a one-dimensional model where the kernel is either a…
In this paper, we present a unified approach to function approximation in reproducing kernel Hilbert spaces (RKHS) that establishes a previously unrecognized optimality property for several well-known function approximation techniques, such…
In this work we consider the problem of finding optimal regularization parameters for general-form Tikhonov regularization using training data. We formulate the general-form Tikhonov solution as a spectral filtered solution using the…
We propose an approach to 3D reconstruction via inverse procedural modeling and investigate two variants of this approach. The first option consists in the fitting set of input parameters using a genetic algorithm. We demonstrate the…
Simple data correlation of flashpoint data of binary mixture has been developed on a basic of rational reciprocal function. The new approximation requires has only two coefficients and needs the flashpoint temperature of the pure flammable…
This paper is devoted to the inverse problem of recovering the unknown distributed flux on an inaccessible part of boundary using measurement data on the accessible part. We establish and verify a variational source condition for this…
We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in an exterior region in $\mathbb{R}^d,$ $d\geq 2$. In this region, we consider a hyperplane $X$ with sufficiently…
Learning convolution kernels in operators from data arises in numerous applications and represents an ill-posed inverse problem of broad interest. With scant prior information, kernel methods offer a natural nonparametric approach with…
We study an inverse problem for Light Sheet Fluorescence Microscopy (LSFM), where the density of fluorescent molecules needs to be reconstructed. Our first step is to present a mathematical model to describe the measurements obtained by an…
We introduce renormalized integrals which generalize conventional measure theoretic integrals. One approximates the integration domain by measure spaces and defines the integral as the limit of integrals over the approximating spaces. This…
We present a probabilistic model for point cloud generation, which is fundamental for various 3D vision tasks such as shape completion, upsampling, synthesis and data augmentation. Inspired by the diffusion process in non-equilibrium…
Enforcing alignment between the internal representations of diffusion or flow-based generative models and those of pretrained self-supervised encoders has recently been shown to provide a powerful inductive bias, improving both convergence…
It is common to have to process signals or images whose values are cyclic and can be represented as points on the complex circle, like wrapped phases, angles, orientations, or color hues. We consider a Tikhonov-type regularization model to…
We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…