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Area of Science:

  • Complex Systems Science
  • Network Science
  • Computational Science

Background:

  • Reconstructing complex networks and predicting their dynamics are challenging due to incomplete information.
  • Real-world applications often suffer from missing data, hindering accurate analysis.

Purpose of the Study:

  • To develop a unified deep-learning framework for network reconstruction and dynamic prediction with incomplete data.
  • To improve the accuracy of inferring network structures and estimating unobserved states.

Main Methods:

  • A collaborative deep-learning framework with three modules: network inference, state estimation, and dynamical learning.
  • An alternating parameter updating strategy to enhance inference and prediction.
  • Validation on synthetic and empirical datasets, including influenza and PM2.5 data.

Main Results:

  • The proposed framework significantly outperforms baseline methods in network inference and dynamical prediction.
  • A reciprocal relationship was observed, where improved network inference enhances dynamical prediction accuracy, and vice versa.
  • Demonstrated superior performance on real-world influenza and PM2.5 datasets.

Conclusions:

  • The unified deep-learning framework effectively addresses challenges of incomplete data in network science.
  • The developed method offers a robust approach for reconstructing complex networks and predicting their dynamics.
  • The findings highlight the synergistic relationship between network structure inference and dynamical prediction.