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While flow optimization has been extensively studied in the continuum regime, its extension to rarefied gas flows remains less explored. Here, based on the Boltzmann model equation, an adjoint topology optimization method is employed to…

Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…

In this paper, we present a general framework for efficiently computing diverse solutions to combinatorial optimization problems. Given a problem instance, the goal is to find $k$ solutions that maximize a specified diversity measure; the…

Optimal design of water distribution networks, which are governed by a series of linear and nonlinear equations, has been extensively studied in the past decades. Due to their NP-hardness, methods to solve the optimization problem have…

The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one and two-body reduced density matrices (RDM) instead of many-electron…

We study topology optimization governed by the incompressible Navier-Stokes flows using a phase field model. Novel stabilized semi-implicit schemes for the gradient flows of Allen-Cahn and Cahn-Hilliard types are proposed for solving the…

We develop a method for multidimensional optimisation using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimising functional correspond to fixed points of the…

We suggest a global perspective on dynamic network flow problems that takes advantage of the similarities to port-Hamiltonian dynamics. Dynamic minimum cost flow problems are formulated as open-loop optimal control problems for general…

We propose a general algorithm to enumerate all solutions of a zero-dimensional polynomial system with respect to a given cost function. The algorithm is developed and is used to study a polynomial system obtained by discretizing the steady…

We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed…

We consider general, steady, balanced flows of a commodity over a network where an instance of the network flow is characterized by edge flows and nodal potentials. Edge flows in and out of a node are assumed to be conserved, thus…

We consider a dissipative flow network that obeys the standard linear nodal flow conservation, and where flows on edges are driven by potential difference between adjacent nodes. We show that in the case when the flow is a monotonically…

Dual descent methods are commonly used to solve network flow optimization problems, since their implementation can be distributed over the network. These algorithms, however, often exhibit slow convergence rates. Approximate Newton methods…

Many power system operation and planning problems use the DC power flow approximation to address computational challenges from the nonlinearity of the AC power flow equations. The DC power flow simplifies the AC power flow equations to a…

A variety of shooting methods for computing fully discrete time-periodic solutions of partial differential equations, including Newton-Krylov and optimization-based methods, are discussed and used to determine the periodic, compressible,…

The solution of potential-driven steady-state flow in large networks is required in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear equations depends…

In this article we challenge the claim that the previously proposed variational method to obtain flow solutions for generalized Newtonian fluids in circular tubes and plane slits is exact only for power law fluids. We also defend the…

We introduce a derivative-free global optimization algorithm that efficiently computes minima for various classes of one-dimensional functions, including non-convex, and non-smooth functions.This algorithm numerically approximates the…

Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…

The accelerated method in solving optimization problems has always been an absorbing topic. Based on the fixed-time (FxT) stability of nonlinear dynamical systems, we provide a unified approach for designing FxT gradient flows (FxTGFs).…