Related papers: Hierarchical Network Partitioning for Solution of …
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 neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural…
Application of nonlinearity continuation method to numerical solution of steady-state groundwater flow in variably saturated conditions is presented. In order to solve the system of nonlinear equations obtained by finite volume…
The problem of minimizing a sum of local convex objective functions over a networked system captures many important applications and has received much attention in the distributed optimization field. Most of existing work focuses on…
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…
Load flow analysis is a fundamental technique used by electrical engineers to simulate and evaluate power system behavior under steady-state conditions. It enables efficient operation and control by determining how active and reactive power…
State-of-the-art data flow systems such as TensorFlow impose iterative calculations on large graphs that need to be partitioned on heterogeneous devices such as CPUs, GPUs, and TPUs. However, partitioning can not be viewed in isolation.…
We develop a randomized Newton's method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton's method randomly chooses equations from the overdetermined nonlinear…
To compute models for Water Distribution Networks (WDN), a large system of non-linear equations needs to be solved. The hallmark algorithm for computing these models is the Newton-Raphson Global Gradient Algorithm (NR-GGA), which solves…
This two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derive a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model is…
The nonlinear programming (NLP) problem to solve distribution-level optimal power flow (D-OPF) poses convergence issues and does not scale well for unbalanced distribution systems. The existing scalable D-OPF algorithms either use…
Inferring network topology from smooth signals is a significant problem in data science and engineering. A common challenge in real-world scenarios is the availability of only partially observed nodes. While some studies have considered…
Recently a distributed algorithm has been proposed for multi-agent networks to solve a system of linear algebraic equations, by assuming each agent only knows part of the system and is able to communicate with nearest neighbors to update…
This paper develops a computationally efficient algorithm which speeds up the probabilistic power flow (PPF) problem by exploiting the inherently low-rank nature of the voltage profile in electrical power distribution networks. The…
Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the…
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…
The aim of this paper is a short survey of models and methods that developed by the authors. These models and methods are used to optimize general networks with nonlinear non-convex restrictions and objectives possessing mixed…
In this work, we explore the state-space formulation of a network process to recover, from partial observations, the underlying network topology that drives its dynamics. To do so, we employ subspace techniques borrowed from system…
This thesis explores a particular class of distributed optimization methods for various separable resource allocation problems, which are of high interest in a wide array of multi-agent settings. A distinctly motivating application for this…
Unsplittable flow problems cover a wide range of telecommunication and transportation problems and their efficient resolution is key to a number of applications. In this work, we study algorithms that can scale up to large graphs and…