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

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…

Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…

A fundamental problem of statistical data analysis, distribution density estimation by experimental data, is considered. A new method with optimal asymptotic behavior, the root density estimator, is developed. The method proposed may be…

Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems,…

Diffusion models have become increasingly popular for generative modeling due to their ability to generate high-quality samples. This has unlocked exciting new possibilities for solving inverse problems, especially in image restoration and…

The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…

In this work, we investigate an inverse problem of recovering multiple orders in a time-fractional diffusion model from the data observed at one single point on the boundary. We prove the unique recovery of the orders together with their…

Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…

Ill-posed inverse problems are fundamental in many domains, ranging from astrophysics to medical imaging. Emerging diffusion models provide a powerful prior for solving these problems. Existing maximum-a-posteriori (MAP) or posterior…

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…

Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic…

This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a…

The aim of this paper is to provide a resampling technique that allows us to make inference on superpopulation parameters in finite population setting. Under complex sampling designs, it is often difficult to obtain explicit results about…

Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse…

This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…

Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem that arises across fields such as mechanical engineering to aerospace engineering. Inverse design is…

The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…

We introduce a nonlinear operator to model diffusion on a complex undirected network under crowded conditions. We show that the asymptotic distribution of diffusing agents is a nonlinear function of the nodes' degree and saturates to a…