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Multi-target tracking (MTT) serves as a cornerstone technology in information fusion, yet faces significant challenges in robustness and efficiency when dealing with model uncertainties, clutter interference, and target interactions.…

A recently introduced family of lattice Boltzmann (LB) models (Karlin, B\"osch, Chikatamarla, Phys. Rev. E, 2014) is studied in detail for incompressible two-dimensional flows. A framework for developing LB models based on entropy…

We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…

Stochastic gradient algorithms are often unstable when applied to functions that do not have Lipschitz-continuous and/or bounded gradients. Gradient clipping is a simple and effective technique to stabilize the training process for problems…

When estimating the risk of a financial position with empirical data or Monte Carlo simulations via a tail-dependent law invariant risk measure such as the Conditional Value-at-Risk (CVaR), it is important to ensure the robustness of the…

The application of reinforcement learning to safety-critical systems is limited by the lack of formal methods for verifying the robustness and safety of learned policies. This paper introduces a novel framework that addresses this gap by…

Deep neural networks are notorious for being sensitive to small well-chosen perturbations, and estimating the regularity of such architectures is of utmost importance for safe and robust practical applications. In this paper, we investigate…

Deep neural networks and Vision Transformers achieve state-of-the-art performance in computer vision but are highly vulnerable to adversarial perturbations. Standard defenses often incur high computational cost or lack formal guarantees. We…

Sensitivity-based robustness certification has emerged as a practical approach for certifying neural network robustness, including in settings that require verifiable guarantees. A key advantage of these methods is that certification is…

Deterministic and probabilistic tools from nonlinear dynamics are used to assess enduring near-surface Lagrangian aspects of the Malvinas Current. The deterministic tools are applied on a multi-year record of velocities derived from…

The pseudopotential lattice Boltzmann method (LBM) is a prominent approach for simulating multiphase flows, valued for its physical intuitiveness and computational tractability. However, existing immiscible pseudopotential methods for…

Reliability-based topology optimization (RBTO) requires repeated estimation of small failure probabilities and their gradients, making conventional nested Monte Carlo approaches computationally prohibitive for large scale structural…

In this work, we extend the Spatiotemporal Tube (STT) framework to address Probabilistic Temporal Reach-Avoid-Stay (PrT-RAS) tasks in dynamic environments with uncertain obstacles. We develop a real-time tube synthesis procedure that…

The off-lattice Boltzmann (OLB) method consists of numerical schemes which are used to solve the discrete Boltzmann equation. Unlike the commonly used lattice Boltzmann method, the spatial and time steps are uncoupled in the OLB method. In…

In this paper we study the reachability problem for discrete-time nonlinear stochastic systems. Our goal is to present a unified framework for calculating the probabilistic reachable set of discrete-time systems in the presence of both…

Existing bounds on the generalization error of deep networks assume some form of smooth or bounded dependence on the input variable, falling short of investigating the mechanisms controlling such factors in practice. In this work, we…

Neural Lyapunov and barrier certificates have recently been used as powerful tools for verifying the safety and stability properties of deep reinforcement learning (RL) controllers. However, existing methods offer guarantees only under…

In the past several years, the last-iterate convergence of the Stochastic Gradient Descent (SGD) algorithm has triggered people's interest due to its good performance in practice but lack of theoretical understanding. For Lipschitz convex…

In a separable real Hilbert space, we study the problem of minimizing a convex function with Lipschitz continuous gradient in the presence of noisy evaluations. To this end, we associate a stochastic Heavy Ball system, incorporating a…

We propose a novel Branch-and-Bound method for reachability analysis of neural networks in both open-loop and closed-loop settings. Our idea is to first compute accurate bounds on the Lipschitz constant of the neural network in certain…