相关论文: A Carleman Semi-Discrete Convexification Method Co…

A new version of the convexification method is developed analytically and tested numerically for a 1-D coefficient inverse problem in the frequency domain. Unlike the previous version, this one does not use the so-called "tail function",…

To compute the spatially distributed dielectric constant from the backscattering data, we study a coefficient inverse problem for a 1D hyperbolic equation. To solve the inverse problem, we establish a new version of Carleman estimate and…

A version of the convexification numerical method for a Coefficient Inverse Problem for a 1D hyperbolic PDE is presented. The data for this problem are generated by a single measurement event. This method converges globally. The most…

We present in this paper a novel numerical reconstruction method for solving a 3D coefficient inverse problem with scattering data generated by a single direction of the incident plane wave. This inverse problem is well-known to be a highly…

A version of the convexification globally convergent numerical method is constructed for a coefficient inverse problem for a wave-like partial differential equation. The presence of the Carleman Weight Function in the corresponding…

A convexification-based numerical method for a Coefficient Inverse Problem for a parabolic PDE is presented. The key element of this method is the presence of the so-called Carleman Weight Function in the numerical scheme. Convergence…

Motivated by the conspicuous use of momentum-based algorithms in deep learning, we study a nonsmooth nonconvex stochastic heavy ball method and show its convergence. Our approach builds upon semialgebraic (definable) assumptions commonly…

We propose a new numerical method to reconstruct the isotropic electrical conductivity from measured restricted Dirichlet-to-Neumann map data in electrical impedance tomography (EIT) model. "Restricted Dirichlet-to-Neumann (DtN) map data"…

Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require…

We propose a new globally convergent numerical method to solve Hamilton-Jacobi equations in $\mathbb{R}^d$, $d \geq 1$. This method is named as the Carleman convexification method. By Carleman convexification, we mean that we use a Carleman…

Oberman gave a stochastic control formulation of the problem of estimating the convex envelope of a non-convex function. Based on this, we develop a reinforcement learning scheme to approximate the convex envelope, using a variant of…

A version of the so-called "convexification" numerical method for a coefficient inverse scattering problem for the 3D Hemholtz equation is developed analytically and tested numerically. Backscattering data are used, which result from a…

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…

Rather than traditional position control, impedance control is preferred to ensure the safe operation of industrial robots programmed from demonstrations. However, variable stiffness learning studies have focused on task performance rather…

This paper establishes convergence rates for learning elliptic pseudo-differential operators, a fundamental operator class in partial differential equations and mathematical physics. In a wavelet-Galerkin framework, we formulate learning…

This paper investigates an inverse source problem for general semilinear stochastic hyperbolic equations. Motivated by the challenges arising from both randomness and nonlinearity, we develop a globally convergent iterative regularization…

It is shown that the contraction mapping principle with the involvement of a Carleman Weight Function works for a Coefficient Inverse Problem for a 1D hyperbolic equation. Using a Carleman estimate, the global convergence of the…

We propose a scalable method for semi-supervised (transductive) learning from massive network-structured datasets. Our approach to semi-supervised learning is based on representing the underlying hypothesis as a graph signal with small…

This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the…

This work addresses an inverse problem for a semi-discrete parabolic equation, consisting of identifying the right-hand side of the equation from solution measurements at an intermediate time and within a spatial subdomain. We apply this…