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FlowGEN: A Generative Model for Flow Graphs

Published: 14 August 2022 Publication History

Abstract

Flow graphs capture the directed flow of a quantity of interest (e.g., water, power, vehicles) being transported through an underlying network. Modeling and generating realistic flow graphs is key in many applications in infrastructure design, transportation, and biomedical and social sciences. However, they pose a great challenge to existing generative models due to a complex dynamics that is often governed by domain-specific physical laws or patterns. We introduce FlowGEN, an implicit generative model for flow graphs, that learns how to jointly generate graph topologies and flows with diverse dynamics directly from data using a novel (flow) graph neural network. Experiments show that our approach is able to effectively reproduce relevant local and global properties of flow graphs, including flow conservation, cyclic trends, and congestion around hotspots.

References

[1]
Réka Albert and Albert-László Barabási. Statistical mechanics of complex networks. Reviews of modern physics, 74(1):47, 2002.
[2]
Martin Arjovsky, Soumith Chintala, and Léon Bottou. Wasserstein generative adversarial networks. In ICML, 2017.
[3]
Aleix Bassolas et al. Hierarchical organization of urban mobility and its connection with city livability. Nature communications, 10(1):1--10, 2019.
[4]
Mikhail Belkin and Partha Niyogi. Laplacian eigenmaps for dimensionality reduction and data representation. Neural computation, 15(6):1373--1396, 2003.
[5]
Aleksandar Bojchevski, Oleksandr Shchur, Daniel Zügner, and Stephan Günnemann. Netgan: Generating graphs via random walks. In ICML, 2018.
[6]
Alberto Bressan et al. Flows on networks: recent results and perspectives. EMS Surveys in Mathematical Sciences, 1(1):47--111, 2014.
[7]
Marc Brockschmidt et al. Generative code modeling with graphs. In ICLR, 2019.
[8]
Francesco Calabrese, Giusy Di Lorenzo, et al. Estimating origin-destination flows using mobile phone location data. IEEE Pervasive Computing, (4):36--44, 2011.
[9]
Matteo Chinazzi et al. The effect of travel restrictions on the spread of the 2019 novel coronavirus (covid-19) outbreak. Science, 368(6489):395--400, 2020.
[10]
Hang Chu, Daiqing Li, et al. Neural turtle graphics for modeling city road layouts. In ICCV, 2019.
[11]
Hanjun Dai et al. Scalable deep generative modeling for sparse graphs. In ICML, 2020.
[12]
Hermann W Dommel and William F Tinney. Optimal power flow solutions. IEEE Transactions on power apparatus and systems, (10):1866--1876, 1968.
[13]
Florian Dörfler et al. Electrical networks and algebraic graph theory: Models, properties, and applications. Proceedings of the IEEE, 106(5):977--1005, 2018.
[14]
Florian Dörfler and Francesco Bullo. Synchronization in complex networks of phase oscillators: A survey. Automatica, 50(6):1539--1564, 2014.
[15]
Paul Erdös and Alfréd Rényi. On random graphs. Publicationes mathematicae, 6(26):290--297, 1959.
[16]
M. Garavello and B. Piccoli. Traffic Flow on Networks: Conservation Laws Model. AIMS series on applied mathematics. AIMS, 2006.
[17]
Justin Gilmer, Samuel S Schoenholz, Patrick F Riley, Oriol Vinyals, and George E Dahl. Neural message passing for quantum chemistry. In ICML, 2017.
[18]
Ian Goodfellow et al. Generative adversarial nets. In NeurIPS, 2014.
[19]
Nikhil Goyal et al. Graphgen: a scalable approach to domain-agnostic labeled graph generation. In Proceedings of The Web Conference 2020, 2020.
[20]
Aditya Grover, Aaron Zweig, and Stefano Ermon. Graphite: Iterative generative modeling of graphs. In ICML, 2019.
[21]
Ishaan Gulrajani et al. Improved training of wasserstein gans. In NeurIPS, 2017.
[22]
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In CVPR, 2016.
[23]
D.J. Hill and Guanrong Chen. Power systems as dynamic networks. In 2006 IEEE International Symposium on Circuits and Systems, 2006.
[24]
Jonas Hörsch et al. Pypsa-eur: An open optimisation model of the european transmission system. Energy strategy reviews, 22:207--215, 2018.
[25]
Junteng Jia, Michael T Schaub, Santiago Segarra, and Austin R Benson. Graph-based semi-supervised & active learning for edge flows. In KDD, 2019.
[26]
Wengong Jin, Regina Barzilay, and Tommi Jaakkola. Junction tree variational autoencoder for molecular graph generation. In ICML, 2018.
[27]
Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
[28]
Diederik P Kingma and Max Welling. Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114, 2013.
[29]
Ryan Kinney et al. Modeling cascading failures in the north american power grid. The European Physical Journal B-Condensed Matter and Complex Systems, 46(1):101--107, 2005.
[30]
Thomas N Kipf and Max Welling. Variational graph auto-encoders. NIPS Workshop on Bayesian Deep Learning, 2016.
[31]
Thomas N Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. In ICLR, 2017.
[32]
Yujia Li et al. Learning deep generative models of graphs. arXiv preprint arXiv:1803.03324, 2018.
[33]
Yujia Li, Daniel Tarlow, Marc Brockschmidt, and Richard Zemel. Gated graph sequence neural networks. In ICLR, 2016.
[34]
Renjie Liao et al. Efficient graph generation with graph recurrent attention networks. In NeurIPS, 2019.
[35]
Jenny Liu, Aviral Kumar, Jimmy Ba, Jamie Kiros, and Kevin Swersky. Graph normalizing flows. In NeurIPS, 2019.
[36]
Mark EJ Newman. Mixing patterns in networks. Physical review E, 2003.
[37]
Chenhao Niu et al. Permutation invariant graph generation via score-based generative modeling. In AISTATS, 2020.
[38]
J. D. Orth, I. Thiele, and B. Ø. Palsson. What is flux balance analysis? Nat Biotechnol, 28(3):245--248, Mar 2010.
[39]
Chence Shi et al. Graphaf: a flow-based autoregressive model for molecular graph generation. In ICLR, 2020.
[40]
Arlei Silva et al. Combining physics and machine learning for network flow estimation. ICLR, 2021.
[41]
Martin Simonovsky and Nikos Komodakis. Graphvae: Towards generation of small graphs using variational autoencoders. In ICANN, 2018.
[42]
Yang Song and Stefano Ermon. Generative modeling by estimating gradients of the data distribution. In NeurIPS, 2019.
[43]
Akash Srivastava et al. Veegan: Reducing mode collapse in gans using implicit variational learning. In NeurIPS, 2017.
[44]
Lucas Theis, Aäron van den Oord, and Matthias Bethge. A note on the evaluation of generative models. arXiv preprint arXiv:1511.01844, 2015.
[45]
Petar Velivc ković et al. Graph attention networks. In ICLR, 2017.
[46]
Duncan J Watts and Steven H Strogatz. Collective dynamics of 'small-world'networks. Nature, 393(6684):440, 1998.
[47]
Carl Yang et al. Conditional structure generation through graph variational generative adversarial nets. In NeurIPS, 2019.
[48]
Jiaxuan You et al. Graphrnn: Generating realistic graphs with deep auto-regressive models. In ICML, 2018.
[49]
Xun Zheng et al. Dags with no tears: Continuous optimization for structure learning. In NeurIPS, 2018.

Cited By

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  • (2024)Pluvial flood emulation with hydraulics-informed message passingProceedings of the 41st International Conference on Machine Learning10.5555/3692070.3693011(23367-23390)Online publication date: 21-Jul-2024

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cover image ACM Conferences
KDD '22: Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining
August 2022
5033 pages
ISBN:9781450393850
DOI:10.1145/3534678
This work is licensed under a Creative Commons Attribution International 4.0 License.

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Published: 14 August 2022

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Author Tags

  1. flow networks
  2. graph generative models
  3. representation learning

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  • (2024)Pluvial flood emulation with hydraulics-informed message passingProceedings of the 41st International Conference on Machine Learning10.5555/3692070.3693011(23367-23390)Online publication date: 21-Jul-2024

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