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Ill-posed inverse problems are ubiquitous in applications. Under- standing of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering…
The extended Kalman filter (EKF) has been the industry standard for state estimation problems over the past sixty years. The classical formulation of the EKF is posed for nonlinear systems defined on global Euclidean spaces. The design…
Ill-posed image reconstruction problems appear in many scenarios such as remote sensing, where obtaining high quality images is crucial for environmental monitoring, disaster management and urban planning. Deep learning has seen great…
We study the variational inference problem of minimizing a regularized R\'enyi divergence over an exponential family. We propose to solve this problem with a Bregman proximal gradient algorithm. We propose a sampling-based algorithm to…
Latent variable time-series models are among the most heavily used tools from machine learning and applied statistics. These models have the advantage of learning latent structure both from noisy observations and from the temporal ordering…
This paper proposes two practical implementations of Four-Dimensional Variational (4D-Var) Ensemble Kalman Filter (4D-EnKF) methods for non-linear data assimilation. Our formulations' main idea is to avoid the intrinsic need for adjoint…
Although extreme learning machine (ELM) has been successfully applied to a number of pattern recognition problems, it fails to pro-vide sufficient good results in hyperspectral image (HSI) classification due to two main drawbacks. The first…
This study considers the data assimilation problem in coupled systems, which consists of two components (sub-systems) interacting with each other through certain coupling terms. A straightforward way to tackle the assimilation problem in…
Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…
In this paper, we introduce a new, local formulation of the ensemble Kalman Filter approach for atmospheric data assimilation. Our scheme is based on the hypothesis that, when the Earth's surface is divided up into local regions of moderate…
The increasing availability of data presents an opportunity to calibrate unknown parameters which appear in complex models of phenomena in the biomedical, physical and social sciences. However, model complexity often leads to…
We are interested in ensemble methods to solve multi-objective optimization problems. An ensemble Kalman method is proposed to solve a formulation of the nonlinear problem using a weighted function approach. An analysis of the mean field…
The a posteriori error estimator using the least-squares functional can be used for adaptive mesh refinement and error control even if the numerical approximations are not obtained from the corresponding least-squares method. This suggests…
Full waveform inversion (FWI) updates the subsurface model from an initial model by comparing observed and synthetic seismograms. Due to high nonlinearity, FWI is easy to be trapped into local minima. Extended domain FWI, including…
Accurate estimation of noise parameters is critical for optimal filter performance, especially in systems where true noise parameter values are unknown or time-varying. This article presents a quaternion left-invariant extended Kalman…
Full-waveform inversion (FWI) is a seismic imaging method that provides quantitative inference about subsurface properties with a wavelength-scale resolution. Its frequency-domain formulation is computationally efficient when processing…
Koopman decomposition is a non-linear generalization of eigen-decomposition, and is being increasingly utilized in the analysis of spatio-temporal dynamics. Well-known techniques such as the dynamic mode decomposition (DMD) and its linear…
In the technique of Electron Backscatter Diffraction (EBSD), the accurate detection and identification of different phases existing in a sample is often limited by overlapping Kikuchi diffraction patterns originating from the extended…
Improved state space models, such as Recurrent State Space Models (RSSMs), are a key factor behind recent advances in model-based reinforcement learning (RL). Yet, despite their empirical success, many of the underlying design choices are…
We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic non-linear observer on Lie groups, for continuous-time systems with discrete observations. One of the main…