Related papers: The Inverse Problem for Single Trajectories of Rou…
In this paper we consider a dynamic computer simulator that produces a time-series response $y_t(x)$ over $L$ time points, for every given input parameter $x$. We propose a method for solving inverse problems, which refer to the finding of…
We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…
We study geometric variations of the discriminating code problem. In the \emph{discrete version} of the problem, a finite set of points $P$ and a finite set of objects $S$ are given in $\mathbb{R}^d$. The objective is to choose a subset…
In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some…
In this paper we consider discrete gradient methods for approximating the solution and preserving a first integral (also called a constant of motion) of autonomous ordinary differential equations. We prove under mild conditions for a large…
By combining the formalism of \cite{RHE} with a discrete approach close to the considerations of \cite{Davie}, we interpret and solve the rough partial differential equation $dy_t=A y_t \, dt+\sum_{i=1}^m f_i(y_t) \, dx^i_t$ ($t\in [0,T]$)…
This work investigates the inverse drift problem in the one-dimensional parabolic equation with the final time data. The authors construct an operator first, whose fixed points are the unknown drift, and then apply it to prove the…
Rough paths techniques give the ability to define solutions of stochastic differential equations driven by signals $X$ which are not semimartingales and whose $p$-variation is finite only for large values of $p$. In this context, rough…
We study the inverse problem of determining a finite weighted graph $(X,E)$ from the source-to-solution map on a vertex subset $B\subset X$ for heat equations on graphs, where the time variable can be either discrete or continuous. We prove…
We study an inverse problem on a finite connected graph G = (X, E), on whose vertices a conductivity {\gamma} is defined. Our data consists in a sequence of partial observations of a fractional random walk on G. The observations are partial…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
This paper proposes an optimization-based approach to predict trajectories of autonomous race cars. We assume that the observed trajectory is the result of an optimization problem that trades off path progress against acceleration and jerk…
We present an algorithm for solving inverse problems on graphs analogous to those arising in diffuse optical tomography for continuous media. In particular, we formulate and analyze a discrete version of the inverse Born series, proving…
This paper is concerned with the adaptive numerical treatment of stochastic partial differential equations. Our method of choice is Rothe's method. We use the implicit Euler scheme for the time discretization. Consequently, in each step, an…
In this paper, we study a multidimensional backward stochastic differential equation (BSDE) with an additional rough drift (rough BSDE), and give the existence and uniqueness of the adapted solution, either when the terminal value and the…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
In this paper we investigate the problem of identifying the source term in an elliptic system from a single noisy measurement couple of the Neumann and Dirichlet data. A variational method of Tikhonov-type regularization with specific…
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…
In this paper we characterize sharp time-data tradeoffs for optimization problems used for solving linear inverse problems. We focus on the minimization of a least-squares objective subject to a constraint defined as the sub-level set of a…