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Flow-based Transformer models have achieved state-of-the-art image generation performance, but often suffer from high inference latency and computational cost due to their large parameter sizes. To improve inference efficiency without…

The Kalman filter is a fundamental tool for state estimation in dynamical systems. While originally developed for linear Gaussian settings, it has been extended to nonlinear problems through approaches such as the extended and unscented…

This paper develops an efficient implementation of the ensemble Kalman filter based on a modified Cholesky decomposition for inverse covariance matrix estimation. This implementation is named EnKF-MC. Background errors corresponding to…

System identification remains an intriguing challenge for lithium-ion batteries, as many models are nonlinear, exhibit multi-physics coupling, and involve a large number of parameters. In this paper, we address this challenge using the…

Ensemble Kalman filter (EnKF) has been widely used in state estimation and parameter estimation for the dynamic system where observational data is obtained sequentially in time. To reduce uncertainty and accelerate posterior inference, a…

Inertial Navigation Systems (INS) are a key technology for autonomous vehicles applications. Recent advances in estimation and filter design for the INS problem have exploited geometry and symmetry to overcome limitations of the classical…

Bayesian linear inverse problems aim to recover an unknown signal from noisy observations, incorporating prior knowledge. This paper analyses a data-dependent method to choose the scale parameter of a Gaussian prior. The method we study…

The ensemble Kalman filter (EnKF) is a popular technique for performing inference in state-space models (SSMs), particularly when the dynamic process is high-dimensional. Unlike reweighting methods such as sequential Monte Carlo (SMC, i.e.…

Inverse problems of partial differential equations are ubiquitous across various scientific disciplines and can be formulated as statistical inference problems using Bayes' theorem. To address large-scale problems, it is crucial to develop…

The Ensemble Kalman Filter (EnKF) is a widely used method for data assimilation in high-dimensional systems, with an ensemble update step equivalent to an empirical version of the Matheron update popular in Gaussian process regression -- a…

We propose a method for inference on moderately high-dimensional, nonlinear, non-Gaussian, partially observed Markov process models for which the transition density is not analytically tractable. Markov processes with intractable transition…

When solving inverse problems, one increasingly popular approach is to use pre-trained diffusion models as plug-and-play priors. This framework can accommodate different forward models without re-training while preserving the generative…

Neural posterior estimation methods based on discrete normalizing flows have become established tools for simulation-based inference (SBI), but scaling them to high-dimensional problems can be challenging. Building on recent advances in…

Ensemble Kalman filters are based on a Gaussian assumption, which can limit their performance in some non-Gaussian settings. This paper reviews two nonlinear, non-Gaussian extensions of the Ensemble Kalman Filter: Gaussian anamorphosis (GA)…

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…

We derive symmetry preserving invariant extended Kalman filters (IEKF) on matrix Lie groups. These Kalman filters have an advantage over conventional extended Kalman filters as the error dynamics for such filters are independent of the…

The Geometrically Intrinsic Nonlinear Recursive Filter, or GI Filter, is designed to estimate an arbitrary continuous-time Markov diffusion process X subject to nonlinear discrete-time observations. The GI Filter is fundamentally different…

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…

We study the ensemble Kalman filter (EnKF) algorithm for sequential data assimilation in a general situation, that is, for nonlinear forecast and measurement models with non-additive and non-Gaussian noises. Such applications traditionally…

The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models. The EnKF originated as a version of the Kalman…