A available-flow neural network for solving the dynamic groundwater network maximum flow problem

Abstract

The normal operation of infrastructure networks such as groundwater networks maintains people's life and work. Therefore, it is of great significance to estimate the residual flow when these networks are damaged to evaluate their anti-risk ability. This paper abstracts these problems as the damage-network time-varying maximum flow problem (DTMFP), where the arc capacity in the network is set as a time-varying function. Since the water network is subject to electric-driven periodic changes, and the network damage is defined by some arcs or nodes in the network doesn't work at all. Although the existing maximum flow algorithms such as Cai-Sha can solve the time-varying maximum flow problem, the uncertainty of the network topology that suffers from random damage makes it difficult for the existing maximum flow algorithms to solve such problems. The uncertainty of network topology which suffer random damage makes such problems difficult to solve by existing maximum flow algorithms. Therefore, the key to solve DTMFPs is to find the topology of damaged network. In this paper, we propose an available flow neural network (AFNN) algorithm for solving DTMFPs. The idea of the AFNN algorithm is to determine the network topology through the back-information neural networks (BINN) algorithm at first, then obtain the residual maximum flow through the single-path neural networks (SPNN) algorithm. In the BINN algorithm, the departure node is continuously activated for a given time period and sends waves along the network to the destination node. The wave contains arcs which can be activated. The Utah channel impact response wireless sensor network, American north marin water district network and New York road network are used to confirm the effectiveness of the proposed AFNN algorithm.

Concentration Inequalities and Optimal Number of Layers for Stochastic Deep Neural Networks

“…Concentration inequalities for SDNNs have been studied in the context of PAC-Bayes bounds and stochastic gradient descent (SGD) solutions. In particular, in [18] the authors propose the Kronecker Flow, an invertible transformationbased method that generalizes the Kronecker product to a nonlinear formulation, and uses this construction to tighten PAC-Bayesian bounds. They show that the KL divergence in the PAC-Bayes bound can be estimated with high probability (they give a Hoeffding-type concentration result), and demonstrate the generalization gap can be further reduced and explained by leveraging structure in parameter space.…”