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Autonomous inference of complex network dynamics from incomplete and noisy data

Nature Computational Science volume 2, pages 160–168 (2022)Cite this article

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A Publisher Correction to this article was published on 29 April 2022

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A preprint version of the article is available at arXiv.

Abstract

The availability of empirical data that capture the structure and behaviour of complex networked systems has been greatly increased in recent years; however, a versatile computational toolbox for unveiling a complex system’s nodal and interaction dynamics from data remains elusive. Here we develop a two-phase approach for the autonomous inference of complex network dynamics, and its effectiveness is demonstrated by the tests of inferring neuronal, genetic, social and coupled oscillator dynamics on various synthetic and real networks. Importantly, the approach is robust to incompleteness and noises, including low resolution, observational and dynamical noises, missing and spurious links, and dynamical heterogeneity. We apply the two-phase approach to infer the early spreading dynamics of influenza A flu on the worldwide airline network, and the inferred dynamical equation can also capture the spread of severe acute respiratory syndrome and coronavirus disease 2019. These findings together offer an avenue to discover the hidden microscopic mechanisms of a broad array of real networked systems.

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Fig. 1: Overview of the two-phase inference approach.
Fig. 2: Inferring FHN neuronal network dynamics on synthetic and real topologies.
Fig. 3: Inference accuracy for other four typical nonlinear network dynamics.
Fig. 4: Inferrability of network dynamics.
Fig. 5: Inference robustness against incompleteness and noises.
Fig. 6: Inference of early spreading dynamics from empirical data.

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Data availability

Source data are provided with this paper. The empirical network data include C. elegans connectome54,55,56, the mushroom-body region of Drosophila57, Northern Europe power grid58, the US power grid59, Advogato social network60 retrieved from https://networkrepository.com/ and worldwide airline network data retrieved from OpenFlights (https://openflights.org/data.html). The empirical data of epidemic spreading include daily reported numbers of H1N1 and SARS cases available at Kaggle (https://www.kaggle.com/lnunes/a-brief-comparative-study-of-epidemics/data) and the daily reported numbers of COVID-19 cases61.

Code availability

All the source codes are publicly available at the Code Ocean capsule62.

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Acknowledgements

T.-T.G. and G.Y. are supported by the National Key Research and Development Program of China (grant no. 2021ZD0204500), National Natural Science Foundation of China (grant nos. 12161141016 and 11875043), Shanghai Municipal Science and Technology Major Project (grant no. 2021SHZDZX0100), Shanghai Municipal Commission of Science and Technology Project (grant nos. 18ZR1442000 and 19511132101) and Fundamental Research Funds for the Central Universities. We are also grateful for the helpful discussion with B. Barzel, J. Moore, X. Ru and T. Li.

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Authors and Affiliations

  1. MOE Key Laboratory of Advanced Micro-Structured Materials and School of Physics Science and Engineering, Tongji University, Shanghai, People’s Republic of China

    Ting-Ting Gao & Gang Yan

  2. Frontiers Science Center for Intelligent Autonomous Systems, Tongji University, Shanghai, People’s Republic of China

    Ting-Ting Gao & Gang Yan

  3. Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Shanghai, People’s Republic of China

    Gang Yan

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  1. Ting-Ting Gao
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  2. Gang Yan
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Contributions

G.Y. conceived the research. G.Y. and T.-T.G. designed the research. T.-T.G. performed the research. T.-T.G. and G.Y. analysed the results. G.Y. and T.-T.G. wrote the manuscript.

Corresponding author

Correspondence to Gang Yan.

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Peer review information

Nature Computational Science thanks Matthieu Gilson and the other, anonymous reviewer(s) for their contribution to the peer review of this work. Handling editor: Jie Pan, in collaboration with the Nature Computational Science team.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–20, Sections I–VI and Tables 1–5.

Source data

Source Data Fig. 1

True and inferred trajectories data.

Source Data Fig. 2

Unprocessed inferred results, time-series data and trajectories data.

Source Data Fig. 3

Unprocessed inferred results, time-series data and trajectories data.

Source Data Fig. 4

Statistical source data and trajectories data.

Source Data Fig. 5

Statistical source data.

Source Data Fig. 6

Raw empirical data and time-series data.

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Gao, TT., Yan, G. Autonomous inference of complex network dynamics from incomplete and noisy data. Nat Comput Sci 2, 160–168 (2022). https://doi.org/10.1038/s43588-022-00217-0

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