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Using Domain Decomposition (DD) algorithm on non--overlapping domains, we compare couplings of different discretisation models, such as Finite Element (FEM) and Reduced Order (ROM) models for separate subcomponents. In particular, we…
The DC Optimal Power Flow (DC-OPF) problem is fundamental to power system operations, requiring rapid solutions for real-time grid management. While traditional optimization solvers provide optimal solutions, their computational cost…
We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…
We consider the gradient flow of a quadratic non-autonomous energy under monotonicity constraint in time and natural regularity assumptions. We provide first a notion of weak solution, inspired by the theory of curves of maximal slope, and…
Power grid operators typically solve large-scale, nonconvex optimal power flow (OPF) problems throughout the day to determine optimal setpoints for generators while adhering to physical constraints. Despite being at the heart of many OPF…
We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…
Computational fluid dynamics (CFD) is a specialised branch of fluid mechanics that utilises numerical methods and algorithms to solve and analyze fluid-flow problems. One promising avenue to enhance CFD is the use of quantum computing,…
This paper proposes and justifies two globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are…
Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
In the continuum flow regime, the Navier-Stokes equations are usually used for the description of gas dynamics. On the other hand, the Boltzmann equation is applied for the rarefied gas dynamics. Both equations are constructed from modeling…
This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…
Energy distribution networks are crucial for human societies and since they often cover large geographical areas, their physical analysis is challenging. Modeling and simulation can be used to analyze such complex energy networks. In this…
This work aims to control the dynamics of certain non-Newtonian fluids in a bounded domain of $\mathbb{R}^d$, $d=2,3$ perturbed by a multiplicative Wiener noise, the control acts as a predictable distributed random force, and the goal is to…
This paper proposes a convex optimization based method that either locates all real roots of a set of power flow equations or declares no real solution exists in the given area. In the proposed method, solving the power flow equations is…
Many engineered systems, such as energy and transportation infrastructures, are networks governed by non-linear physical laws. A primary challenge for operators of these networks is to achieve optimal utilization while maintaining safety…
Modern vision generators transport a base distribution to data through time-indexed measures, implemented as deterministic flows (ODEs) or stochastic diffusions (SDEs). Despite strong empirical performance, standard flow-matching objectives…
The paper presents a dynamic solution method for dynamic minimum parametric networks flow. The solution method solves the problem for a special parametric dynamic network with linear lower bound functions of a single parameter. Instead…
Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…
We consider a class of optimization problems on the space of probability measures motivated by the mean-field approach to studying neural networks. Such problems can be solved by constructing continuous-time gradient flows that converge to…