Related papers: Unscented Kalman Inversion: Efficient Gaussian App…

Recent years have witnessed growing interest in semi-implicit variational inference (SIVI) methods due to their ability to rapidly generate samples from complex distributions. However, since the likelihood of these samples is non-trivial to…

A general inversion technique for the recovery of the underlying distribution function for observed galactic disks is presented and illustrated. Under the assumption that these disks are axi-symmetric and thin, the proposed method yields…

The Ensemble Kalman methodology in an inverse problems setting can be viewed as an iterative scheme, which is a weakly tamed discretization scheme for a certain stochastic differential equation (SDE). Assuming a suitable approximation…

Accurate modeling is crucial in many engineering and scientific applications, yet obtaining a reliable process model for complex systems is often challenging. To address this challenge, we propose a novel framework, reservoir computing with…

This report derives a generalized, converted measurement Kalman filter for the class of filtering problems with a linear state equation and nonlinear measurement equation, for which a bijective mapping exists between the state and…

Heavy tails is a common feature of filtering distributions that results from the nonlinear dynamical and observation processes as well as the uncertainty from physical sensors. In these settings, the Kalman filter and its ensemble version -…

Seismic full waveform inversion (FWI) is a powerful technique to generate high resolution images of the Earth's interior. However, significant uncertainty exists in all FWI solutions due to imperfect acquisition geometries, inherent noise…

A priori state vector and error covariance computation for the Unscented Kalman Filter (UKF) is described. The original UKF propagates multiple sigma points to compute the a priori mean state vector and the error covariance, resulting in a…

The Ensemble Kalman Filter (EnKF) belongs to the class of iterative particle filtering methods and can be used for solving control--to--observable inverse problems. In this context, the EnKF is known as Ensemble Kalman Inversion (EKI). In…

Accurate state estimation of large-scale lithium-ion battery packs is necessary for the advanced control of batteries, which could potentially increase their lifetime through e.g. reconfiguration. To tackle this problem, an enhanced…

Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…

In inverse problems, uncertainty quantification (UQ) deals with a probabilistic description of the solution nonuniqueness and data noise sensitivity. Setting seismic imaging into a Bayesian framework allows for a principled way of studying…

This paper focuses on a challenging class of inverse problems that is often encountered in applications. The forward model is a complex non-linear black-box, potentially non-injective, whose outputs cover multiple decades in amplitude.…

Bayesian experimental design (BED) for complex physical systems is often limited by the nested inference required to estimate the expected information gain (EIG) or its gradients. Each outer sample induces a different posterior, creating a…

The rigorous quantification of uncertainty in geophysical inversions is a challenging problem. Inversions are often ill-posed and the likelihood surface may be multi-modal; properties of any single mode become inadequate uncertainty…

Counter-adversarial system design problems have lately motivated the development of inverse Bayesian filters. For example, inverse Kalman filter (I-KF) has been recently formulated to estimate the adversary's Kalman-filter-tracked estimates…

Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with the size of the state space. This is particularly…

Inverse medium scattering solvers generally reconstruct a single solution without an associated measure of uncertainty. This is true both for the classical iterative solvers and for the emerging deep learning methods. But ill-posedness and…

Variational inference (VI) is widely used as an efficient alternative to Markov chain Monte Carlo. It posits a family of approximating distributions $q$ and finds the closest member to the exact posterior $p$. Closeness is usually measured…

There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…