Related papers: On Weak Observability For Evolution Systems with S…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
We show that for linear dynamical systems with skew-adjoint generators, the initial state estimate given by the back and forth nudging method with colocated feedback, converges to the minimizer of the discrepancy between the measured and…
We study formally determined inverse problems with passive measurements for one dimensional evolution equations where the goal is to simultaneously determine both the initial data as well as the variable coefficients in such an equation…
Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
We study generalized solutions of an evolutionary equation related to a densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and find…
We review some results on the logarithmic convexity for evolution equations, a well-known method in inverse and ill-posed problems. We start with the classical case of self-adjoint operators. Then, we analyze the case of analytic…
We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution. Physical examples and applications in stochastic…
The present article delves into the investigation of observability inequalities pertaining to backward stochastic evolution equations. We employ a combination of spectral inequalities, interpolation inequalities, and the telegraph series…
The paper contributes to strengthening the relation between machine learning and the theory of differential equations. In this context, the inverse problem of fitting the parameters, and the initial condition of a differential equation to…
First-order optimization algorithms, often preferred for large problems, require the gradient of the differentiable terms in the objective function. These gradients often involve linear operators and their adjoints, which must be applied…
Procedures to recover explicitly discrete and continuous skew-selfadjoint Dirac systems on semi-axis from rational Weyl matrix functions are considered. Their stability is shown. Some new facts on asymptotics of pseudo-exponential…
The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary…
We discuss the possibility to learn a data-driven explicit model correction for inverse problems and whether such a model correction can be used within a variational framework to obtain regularised reconstructions. This paper discusses the…
Inverse problems consist in reconstructing signals from incomplete sets of measurements and their performance is highly dependent on the quality of the prior knowledge encoded via regularization. While traditional approaches focus on…
We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set, which is characterized by a constraint on the absolute value of the gradient that depends…
In this paper, we consider first-order convergence theory and algorithms for solving a class of non-convex non-concave min-max saddle-point problems, whose objective function is weakly convex in the variables of minimization and weakly…
This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin…
We consider the observability problem for non-autonomous evolution systems (i.e., the operators governing the system depend on time). We introduce an averaged Hautus condition and prove that for skew-adjoint operators it characterizes exact…
Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems…