相关论文: Computing Lipschitz Constants for Hydraulic Models…

Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz constant in neural…

The Lipschitz constant of a neural network is connected to several important properties of the network such as its robustness and generalization. It is thus useful in many settings to estimate the Lipschitz constant of a model. Prior work…

This paper reports the initial steps in the development of WaterLab, an ambitious experimental facility for the testing of new cyber-physical technologies in drinking water distribution networks (DWDN). WaterLab's initial focus is on…

The shallow water flow model is widely used to describe water flows in rivers, lakes, and coastal areas. Accounting for uncertainty in the corresponding transport-dominated nonlinear PDE models presents theoretical and numerical challenges…

Viewing recurrent neural networks (RNNs) as continuous-time dynamical systems, we propose a recurrent unit that describes the hidden state's evolution with two parts: a well-understood linear component plus a Lipschitz nonlinearity. This…

As the power system continues to be flooded with intermittent resources, it becomes more important to accurately assess the role of hydro and its impact on the power grid. While hydropower generation has been studied for decades, dependency…

We derive hydrodynamics of a prototypical one dimensional model, having variable-range hopping, which mimics passive diffusion and ballistic motion of active, or self-propelled, particles. The model has two main ingredients - the hardcore…

Lipschitz constants are connected to many properties of neural networks, such as robustness, fairness, and generalization. Existing methods for computing Lipschitz constants either produce relatively loose upper bounds or are limited to…

The high-pressure transportation process of pipeline necessitates an accurate hydraulic transient simulation tool to prevent slack line flow and over-pressure, which can endanger pipeline operations. However, current numerical solution…

The expansion of data centers (DCs) drives a sustained increase in electricity demand and associated water withdrawals at generation sites. These withdrawals occur at generation sites and are virtually allocated to demand based on network…

Dynamic programming equations for mean field control problems with a separable structure are Eikonal equations on the Wasserstein space. Standard differentiation using linear derivatives yield a direct extension of the classical viscosity…

This paper examines aspirational requirements for software addressing mixed-integer optimization problems constrained by the nonlinear Shallow Water partial differential equations (PDEs), motivated by applications such as river-flow…

\v{C}ech Persistence diagrams (PDs) are topological descriptors routinely used to capture the geometry of complex datasets. They are commonly compared using the Wasserstein distances $OT_{p}$; however, the extent to which PDs are stable…

Facing climate change, the already limited availability of drinking water will decrease in the future rendering drinking water an increasingly scarce resource. Considerable amounts of it are lost through leakages in water transportation and…

We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales.…

Nonlinear dynamic systems can be classified into various classes depending on the modeled nonlinearity. These classes include Lipschitz, bounded Jacobian, one-sided Lipschitz (OSL), and quadratically inner-bounded (QIB). Such classes…

We consider several different bidirectional Whitham equations that have recently appeared in the literature. Each of these models combine the full two-way dispersion relation from the incompressible Euler equations with a canonical shallow…

We consider a general class of nonlinear diffusive models with bulk dissipation and boundary driving, and derive its hydrodynamic description in the large size limit. Both the average macroscopic behavior and the fluctuating properties of…

In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various deep neural network architectures which numerically predict…

Recent control trends are increasingly relying on communication networks and wireless channels to close the loop for Internet-of-Things applications. Traditionally these approaches are model-based, i.e., assuming a network or channel model…