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Inferring the state and unknown parameters of a network of coupled oscillators is of utmost importance. This task is made harder when only partial and noisy observations are available, which is a typical scenario in realistic…
Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving 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.…
Data assimilation provides algorithms for widespread applications in various fields. It is of practical use to deal with a large amount of information in the complex system that is hard to estimate. Weather forecasting is one of the…
Complex systems are often described with competing models. Such divergence of interpretation on the system may stem from model fidelity, mathematical simplicity, and more generally, our limited knowledge of the underlying processes.…
Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in…
Prediction of physiologic states are important in medical practice because interventions are guided by predicted impacts of interventions. But prediction is difficult in medicine because the generating system is complex and difficult to…
This article focuses on the measurement and evolution modeling of Standardized Kalman filtering for brain activity estimation using non-invasive electroencephalography data. Here, we propose new parameter tuning and a model that uses the…
Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous…
This paper presents an approach for employing artificial neural networks (NN) to emulate an ensemble Kalman filter (EnKF) as a method of data assimilation. The assimilation methods are tested in the Simplified Parameterizations…
A turbulent boundary layer is an essential flow case of fundamental and applied fluid mechanics. However, accurate measurements of turbulent boundary layer parameters (e.g., friction velocity $u_\tau$ and wall shear $\tau_w$), are…
Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The…
Objective Kalman filtering has previously been applied to track neural model states and parameters, particularly at the scale relevant to EEG. However, this approach lacks a reliable method to determine the initial filter conditions and…
This study presents a novel approach to applying data assimilation techniques for particle-based simulations using the Ensemble Kalman Filter. While data assimilation methods have been effectively applied to Eulerian simulations, their…
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…
Ensemble transform Kalman filtering (ETKF) data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliable state representations in dynamical systems. However, it is…
Data-driven prediction and physics-agnostic machine-learning methods have attracted increased interest in recent years achieving forecast horizons going well beyond those to be expected for chaotic dynamical systems. In a separate strand of…
The analysis of high-dimensional dynamical systems generally requires the integration of simulation data with experimental measurements. Experimental data often has substantial amounts of measurement noise that compromises the ability to…
Electroencephalogram (EEG) is a very promising and widely implemented procedure to study brain signals and activities by amplifying and measuring the post-synaptical potential arising from electrical impulses produced by neurons and…
Localizing neuronal activity in the brain, both in time and in space, is a central challenge to advance the understanding of brain function. Because of the inability of any single neuroimaging techniques to cover all aspects at once, there…