Related papers: Iterative Direct Sampling Method for Elliptic Inve…
We introduce and analyze a fast iterative method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. The key idea, in contrast to the standard Landweber method, is to use multiple search directions per…
In this paper, we consider the direct and inverse problem for isotropic scatterers with two conductive boundary conditions. First, we show the uniqueness for recovering the coefficients from the known far-field data at a fixed incident…
Steerable networks, which process data with intrinsic symmetries, often use Fourier-based nonlinearities that require sampling from the entire group, leading to a need for discretization in continuous groups. As the number of samples…
Consider the problem of inverse scattering of time-harmonic point sources from an infinite, penetrable rough interface with bounded obstacles buried in the lower half-space, where the interface is assumed to be a local perturbation of a…
A problem of a wave identification is formulated. An example is considered in conditions of one-dimensional Cauchy problem for conventional string equation in matrix form and its inhomogeneous two-component version. The acoustic and…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
We introduce an extension of Dual Dynamic Programming (DDP) to solve convex nonlinear dynamic programming equations. We call Inexact DDP (IDDP) this extension which applies to situations where some or all primal and dual subproblems to be…
Sparse signal recovery problems from noisy linear measurements appear in many areas of wireless communications. In recent years, deep learning (DL) based approaches have attracted interests of researchers to solve the sparse linear inverse…
We consider an inverse boundary value problem for the doubly nonlinear parabolic equation \[ \epsilon(x)\partial_t u^m-\nabla\cdot\bigl(\gamma(x)|\nabla u|^{p-2}\nabla u\bigr)=0 \quad\text{in }(0,T)\times\Omega, \] where…
In this work, we develop an efficient solver based on neural networks for second-order elliptic equations with variable coefficients and singular sources. This class of problems covers general point sources, line sources and the combination…
We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct…
Sampling from flat modes in discrete spaces is a crucial yet underexplored problem. Flat modes represent robust solutions and have broad applications in combinatorial optimization and discrete generative modeling. However, existing sampling…
This study is devoted to proving the existence of weak solutions for a nonlinear elliptic problem with Neumann-type boundary data. The problem is driven by a discontinuous power nonlinearity and a nonsmooth prescribed data. Additionally, we…
We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…
In this paper we use a natural iteration technique to prove existence of solutions to nonlinear Dirichlet problems. Among the examples included is the prescribed mean curvature equation. The nature of the technique allows applications to…
This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effective sampling schemes for location acquisition of the sources…
In this paper, we consider a class of continuous-time, continuous-space stochastic optimal control problems. Building upon recent advances in Markov chain approximation methods and sampling-based algorithms for deterministic path planning,…
Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information…
A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured…
Sampling-based model predictive control (MPC) is effective for nonlinear systems but often produces non-smooth control inputs due to random sampling. To address this issue, we extend the model predictive path integral (MPPI) framework with…