Related papers: A reduced order Kalman Filter model for sequential…
Data assimilation is concerned with sequentially estimating a temporally-evolving state. This task, which arises in a wide range of scientific and engineering applications, is particularly challenging when the state is high-dimensional and…
In this paper, we consider the task of designing a Kalman Filter (KF) for an unknown and partially observed autonomous linear time invariant system driven by process and sensor noise. To do so, we propose studying the following two step…
Accurate data assimilation (DA) for systems with piecewise-smooth or discontinuous state variables remains a significant challenge, as conventional covariance-based ensemble Kalman filter approaches often fail to effectively balance…
This research enhances linear regression models by integrating a Kalman filter and analysing curve areas to minimize loss. The goal is to develop an optimal linear regression equation using stochastic gradient descent (SGD) for weight…
The performance of ensemble-based data assimilation techniques that estimate the state of a dynamical system from partial observations depends crucially on the prescribed uncertainty of the model dynamics and of the observations. These are…
Stochastic models in biomolecular contexts can have a state-dependent process noise covariance. The choice of the process noise covariance is an important parameter in the design of a Kalman Filter for state estimation and the theoretical…
This paper introduces a computational framework to reconstruct and forecast a partially observed state that evolves according to an unknown or expensive-to-simulate dynamical system. Our reduced-order autodifferentiable ensemble Kalman…
We introduce Kalman Gradient Descent, a stochastic optimization algorithm that uses Kalman filtering to adaptively reduce gradient variance in stochastic gradient descent by filtering the gradient estimates. We present both a theoretical…
Data assimilation (DA) for compressible flows with shocks is challenging because many classical DA methods generate spurious oscillations and nonphysical features near uncertain shocks. We focus here on the ensemble Kalman filter (EnKF). We…
We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty.…
Reduced-order models of flame dynamics can be used to predict and mitigate the emergence of thermoacoustic oscillations in the design of gas turbine and rocket engines. This process is hindered by the fact that these models, although often…
Common filters are usually based on the linear approximation of the optimal minimum mean square error estimator. The Extended and Unscented Kalman Filters handle nonlinearity through linearization and unscented transformation, respectively,…
In recent years, machine learning methods represented by deep neural networks (DNN) have been a new paradigm of turbulence modeling. However, in the scenario of high Reynolds numbers, there are still some bottlenecks, including the lack of…
Bayesian uncertainty quantification (UQ) is of interest to industry and academia as it provides a framework for quantifying and reducing the uncertainty in computational models by incorporating available data. For systems with very high…
The models of partially observed linear stochastic differential equations with unknown initial values of the non-observed component are considered in two situations. In the first problem, the initial value is deterministic, and in the…
System identification poses a significant bottleneck to characterizing and controlling complex systems. This challenge is greatest when both the system states and parameters are not directly accessible leading to a dual-estimation problem.…
This paper investigates the state estimation problem for unknown linear systems subject to both process and measurement noise. Based on a prior input-output trajectory sampled at a higher frequency and a prior state trajectory sampled at a…
In an age of exponentially increasing data generation, performing inference tasks by utilizing the available information in its entirety is not always an affordable option. The present paper puts forth approaches to render tracking of…
Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state of the system is high dimensional, ensemble Kalman filters are often the method of choice.…
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…