Related papers: The Ensemble Inverse Problem: Applications and Met…
Power system state estimation (PSSE) is commonly formulated as weighted least-square (WLS) algorithm and solved using iterative methods such as Gauss-Newton methods. However, iterative methods have become more sensitive to system operating…
The recently developed globally convergent numerical method for an inverse medium problem for the Helmholtz equation is tested on experimental data. The data were originally collected in the time domain, whereas the method works in the…
Quantifying the uncertainty of predictions is a core problem in modern statistics. Methods for predictive inference have been developed under a variety of assumptions, often -- for instance, in standard conformal prediction -- relying on…
In the scope of "AI for Science", solving inverse problems is a longstanding challenge in materials and drug discovery, where the goal is to determine the hidden structures given a set of desirable properties. Deep generative models are…
We consider the inverse elastic scattering problems using the far field data due to one incident plane wave. A simple method is proposed to reconstruct the location and size of the obstacle using different components of the far field…
In this book chapter, we discuss recent advances in data-driven approaches for inverse problems. In particular, we focus on the \emph{paired autoencoder} framework, which has proven to be a powerful tool for solving inverse problems in…
Ensemble forecasting of nonlinear systems involves the use of a model to run forward a discrete ensemble (or set) of initial states. Data assimilation techniques tend to focus on estimating the true state of the system, even though model…
The reliable estimation of forecast uncertainties is crucial for risk-sensitive optimal decision making. In this paper, we propose implicit generative ensemble post-processing, a novel framework for multivariate probabilistic electricity…
From a Bayesian perspective, score-based diffusion solves inverse problems through joint inference, embedding the likelihood with the prior to guide the sampling process. However, this formulation fails to explain its practical behavior:…
Ensembles of models often yield improvements in system performance. These ensemble approaches have also been empirically shown to yield robust measures of uncertainty, and are capable of distinguishing between different \emph{forms} of…
Standard Bayesian inference schemes are infeasible for inverse problems with computationally expensive forward models. A common solution is to replace the model with a cheaper surrogate. To avoid overconfident conclusions, it is essential…
Hyperspectral image reconstruction from a compressed measurement is a highly ill-posed inverse problem. Current data-driven methods suffer from hallucination due to the lack of spectral diversity in existing hyperspectral image datasets,…
In this paper, we develop a generalized Bayesian inference framework for a collection of signal-plus-noise matrix models arising in high-dimensional statistics and many applications. The framework is built upon an asymptotically unbiased…
We consider the inverse Ising problem, i.e. the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the…
Subsampling techniques can reduce the computational costs of processing big data. Practical subsampling plans typically involve initial uniform sampling and refined sampling. With a subsample, big data inferences are generally built on the…
To accelerate learning process with few samples, meta-learning resorts to prior knowledge from previous tasks. However, the inconsistent task distribution and heterogeneity is hard to be handled through a global sharing model…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
We introduce a framework for analyzing and designing EIS inversion algorithms. Our framework stems from the observation of four features common to well-defined EIS inversion algorithms, namely (1) the representation of unknown…
Pretrained diffusion models have demonstrated strong capabilities in zero-shot inverse problem solving by incorporating observation information into the generation process of the diffusion models. However, this presents an inherent dilemma:…
We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…