相关论文: Inverse coefficient problem for cascade system of …
We apply the method of inverse iteration to the Laplace eigenvalue problem with Robin and mixed Dirichlet-Neumann boundary conditions, respectively. For each problem, we prove convergence of the iterates to a non-trivial principal…
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…
Inverse energy cascade regime of two dimensional turbulence is investigated by means of high resolution numerical simulations. Numerical computations of conditional averages of transverse pressure gradient increments are found to be…
Minimax problems are notoriously challenging to optimize. However, we present that the two-timescale extragradient method can be a viable solution. By utilizing dynamical systems theory, we show that it converges to points that satisfy the…
A class of inverse problems for a heat equation with involution perturbation is considered using four different boundary conditions, namely, Dirichlet, Neumann, periodic and anti-periodic boundary conditions. Proved theorems on existence…
This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…
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…
We consider a class of finite element approximations for fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. In our approach, we first solve a variational problem…
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…
In these two lectures we shall discuss how the cavity approach can be used efficiently to study optimization problems with global (topological) constraints and how the same techniques can be generalized to study inverse problems in…
We approximate an elliptic problem with oscillatory coefficients using a problem of the same type, but with constant coefficients. We deliberately take an engineering perspective, where the information on the oscillatory coefficients in the…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
In this paper we consider the " exterior approach " to solve the inverse obstacle problem for the heat equation. This iterated approach is based on a quasi-reversibility method to compute the solution from the Cauchy data while a simple…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…
We analyze in this paper the performance of a newly developed globally convergent numerical method for a coefficient inverse problem for the case of multi-frequency experimental backscatter data associated to a single incident wave. These…
We examine inverse problems for the variable-coefficient nonlocal parabolic operator $(\partial_t - \Delta_g)^s$, where $0 < s < 1$. This article makes two primary contributions. First, we introduce a novel entanglement principle for these…
In this paper we consider the inverse problem of identifying the initial data in a fractionally damped wave equation from time trace measurements on a surface, as relevant in photoacoustic or thermoacoustic tomography. We derive and analyze…
Considering a wave-reaction-diffusion PDE cascade system with wave Neumann control, we first establish controllability properties in a suitable Hilbert space depending on the coupling cascade term. This is done by deriving an observability…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
In this work, we study the inverse problem of determining a potential coefficient in an abstract wave equation that includes a lower-order term. The equation incorporates a time-fractional derivative in the Caputo sense, as well as a…