Related papers: Bayesian KalmanNet: Quantifying Uncertainty in Dee…

In this work, we study the emergence of sparsity and multiway structures in second-order statistical characterizations of dynamical processes governed by partial differential equations (PDEs). We consider several state-of-the-art multiway…

In recent years, operator learning, particularly the DeepONet, has received much attention for efficiently learning complex mappings between input and output functions across diverse fields. However, in practical scenarios with limited and…

Dynamical models estimate and predict the temporal evolution of physical systems. State Space Models (SSMs) in particular represent the system dynamics with many desirable properties, such as being able to model uncertainty in both the…

The ensemble Kalman filter (EnKF) is widely used for nonlinear and high-dimensional state estimation because it replaces complex covariance propagation with simple ensemble statistics. However, conventional EnKF implementations can become…

Modeling biological dynamical systems is challenging due to the interdependence of different system components, some of which are not fully understood. To fill existing gaps in our ability to mechanistically model physiological systems, we…

Learning high-performance deep neural networks for dynamic modeling of high Degree-Of-Freedom (DOF) robots remains challenging due to the sampling complexity. Typical unknown system disturbance caused by unmodeled dynamics (such as internal…

State estimation is a fundamental problem in control and signal processing, for which the Kalman Filter provides an optimal solution under linear dynamics, Gaussian noise, and known noise covariances. However, these assumptions often fail…

The dynamic structural load identification capabilities of the gated recurrent unit, long short-term memory, and convolutional neural networks are examined herein. The examination is on realistic small dataset training conditions and on a…

Ultra-wideband (UWB) indoor localization provides centimeter-level accuracy and low latency, but its measurement reliability degrades severely under Non-Line-of-Sight (NLOS) conditions, leading to meter-scale ranging errors and inconsistent…

In this paper, in order to enhance the numerical stability of the unscented Kalman filter (UKF) used for power system dynamic state estimation, a new UKF with guaranteed positive semidifinite estimation error covariance (UKF-GPS) is…

Data assimilation has been applied to coastal hydrodynamic models to better estimate system states or parameters by incorporating observed data into the model. Kalman Filter (KF) is one of the most studied data assimilation methods whose…

We propose a new extension of Kalman filtering for continuous-discrete systems with nonlinear state-space models that we name as the level set Kalman filter (LSKF). The LSKF assumes the probability distribution can be approximated as a…

Learning in a non-stationary environment is an inevitable problem when applying machine learning algorithm to real world environment. Learning new tasks without forgetting the previous knowledge is a challenge issue in machine learning. We…

This paper considers the problem of data-driven robust control design for nonlinear systems, for instance, obtained when discretizing nonlinear partial differential equations (PDEs). A robust learning control approach is developed for…

The extended Kalman filter (EKF) is a widely adopted method for sensor fusion in navigation applications. A crucial aspect of the EKF is the online determination of the process noise covariance matrix reflecting the model uncertainty. While…

The problem of system identification for the Kalman filter, relying on the expectation-maximization (EM) procedure to learn the underlying parameters of a dynamical system, has largely been studied assuming that observations are sampled at…

This paper introduces a novel approach to quantify the uncertainties in fault diagnosis of motor drives using Bayesian neural networks (BNN). Conventional data-driven approaches used for fault diagnosis often rely on point-estimate neural…

Biomolecular systems are often modeled with partially known nonlinear stochastic dynamics, making state and parameter estimation a central challenge. While Kalman filtering techniques are widely used in this setting, their performance…

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…

The Kalman filter is a fundamental filtering algorithm that fuses noisy sensory data, a previous state estimate, and a dynamics model to produce a principled estimate of the current state. It assumes, and is optimal for, linear models and…