In this work, we demonstrate how physical principles—such as symmetries, invariances and
conservation laws—can be integrated into the dynamic mode decomposition (DMD). DMD is …

We consider the problem of reducing the dimensions of parameters and data in non-
Gaussian Bayesian inference problems. Our goal is to identify an" informed" subspace of the …

We study the instantaneous inference of an unbounded planar flow from sparse noisy
pressure measurements. The true flow field comprises one or more regularized point …

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 …

This study presents a cluster-based Bayesian methodology for state estimation under
realistic conditions including noisy data from sparse sensors. The proposed approach is …

Smoothing is a specialized form of Bayesian inference for state-space models that
characterizes the posterior distribution of a collection of states given an associated …

Formulating dynamical models for physical phenomena is essential for understanding the
interplay between the different mechanisms and predicting the evolution of physical states …

Probabilistic modeling and Bayesian inference in non-Gaussian settings are pervasive
challenges for science and engineering applications. Transportation of measure provides a …

We consider the problem of computing tractable approximations of time-dependent d× d
large positive semi-definite (PSD) matrices defined as solutions of a matrix differential …

The distributed filtering problem sequentially estimates a global state variable using
observations from a network of local sensors with different measurement models. In this …