Related papers: On inverse problems in multi-population aggregatio…

Recovering signals from low-order moments is a fundamental yet notoriously difficult task in inverse problems. This recovery process often reduces to solving ill-conditioned systems of polynomial equations. In this work, we propose a new…

Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear…

Recovering high-dimensional signals from corrupted measurements is a central challenge in inverse problems. Recent advances in generative diffusion models have shown remarkable empirical success in providing strong data-driven priors, but…

This paper is concerned with reconstructing an acoustic obstacle and its excitation sources from the phaseless near-field measurements. By supplementing some artificial sources to the inverse scattering system, this co-inversion problem can…

We propose a novel method for sampling and optimization tasks based on a stochastic interacting particle system. We explain how this method can be used for the following two goals: (i) generating approximate samples from a given target…

In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear interaction functions and time-fractional orders. In these coupled…

The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of…

This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…

The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…

A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally…

In this paper, we revisit the computation of controlled invariant sets for linear discrete-time systems through a trajectory-based viewpoint. We begin by introducing the notion of convex feasible points, which provides a new…

This article reviews recent inverse statistical-mechanical methodologies that we have devised to optimize interaction potentials in soft matter systems that correspond to stable "target" structures. We are interested in finding the…

The inverse problem method is tested for a class of monomer-dimer statistical mechanics models that contain also an attractive potential and display a mean-field critical point at a boundary of a coexistence line. The inversion is obtained…

Bayesian approaches are one of the primary methodologies to tackle an inverse problem in high dimensions. Such an inverse problem arises in hydrology to infer the permeability field given flow data in a porous media. It is common practice…

Using recent advances in generative artificial intelligence (AI) brought by diffusion models, this paper introduces a new synergistic method for spectral computed tomography (CT) reconstruction. Diffusion models define a neural network to…

Crowd dynamics and many large biological systems can be described as populations of agents or particles, which can only be observed on aggregate population level. Identifying the dynamics of agents is crucial for understanding these large…

A new method is presented to reconstruct the potential of a quantum mechanical many-body system from observational data, combining a nonparametric Bayesian approach with a Hartree-Fock approximation. A priori information is implemented as a…

This paper proposes new estimators for the propensity score that aim to maximize the covariate distribution balance among different treatment groups. Heuristically, our proposed procedure attempts to estimate a propensity score model by…

Collaboration between different data centers is often challenged by heterogeneity across sites. To account for the heterogeneity, the state-of-the-art method is to re-weight the covariate distributions in each site to match the distribution…

We study the problem of asymptotic consensus as it occurs in a wide range of applications in both man-made and natural systems. In particular, we study systems with directed communication graphs that may change over time. We recently…