Related papers: Comprehensive Framework for Controlling Nonlinear …
Advection-Diffusion-Reaction (ADR) Partial Differential Equations (PDEs) appear in a wide spectrum of applications such as chemical reactors, concentration flows, and biological systems. A large number of these applications require the…
A state-space representation of water quality dynamics describing disinfectant (e.g., chlorine) transport dynamics in drinking water distribution networks has been recently proposed. Such representation is a byproduct of space- and…
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…
The evolution of dynamical systems is generically governed by nonlinear partial differential equations (PDEs), whose solution, in a simulation framework, requires vast amounts of computational resources. In this work, we present a novel…
We consider constrained bilinear optimal control of second-order linear evolution partial differential equations (PDEs) with a reaction term on the half line, where control arises as a time-dependent reaction coefficient and constraints are…
In this paper, we present a new control model for optimizing pressure and water quality operations in water distribution networks. Our formulation imposes a set of time-coupling constraints to manage temporal pressure variations, which are…
A data-driven parametric model order reduction (MOR) method using a deep artificial neural network is proposed. The present network, which is the least-squares hierarchical variational autoencoder (LSH-VAE), is capable of performing…
Chlorine is a widely used disinfectant and proxy for water quality (WQ) monitoring in water distribution networks (WDN). Chlorine-based WQ regulation and control aims to maintain pathogen-free water. Chlorine residual evolution within WDN…
This paper deals with the joint reduction of the number of dynamic and algebraic states of a nonlinear differential-algebraic equation (NDAE) model of a power network. The dynamic states depict the internal states of generators, loads,…
We propose a new reduced order modeling strategy for tackling parametrized Partial Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in which the constraint is given by mass conservation. Our approach…
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…
Control of water distribution networks (WDNs) can be represented by an optimization problem with hydraulic models describing the nonlinear relationship between head loss, water flow, and demand. The problem is difficult to solve due to the…
We present an exact dimensional reduction for high-dimensional dynamical systems composed of $N$ identical dynamical units governed by quasi-linear ordinary differential equations (ODEs) of order $M$. In these systems, each unit follows a…
We propose a novel type of nonlinear solver acceleration for systems of nonlinear partial differential equations (PDEs) that is based on online/adaptive learning. It is applied in the context of multiphase flow in porous media. The proposed…
We develop a complementarity-constrained nonlinear optimization model for the time-dependent control of district heating networks. The main physical aspects of water and heat flow in these networks are governed by nonlinear and hyperbolic…
Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…
Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
Model discovery aims to uncover governing differential equations of dynamical systems directly from experimental data. Benchmarking such methods is essential for tracking progress and understanding trade-offs in the field. While prior…
In order to investigate correspondences between 3D shapes, many methods rely on a feature descriptor which is invariant under almost isometric transformations. An interesting class of models for such descriptors relies on partial…