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The stable operation of gas networks is an important optimization target. While for this task commonly finite volume methods are used, we introduce a new finite difference approach. With a summation by part formulation for the spatial…
The optimal power flow (OPF) problem minimizes power system operating cost subject to both engineering and network constraints. With the potential to find global solutions, significant research interest has focused on convex relaxations of…
The majority of overland transport needs for crude petroleum and refined petroleum products are met using pipelines. Numerous studies have developed optimization methods for design of these systems in order to minimize construction costs…
Physical dynamic networks most commonly consist of interconnections of physical components that can be described by diffusive couplings. These diffusive couplings imply that the cause-effect relationships in the interconnections are…
This paper considers the network flow stabilization problem in power systems and adopts an output regulation viewpoint. Building upon the structure of a heterogeneous port-Hamiltonian model, we integrate network aspects and develop a…
A strongly polynomial algorithm is developed for finding an integer-valued feasible $st$-flow of given flow-amount which is decreasingly minimal on a specified subset $F$ of edges in the sense that the largest flow-value on $F$ is as small…
Recent development of techniques that improve the convergence properties of power flow simulation have been demonstrated to facilitate scaling to large system sizes (80k+ buses). However, the problem remains to reliably identify cases that…
This paper proves that non-convex quadratically constrained quadratic programs can be solved in polynomial time when their underlying graph is acyclic, provided the constraints satisfy a certain technical condition. When this condition is…
We consider integer programming problems with bounded general-integer variables belonging to the general class of network flow problems. For those, we computationally investigate the effect on mixed-integer linear programming (MIP) solvers…
We consider a network design problem with random arc capacities and give a formulation with a probabilistic capacity constraint on each cut of the network. To handle the exponentially-many probabilistic constraints a separation procedure…
Many complex systems demand manifold resources to be supplied from distinct channels to function properly, i.e, water, gas, and electricity for a city. Here, we study a model for viability of such systems demanding more than one type of…
High penetration of renewable energy sources and the increasing share of stochastic loads require the explicit representation of uncertainty in tools such as the optimal power flow (OPF). Current approaches follow either a linearized…
Generative Flow Networks (GFlowNets) are recently proposed models for learning stochastic policies that generate compositional objects by sequences of actions with the probability proportional to a given reward function. The central problem…
Power flow solvable boundary plays an important role in contingency analysis, security assessment, and planning processes. However, to construct the real solvable boundary in multidimensional parameter space is burdensome and time…
In this paper we propose a general methodology for the optimal automatic routing of spatial pipelines motivated by a recent collaboration with Ghenova, a leading Naval Engineering company. We provide a minimum cost multicommodity network…
We consider two different variational models of transport networks, the so-called branched transport problem and the urban planning problem. Based on a novel relation to Mumford-Shah image inpainting and techniques developed in that field,…
The Max-Flow Min-Cut theorem is the classical duality result for the Max-Flow problem, which considers flow of a single commodity. We study a multiple commodity generalization of Max-Flow in which flows are composed of real-valued k-vectors…
We introduce and investigate reroutable flows, a robust version of network flows in which link failures can be mitigated by rerouting the affected flow. Given a capacitated network, a path flow is reroutable if after failure of an arbitrary…
We introduce a methodology to study the possible matter flows of an ecosystem defined by observational biomass data and realistic biological constraints. The flows belong to a polyhedron in a multi dimensional space making statistical…
We propose a unified approach to the formal long-wave reduction of several fluid models for thin-layer incompressible homogeneous flows driven by a constant external force like gravity. The procedure is based on a mathematical coherence…