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We develop time-series machine learning (ML) methods for closure modeling of the Unsteady Reynolds Averaged Navier Stokes (URANS) equations applied to stably stratified turbulence (SST). SST is strongly affected by fine balances between…
Frequency-limited model order reduction aims to approximate a high-order model with a reduced-order model that maintains high fidelity within a specific frequency range. Beyond this range, a decrease in accuracy is acceptable due to the…
This research explores the development and application of the High-Order Dynamic Integration Method for solving integro-differential equations, with a specific focus on turbulent fluid dynamics. Traditional numerical methods, such as the…
Gaussian Mixture Models (GMMs) are one of the most potent parametric density models used extensively in many applications. Flexibly-tied factorization of the covariance matrices in GMMs is a powerful approach for coping with the challenges…
Recently, machine learning techniques, particularly deep learning, have demonstrated superior performance over traditional time series forecasting methods across various applications, including both single-variable and multi-variable…
Branch and bound algorithms have been developed for reliability analysis of coherent systems. They exhibit a set of advantages; in particular, they can find a computationally efficient representation of a system failure or survival event,…
Hidden Markov models (HMMs) are popular models to identify a finite number of latent states from sequential data. However, fitting them to large data sets can be computationally demanding because most likelihood maximization techniques…
In the reordering buffer management problem (RBM) a sequence of $n$ colored items enters a buffer with limited capacity $k$. When the buffer is full, one item is removed to the output sequence, making room for the next input item. This step…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…
We introduce a novel framework to approximate the aggregate frequency dynamics of coherent generators. By leveraging recent results on dynamics concentration of tightly connected networks, and frequency weighted balanced truncation, a…
In system identification, it is often difficult to find a physical intuition to choose a noise model structure. The importance of this choice is that, for the prediction error method (PEM) to provide asymptotically efficient estimates, the…
Electromagnetic (EM) wave scattering in electrically large, irregularly shaped, environments is a common phenomenon. The deterministic, or first principles, study of this process is usually computationally expensive and the results exhibit…
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…
We introduce a new class of algorithms, Stochastic Generalized Method of Moments (SGMM), for estimation and inference on (overidentified) moment restriction models. Our SGMM is a novel stochastic approximation alternative to the popular…
In this study, we propose a general model capable of addressing heterogeneity in higher-order moments while preserving mean and variance, including the t, Laplace, and skew-normal distributions as special cases. Our model flexibly…
Moment methods are classical approaches that approximate the mesoscopic radiative transfer equation by a system of macroscopic moment equations. An expansion in the angular variables transforms the original equation into a system of…
Model order reduction (MOR) has long been a mainstream strategy to accelerate large-scale transient circuit simulation. Dynamic Mode Decomposition (DMD) represents a novel data-driven characterization method, extracting dominant dynamical…
We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…
The conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables, a prominent example being instrumental variable regression. A standard approach reduces the problem to a finite…
Accurate platform localization is an integral component of most robotic systems. As these robotic systems become more ubiquitous, it is necessary to develop robust state estimation algorithms that are able to withstand novel and…