Graph Neural Modeling of Network Flows
Victor-Alexandru Darvariu, Stephen Hailes, Mirco Musolesi
TL;DR
This paper introduces PEW, a novel graph neural network architecture for network flow problems, demonstrating its effectiveness in internet flow routing and analyzing the impact of graph structure on performance.
Contribution
The paper proposes PEW, a new graph learning architecture with per-edge parametrization, and provides extensive evaluation and analysis of graph structure effects on routing performance.
Findings
PEW outperforms architectures with global message functions.
MLP is competitive with standard graph architectures.
Graph structure significantly influences predictive performance.
Abstract
Network flow problems, which involve distributing traffic such that the underlying infrastructure is used effectively, are ubiquitous in transportation and logistics. Among them, the general Multi-Commodity Network Flow (MCNF) problem concerns the distribution of multiple flows of different sizes between several sources and sinks, while achieving effective utilization of the links. Due to the appeal of data-driven optimization, these problems have increasingly been approached using graph learning methods. In this paper, we propose a novel graph learning architecture for network flow problems called Per-Edge Weights (PEW). This method builds on a Graph Attention Network and uses distinctly parametrized message functions along each link. We extensively evaluate the proposed solution through an Internet flow routing case study using Service Provider topologies and routing schemes.…
Peer Reviews
Decision·Submitted to ICLR 2024
1. The paper is motivated by a real problem in flow networks, which is ubiquitous in communications, transportation and logistics. This potentially makes this work relevant to a wider audience, e.g., the communication networks community. 2. The main observation behind PEW is meaningful. One expects that edges cannot play the same role in the underlying flow network, so that we cannot uniformly aggregate the messages received along each edge. The fact that the proposed methodology uses a differen
1. The ML/AI contribution seems to be rather limited. Using a different message function per edge as opposed to identical message functions across all edges is meaningful in the context of flow networks, but the novelty is rather low otherwise. The PEW architecture is a variation of the across-relation variant of relational GATS, so the proposed architecture cannot be viewed as a novel contribution of this work. 2. I am not exactly clear what the motivation behind this paper is. The authors des
The paper proposes a novel and simple modification to graph neural networks for network flow prediction problems by using per-edge weight matrices. The writing is mostly clear and easy to follow. Extensive experiments are presented. The analyses provide valuable insights.
Regarding PEW: - Limitation for handing diverse topologies. Graphs are inherently dynamic and can have varying sizes and structures, and GNNs are typically designed with the flexibility to handle that. It is unclear to me how can PEW handle graphs with varying sizes and structures. Do we have to train a respective PEW-GNN for diverse real-world graph topologies? Is there a solid reason for just overfitting a specific topology? - Variance to node permutation. One importance feature a GNN should
- The experimental evaluation of the proposed model is thorough and convincing. Several different network topologies are considered and also several demand matrices are constructed which led to a very large number of training runs. - The proposed PEW approach outperforms the baseline models on most datasets. On some datasets the difference in performance between PEW and the baselines is significant. - The presentation is clear and the paper is easy to read.
- The proposed method assumes that there is a single network topology which is static and does not change. This suggests that a different model needs to be trained on each network topology and also that a model trained on one topology cannot generalize to other topologies. This renders the proposed approach impractical for several applications. - Another weakness of the work (which is also discussed in section 6) is that the number of parameters of the proposed model depends on the number of ed
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Taxonomy
TopicsNeural Networks and Applications
Methodstravel james