Related papers: Dynamic Flows with Time-Dependent Capacities
The robust minimum cost flow problem under consistent flow constraints (RobMCF$\equiv$) is a new extension of the minimum cost flow (MCF) problem. In the RobMCF$\equiv$ problem, we consider demand and supply that are subject to uncertainty.…
A physics-informed convolutional neural network is proposed to simulate two phase flow in porous media with time-varying well controls. While most of PICNNs in existing literatures worked on parameter-to-state mapping, our proposed network…
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…
This article deals with the consensus problem involving agents with time-varying singularities in the dynamics or communication in undirected graph networks. Existing results provide control laws which guarantee asymptotic consensus. These…
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…
As a first step toward realizing a dynamical system that evolves while spontaneously determining its own rule for time evolution, function dynamics (FD) is analyzed. FD consists of a functional equation with a self-referential term, given…
In this work, physics-informed neural networks are applied to incompressible two-phase flow problems. We investigate the forward problem, where the governing equations are solved from initial and boundary conditions, as well as the inverse…
Modelling the flow in a thin accretion disc like a dynamical system, we analyse the nature of the critical points of the steady solutions of the flow. For the simple inviscid disc there are two critical points, with the outer one being a…
In this study we are interested in the Navier-Stokes-like system for generalized viscous fluids whose viscosity has a power-structure with exponent q. We develop an existence theory of periodic in time weak solutions to the…
This article focuses on a biobjective extension of the maximum flow network interdiction problem, where each arc in the network is associated with two capacity values. Two maximum flows from a source to a sink are to be computed…
Our goal in this paper is to investigate the fluid picture associated with an open large scale storage network of non-reliable file servers with finite capacity. In this storage system, new files can be added and a file with only one copy…
Being fundamentally a non-equilibrium process, synchronization comes with unavoidable energy costs and has to be maintained under the constraint of limited resources. Such resource constraints are often reflected as a finite coupling budget…
The design of flow control systems remains a challenge due to the nonlinear nature of the equations that govern fluid flow. However, recent advances in computational fluid dynamics (CFD) have enabled the simulation of complex fluid flows…
Coflow scheduling models communication requests in parallel computing frameworks where multiple data flows between shared resources need to be completed before computation can continue. In this paper, we introduce Path-based Coflow…
In this note, we revisit the problem of flow approximation properties of neural ordinary differential equations (NODEs). The approximation properties have been considered as a flow controllability problem in recent literature. The neural…
The power consumption of enormous network devices in data centers has emerged as a big concern to data center operators. Despite many traffic-engineering-based solutions, very little attention has been paid on performance-guaranteed energy…
Temporal interaction networks capture the history of activities between entities along a timeline. At each interaction, some quantity of data (money, information, kbytes, etc.) flows from one vertex of the network to another. Flow-based…
In the unsplittable flow problem on a path, we are given a capacitated path $P$ and $n$ tasks, each task having a demand, a profit, and start and end vertices. The goal is to compute a maximum profit set of tasks, such that for each edge…
The unreal high flows may appear on the actually congested links in the result when a monotonically increasing link travel time function of flow volume is adopted in traffic assignment. The fixed link flow results of a static traffic…
Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…