Related papers: Computing Lipschitz Constants for Hydraulic Models…

Accurate water consumption forecasting is a crucial tool for water utilities and policymakers, as it helps ensure a reliable supply, optimize operations, and support infrastructure planning. Urban Water Distribution Networks (WDNs) are…

The problem of state estimation for a system of coupled hyperbolic PDEs and ODEs with Lipschitz nonlinearities with boundary measurements is considered. An infinite dimensional observer with a linear boundary injection term is used to solve…

Extracting dynamic models from data is of enormous importance in understanding the properties of unknown systems. In this work, we employ Lipschitz neural networks, a class of neural networks with a prescribed upper bound on their Lipschitz…

Numerical modelling of several coupled passive linear dynamical systems (LDS) is considered. Since such component systems may arise from partial differential equations, transfer function descriptions, lumped systems, measurement data, etc.,…

Obtaining sharp Lipschitz constants for feed-forward neural networks is essential to assess their robustness in the face of perturbations of their inputs. We derive such constants in the context of a general layered network model involving…

We present a novel computational framework for density control in high-dimensional state spaces. The considered dynamical system consists of a large number of indistinguishable agents whose behaviors can be collectively modeled as a…

The Lipschitz constant of the map between the input and output space represented by a neural network is a natural metric for assessing the robustness of the model. We present a new method to constrain the Lipschitz constant of dense deep…

This paper investigates the joint problems of dynamic state estimation of algebraic variables (voltage and phase angle) and generator states (rotor angle and frequency) of nonlinear differential algebraic equation (NDAE) power network…

In this paper, we propose a data-based methodology to solve a multi-period stochastic optimal water flow (OWF) problem for water distribution networks (WDNs). The framework explicitly considers the pump schedule and water network head level…

The static dielectric constant of liquid water is computed using classical force field based molecular dynamics simulation at fixed electric displacement D. The method to constrain the electric displacement is the finite temperature…

Privacy restrictions hinder the sharing of real-world Water Distribution Network (WDN) models, limiting the application of emerging data-driven machine learning, which typically requires extensive observations. To address this challenge, we…

Lipschitz constants of neural networks have been explored in various contexts in deep learning, such as provable adversarial robustness, estimating Wasserstein distance, stabilising training of GANs, and formulating invertible neural…

Normalizing flows model probability distributions by learning invertible transformations that transfer a simple distribution into complex distributions. Since the architecture of ResNet-based normalizing flows is more flexible than that of…

The integration of various power sources, including renewables and electric vehicles, into smart grids is expanding, introducing uncertainties that can result in issues like voltage imbalances, load fluctuations, and power losses. These…

The Lipschitz constant is a key measure for certifying the robustness of neural networks to input perturbations. However, computing the exact constant is NP-hard, and standard approaches to estimate the Lipschitz constant involve solving a…

These notes are an introduction to fluctuating hydrodynamics (FHD) and the formulation of numerical schemes for the resulting stochastic partial differential equations (PDEs). Fluctuating hydrodynamics was originally introduced by Landau…

We formulate a lattice Boltzmann algorithm which solves the hydrodynamic equations of motion for nematic liquid crystals. The applicability of the approach is demonstrated by presenting results for two liquid crystal devices where flow has…

The microscopic description of the local structure of water remains an open challenge. Here, we adopt an agnostic approach to understanding water's hydrogen bond network using data harvested from molecular dynamics simulations of an…

We study the applicability of a Deep Neural Network (DNN) approach to simulate one-dimensional non-relativistic fluid dynamics. Numerical fluid dynamical calculations are used to generate training data-sets corresponding to a broad range of…

Interfaces between two fluids are ubiquitous and of special importance for industrial applications, e.g., stabilisation of emulsions. The dynamics of fluid-fluid interfaces is difficult to study because these interfaces are usually…