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High-fidelity patient-specific modeling of cardiovascular flows and hemodynamics is challenging. Direct blood flow measurement inside the body with in-vivo measurement modalities such as 4D flow magnetic resonance imaging (4D flow MRI)…
The sample covariance matrix of a random vector is a good estimate of the true covariance matrix if the sample size is much larger than the length of the vector. In high-dimensional problems, this condition is never met. As a result, in…
Data assimilation method consists in combining all available pieces of information about a system to obtain optimal estimates of initial states. The different sources of information are weighted according to their accuracy by the means of…
Data assimilation techniques are often confronted with challenges handling complex high dimensional physical systems, because high precision simulation in complex high dimensional physical systems is computationally expensive and the exact…
We develop an optimal experimental design framework for adapting the covariance inflation and localization in data assimilation problems. Covariance inflation and localization are ubiquitously employed to alleviate the effect of using…
This paper presents a comparison of two reduced-order, sequential and variational data assimilation methods: the SEEK filter and the R-4D-Var. A hybridization of the two, combining the variational framework and the sequential evolution of…
Nonlinear/non-Gaussian filtering has broad applications in many areas of life sciences where either the dynamic is nonlinear and/or the probability density function of uncertain state is non-Gaussian. In such problems, the accuracy of the…
Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Ito process. This work…
There is a recent proliferation of research on the integration of machine learning and optimization. One expansive area within this research stream is predictive-model embedded optimization, which proposes the use of pre-trained predictive…
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…
Ensemble models are widely used to solve complex tasks by their decomposition into multiple simpler tasks, each one solved locally by a single member of the ensemble. Decoding of error-correction codes is a hard problem due to the curse of…
AI and data-driven models have large potential for data assimilation applications by creating fast and accurate forecasts. Their tendency to produce spurious inaccurate, nonphysical results -- hallucination -- however, raises a serious…
Deep learning-based fault diagnosis (FD) approaches require a large amount of training data, which are difficult to obtain since they are located across different entities. Federated learning (FL) enables multiple clients to collaboratively…
The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations…
A novel strategy is proposed to improve the accuracy of state estimation and reconstruction from low-fidelity models and sparse data from sensors. This strategy combines ensemble Data Assimilation (DA) and Machine Learning (ML) tools,…
Ensembles of models often yield improvements in system performance. These ensemble approaches have also been empirically shown to yield robust measures of uncertainty, and are capable of distinguishing between different \emph{forms} of…
Complexity analysis has become an important tool in the convergence analysis of optimization algorithms. For derivative-free optimization algorithms, it is not different. Interestingly, several constants that appear when developing…
In this short note, the recently popular modifier-adaptation framework for real-time optimization is discussed in tandem with the well-developed trust-region framework of numerical optimization, and it is shown that the basic version of the…
Discovering the underlying physical behavior of complex systems is a crucial, but less well-understood topic in many engineering disciplines. This study proposes a finite-difference inspired convolutional neural network framework to learn…
Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing…