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Attack detection and mitigation strategies for cyberphysical systems (CPS) are an active area of research, and researchers have developed a variety of attack-detection tools such as dynamic watermarking. However, such methods often make…
This paper focuses on the performance and the robustness analysis of stochastic jump linear systems. The state trajectory under stochastic jump process becomes random variables, which brings forth the probability distributions in the system…
From the structural perspective, this paper investigates a new formulation of the concept of input-to-state stability (ISS), and based on this formulation, proposes a new stability analysis approach for a class of interconnected system. The…
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
Global stability analysis and direct numerical simulation (DNS) are performed to study boundary layer flows with an isolated roughness element. Wall-attached cuboids with aspect ratios $\eta=1$ and $\eta=0.5$ are investigated for fixed…
Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…
Wasserstein distributionally robust optimization (WDRO) optimizes against worst-case distributional shifts within a specified uncertainty set, leading to enhanced generalization on unseen adversarial examples, compared to standard…
Score Distillation Sampling (SDS) and its variants have been widely used for text-to-3D generation by distilling 2D image diffusion priors. However, the standard SDS objective is prone to severe mode collapse, frequently yielding…
We study the Wasserstein natural gradient in parametric statistical models with continuous sample spaces. Our approach is to pull back the $L^2$-Wasserstein metric tensor in the probability density space to a parameter space, equipping the…
Gradient boosting is a sequential ensemble method that fits a new weaker learner to pseudo residuals at each iteration. We propose Wasserstein gradient boosting, a novel extension of gradient boosting that fits a new weak learner to…
An attractor of a dynamical system may represent the system's 'desirable' state. Perturbations to the system may push the system out of the basin of attraction of the desirable attractor and into undesirable states. Hence, it is important…
Modern technological advances have expanded the scope of applications requiring analysis of large-scale datastreams that comprise multiple indefinitely long time series. There is an acute need for statistical methodologies that perform…
Large-scale interconnected networks, composed of multiple low-dimensional subsystems, serve as a crucial framework for modeling a wide range of real-world applications. Despite offering computational scalability, the inherent…
Many scientific systems, such as cellular populations or economic cohorts, are naturally described by probability distributions that evolve over time. Predicting how such a system would have evolved under different forces or initial…
The stratified inclined duct (SID) experiment consists of a zero-net-volume exchange flow in a long tilted rectangular duct, which allows the study of realistic stratified shear flows with sustained internal forcing. We present the first…
In this paper, we study input-to-state stability (ISS) of an equilibrium for a scalar conservation law with nonlocal velocity and measurement error arising in a highly re-entrant manufacturing system. By using a suitable Lyapunov function,…
Despite superior performance in many situations, deep neural networks are often vulnerable to adversarial examples and distribution shifts, limiting model generalization ability in real-world applications. To alleviate these problems,…
This paper addresses the input-to-state stability (ISS) and integral input-to-state stability (iISS) for a class of nonlinear higher dimensional parabolic partial differential equations (PDEs) with different types of boundary disturbances…
Modeling real-world distributions can often be challenging due to sample data that are subjected to perturbations, e.g., instrumentation errors, or added random noise. Since flow models are typically nonlinear algorithms, they amplify these…
While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the…