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Solving inverse partial differential equation (PDE) problems is a fundamental topic in scientific research due to its broad significance across a wide range of real-world applications. Inverse PDE problems arise across medical imaging,…
Accurate hyperspectral image (HSI) interpretation is critical for providing valuable insights into various earth observation-related applications such as urban planning, precision agriculture, and environmental monitoring. However, existing…
In geophysics, inverse modelling can be applied to a wide range of goals, including, for instance, mapping the distribution of rock physical parameters in applied geophysics and calibrating models to forecast the behaviour of natural…
The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…
Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are…
This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…
This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been…
Current deep learning-based solutions for image analysis tasks are commonly incapable of handling problems to which multiple different plausible solutions exist. In response, posterior-based methods such as conditional Diffusion Models and…
Mechanistic simulation models are inverted against observations in order to gain inference on modeled processes. However, with the increasing ability to collect high resolution observations, these observations represent more patterns of…
We study semiparametric factor models in high-dimensional panels where the factor loadings consist of a nonparametric component explained by observed covariates and an idiosyncratic component capturing unobserved heterogeneity. A key…
We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quantities. The formulation of the problem and modeling framework define a solution as a…
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…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
Spectral variability in hyperspectral images can result from factors including environmental, illumination, atmospheric and temporal changes. Its occurrence may lead to the propagation of significant estimation errors in the unmixing…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…
Second-order partial differential equations in non-divergence form are considered. Equations of this kind typically arise as subproblems for the solution of Hamilton-Jacobi-Bellman equations in the context of stochastic optimal control, or…
We consider the inverse problem of fitting atmospheric dispersion parameters based on time-resolved back-scattered differential absorption Lidar (DIAL) measurements. The obvious advantage of light-based remote sensing modalities is their…
In solving Bayesian inverse problems, it is often desirable to use a common density parameterization to denote the prior and posterior. Typically we seek a density from the same family as the prior which closely approximates the true…
We show that density models describing multiple observables with (i) hard boundaries and (ii) dependence on external parameters may be created using an auto-regressive Gaussian mixture model. The model is designed to capture how observable…