Related papers: On Weak Observability For Evolution Systems with S…

We present a framework which enables the analysis of dynamic inverse problems for wave phenomena that are modeled through second-order hyperbolic PDEs. This includes well-posedness and regularity results for the forward operator in an…

Adjoint-based data assimilation for turbulent Navier-Stokes flows is fundamentally limited by the behavior of the adjoint dynamics: in backward time, adjoint fields exhibit exponential growth and become increasingly dominated by small-scale…

In this paper we study the question of how to reconstruct the state of a power system using Phasor Measurement Units (PMUs). In our previous research we proved that this question has an affirmative answer imposing some rather strict…

We investigate learning the eigenfunctions of evolution operators for time-reversal invariant stochastic processes, a prime example being the Langevin equation used in molecular dynamics. Many physical or chemical processes described by…

In this paper, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that contraction is a concept naturally suitable…

In our paper [SIAM J.\ Appl.~Math.\ 79-6 (2019), https://doi.org/10.1137/19M1269403] we considered full waveform inversion (FWI) in the viscoelastic regime. FWI entails the nonlinear inverse problem of recovering parameter functions of the…

We investigate the increasing stability of the inverse Schr\"{o}dinger potential problem with integer power type nonlinearities at a large wavenumber. By considering the first order linearized system with respect to the unknown potential…

The contraction semigroup $S(t)={\rm e}^{t\mathbb{A}}$ generated by the abstract linear dissipative evolution equation $$ \ddot u + A u + f(A) \dot u=0 $$ is analyzed, where $A$ is a strictly positive selfadjoint operator and $f$ is an…

In this work, we study the inverse spectral problem, using the Weyl matrix as the input data, for the matrix Schrodinger operator on the half-line with the boundary condition being the form of the most general self-adjoint. We prove the…

Weak consistency and asymptotic normality of the ordinary least-squares estimator in a linear regression with adaptive learning is derived when the crucial, so-called, `gain' parameter is estimated in a first step by nonlinear least squares…

In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…

The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by deep generative networks). In this work, we study the…

In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave…

This work addresses the problem of designing an equivariant observer for a first order dynamical system on the unit-sphere. Building upon the established case of unit bearing vector dynamics with angular velocity inputs, we introduce an…

Neural networks allow solving many ill-posed inverse problems with unprecedented performance. Physics informed approaches already progressively replace carefully hand-crafted reconstruction algorithms in real applications. However, these…

We consider a neural network architecture designed to solve inverse problems where the degradation operator is linear and known. This architecture is constructed by unrolling a forward-backward algorithm derived from the minimization of an…

Inverse problem to recover the skew-self-adjoint Dirac-type system from the generalized Weyl matrix function is treated in the paper. Sufficient conditions under which the unique solution of the inverse problem exists, are formulated in…

Misalignment angle will result in a considerable error for the integration of Doppler Velocity Log (DVL) and of Strapdown Inertial Navigation System (SINS). In this paper, a robust initial alignment method for SINS/DVL is proposed to solve…

Solving inverse problems requires the knowledge of the forward operator, but accurate models can be computationally expensive and hence cheaper variants that do not compromise the reconstruction quality are desired. This chapter reviews…

Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge…