Related papers: Inverse problem for the mean-field monomer-dimer m…
A system of two coupled nonlinear parabolic partial differential equations with two opposite directions of time is considered. In fact, this is the so-called "Mean Field Games System" (MFGS), which is derived in the mean field games (MFG)…
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…
When dealing with difficult inverse problems such as inverse rendering, using Monte Carlo estimated gradients to optimise parameters can slow down convergence due to variance. Averaging many gradient samples in each iteration reduces this…
The inverse problem of amplitude reconstruction on an inclined line based on the values of amplitude or its module as recorded on semi-infinite line orthogonal to the beam propagation direction is considered within the framework of 2D…
In this paper we consider the possibility of application of the quantum inverse scattering method for studying the superconformal field theory and it's integrable perturbations. The classical limit of the considered constructions is based…
In numerous practical applications, especially in medical image reconstruction, it is often infeasible to obtain a large ensemble of ground-truth/measurement pairs for supervised learning. Therefore, it is imperative to develop unsupervised…
Matrix inversion problems are often encountered in experimental physics, and in particular in high-energy particle physics, under the name of unfolding. The true spectrum of a physical quantity is deformed by the presence of a detector,…
Recovering microscopic couplings directly from data provides a route to solving the inverse problem in statistical field theories, one that complements the traditional-often computationally intractable-forward approach of predicting…
We introduce a novel reformulation of the mean-field system for pulse-coupled oscillators. It is based on writing a closed equation for the inverse distribution function associated to the probability density of oscillators with a given…
We establish the theoretical framework for implementing the maximumn entropy on the mean (MEM) method for linear inverse problems in the setting of approximate (data-driven) priors. We prove a.s. convergence for empirical means and further…
This paper is concerned with the inverse problem to recover a compactly supported Schr{\"o}dinger potential given the differential scattering cross section, i.e. the modulus, but not the phase of the scattering amplitude. To compensate for…
A pre-trained unconditional diffusion model, combined with posterior sampling or maximum a posteriori (MAP) estimation techniques, can solve arbitrary inverse problems without task-specific training or fine-tuning. However, existing…
One of the main computational drawbacks in the application of 3-D iterative inversion techniques is the requirement of solving the field quantities for the updated contrast in every iteration. In this paper, the 3-D electromagnetic inverse…
Generative models are powerful tools for sampling from a learned distribution $\mathcal{P}(Y \mid X)$, and inverse-design methods invert this map to find an input $x$ that produces a desired point output $y^*$. However, many design goals…
We consider a model for a polymer interacting with an attractive wall through a random sequence of charges. We focus on the so-called diluted limit, when the charges are very rare but have strong intensity. In this regime, we determine the…
This book deals with functions allowing to express the dissimilarity (discrepancy) between two data fields or ''divergence functions'' with the aim of applications to linear inverse problems. Most of the divergences found in the litterature…
In this paper, we tackle a critical issue in nonparametric inference for systems of interacting particles on Riemannian manifolds: the identifiability of the interaction functions. Specifically, we define the function spaces on which the…
The general solution of the inverse Frobenius-Perron problem considering the construction of a fully chaotic dynamical system with given invariant density is obtained within the class of one-dimensional unimodal maps. Some interesting…
The use of Mean-Field theory to unwrap principal phase patterns has been recently proposed. In this paper we generalize the Mean-Field approach to process phase patterns with arbitrary degree of undersampling. The phase unwrapping problem…
This paper is devoted to multi-dimensional inverse problems. In this setting, we address a goodness-of-fit testing problem. We investigate the separation rates associated to different kinds of smoothness assumptions and different degrees of…