Related papers: Hyper-Differential Sensitivity Analysis for Invers…
We describe a novel framework for estimating subsurface properties, such as rock permeability and porosity, from time-lapse observed seismic data by coupling full-waveform inversion, subsurface flow processes, and rock physics models. For…
In the framework of solid mechanics, the task of deriving material parameters from experimental data has recently re-emerged with the progress in full-field measurement capabilities and the renewed advances of machine learning. In this…
Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing…
This paper deals with the reconstruction of small-amplitude perturbations in the electric properties (permittivity and conductivity) of a medium from boundary measurements of the electric field at a fixed frequency. The underlying model is…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This is accomplished by a function-space diffusion model and…
The estimation of high-dimensional physical parameters constrained by partial differential equations (PDEs) from limited and indirect measurements is a highly ill-posed problem. Traditional methods face significant accuracy and efficiency…
Probabilistic sensitivity analysis identifies the influential uncertain input to guide decision-making. We propose a general sensitivity framework with respect to the input distribution parameters that unifies a wide range of sensitivity…
Inverse problems are fundamental to science and engineering, where the goal is to infer an underlying signal or state from incomplete or noisy measurements. Recent approaches employ diffusion models as powerful implicit priors for such…
Computational inverse problems for biomedical simulators suffer from limited data and relatively high parameter dimensionality. This often requires sensitivity analysis, where parameters of the model are ranked based on their influence on…
We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems,…
Frequency-domain thermoreflectance (FDTR) is a widely used technique for characterizing thermal properties of multilayer thin films. However, extracting multiple parameters from FDTR measurements presents a nonlinear inverse problem due to…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…
We consider the statistical inverse problem of recovering a parameter $\theta\in H^\alpha$ from data arising from the Gaussian regression problem \begin{equation*} Y = \mathscr{G}(\theta)(Z)+\varepsilon \end{equation*} with nonlinear…
Anomaly detection (AD) in images is a fundamental computer vision problem by deep learning neural network to identify images deviating significantly from normality. The deep features extracted from pretrained models have been proved to be…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
In the field of inverse estimation for systems modeled by partial differential equations (PDEs), challenges arise when estimating high- (or even infinite-) dimensional parameters. Typically, the ill-posed nature of such problems…
This work explores a novel approach for adaptive, differentiable parametrization of large-scale non-stationary random fields. Coupled with any gradient-based algorithm, the method can be applied to variety of optimization problems,…
Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely…