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Many decision-facing stochastic systems are observed through aggregate distributions rather than scalar trajectories: queue occupancies, mobility shares, public-health mixtures, generation-source shares, ecological compositions, and…
Shallow water equations are extensively considered in the domains of oceans, atmospheric modelling, and engineering research (Franca et al., 2022), which play significant roles in floods and tsunami governance. Nonetheless, the accurate…
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid…
Stochastic dominance is an important concept in probability theory, econometrics and social choice theory for robustly modeling agents' preferences between random outcomes. While many works have been dedicated to the univariate case, little…
Data assimilation (DA) provides a general framework for estimation in dynamical systems based on the concepts of Bayesian inference. This constitutes a common basis for the different linear and nonlinear filtering and smoothing techniques…
We consider the problem of data-driven stochastic optimal control of an unknown LTI dynamical system. Assuming the process noise is normally distributed, we pose the problem of steering the state's mean and covariance to a target normal…
The dynamics of molecules are governed by rare event transitions between long-lived (metastable) states. To explore these transitions efficiently, many enhanced sampling protocols have been introduced that involve using simulations with…
Optimal transport is widely used to learn distributions, enforce distributional constraints, and model uncertainty. In applications, transport losses are often computed from samples through tractable representations, such as one-dimensional…
This paper details how to parameterize the posterior distribution of state-space systems to generate improved optimization problems for system identification using variational inference. Three different parameterizations of the assumed…
Stochastic nested optimization, including stochastic compositional, min-max and bilevel optimization, is gaining popularity in many machine learning applications. While the three problems share the nested structure, existing works often…
Simultaneous localization and tracking (SLAT) in sensor networks aims to determine the positions of sensor nodes and a moving target in a network, given incomplete and inaccurate range measurements between the target and each of the…
In stochastic optimal control, change of measure arguments have been crucial for stochastic analysis. Such an approach is often called static reduction in dynamic team theory (or decentralized stochastic control) and has been an effective…
Despite an extensive body of literature on deep learning optimization, our current understanding of what makes an optimization algorithm effective is fragmented. In particular, we do not understand well whether enhanced optimization…
We introduce the Smoothed Online Optimization for Target Tracking (SOOTT) problem, a new framework that integrates three key objectives in online decision-making under uncertainty: (1) tracking cost for following a dynamically moving…
Molecular design requires systematic and broadly applicable methods to extract structure-property relationships. The focus of this study is on learning thermodynamic properties from molecular-liquid simulations. The methodology relies on an…
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…
Standardization has been a widely adopted practice in multiple testing, for it takes into account the variability in sampling and makes the test statistics comparable across different study units. However, despite conventional wisdom to the…
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,…
Continuous data assimilation methods, such as the nudging algorithm introduced by Azouani, Olson, and Titi (AOT) [2], are known to be highly effective in deterministic settings for asymptotically synchronizing approximate solutions with…
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…