Related papers: Hierarchical Network Partitioning for Solution of …
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
We prove the well-posedness of entropy solutions for a wide class of nonlocal transport equations with nonlinear mobility in one spatial dimension. The solution is obtained as the limit of approximations constructed via a deterministic…
We analyze transport on a graph with multiple constraints and where the weight of the edges connecting the nodes is a dynamical variable. The network dynamics results from the interplay between a nonlinear function of the flow, dissipation,…
Applications such as megaregional planning require efficient methods for solving traffic assignment problems (TAPs) on large-scale networks. We propose a decomposition heuristic that generates approximate TAP solutions by partitioning the…
It is crucial for maintaining the security of supply that transmission networks continue to operate even if a single line fails. Modeling $\mathcal{N} - 1$ security in power system capacity expansion problems introduces many extra…
Boolean networks have been used successfully in modeling biological networks and provide a good framework for theoretical analysis. However, the analysis of large networks is not trivial. In order to simplify the analysis of such networks,…
We are concerned with the simulation and optimization of large-scale gas pipeline systems in an error-controlled environment. The gas flow dynamics is locally approximated by sufficiently accurate physical models taken from a hierarchy of…
In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally…
Many problems in applied mathematics require root finding algorithms. Unfortunately, root finding methods have limitations. Firstly, regarding the convergence, there is a trade-off between the size of it's domain and it's rate. Secondly the…
Sequential implicit (SI) formulations are gaining increasing interest due to their ability to decouple reservoir simulation problems into distinct flow and transport subproblems, allowing for the use of specialized solvers tailored to each.…
This letter presents a novel non-iterative power flow solution for radial distribution systems. In the pursuit of a linear power flow solution that seamlessly integrates into other power system operations, an approximate solution via…
The classical optimal power flow problem optimizes the power flow in a power network considering the associated flow and operating constraints. In this paper, we investigate optimal power flow in the context of utility-maximizing demand…
The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…
Network compression is crucial to making the deep networks to be more efficient, faster, and generalizable to low-end hardware. Current network compression methods have two open problems: first, there lacks a theoretical framework to…
In this paper, we propose a solution to the distributed topology formation problem for large-scale sensor networks with multi-source multicast flows. The proposed solution is based on game-theoretic approaches in conjunction with network…
Developing a unified small-signal model for modern, large-scale power systems that remains accurate across a wide range of operating ranges presents a formidable challenge. Traditional methods, spanning mechanistic modeling, modal…
We study the problem of minimizing a sum of convex objective functions where the components of the objective are available at different nodes of a network and nodes are allowed to only communicate with their neighbors. The use of…
Large-scale cyber-physical systems require that control policies are distributed, that is, that they only rely on local real-time measurements and communication with neighboring agents. Optimal Distributed Control (ODC) problems are,…
Hierarchical learning algorithms that gradually approximate a solution to a data-driven optimization problem are essential to decision-making systems, especially under limitations on time and computational resources. In this study, we…
This paper considers unbalanced multiphase distribution systems with generic topology and different load models, and extends the Z-bus iterative load-flow algorithm based on a fixed-point interpretation of the AC load-flow equations.…