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Learning interpretable dynamics of stochastic complex systems from experimental data.

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We developed a Langevin graph network to infer hidden stochastic differential equations in complex systems. This method accurately models bird flocking and tau pathology spread in brains, enabling new control applications.

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Area of Science:

  • Complex Systems
  • Network Science
  • Computational Neuroscience

Background:

  • Complex systems with numerous interacting components exhibit inherent randomness, best modeled by stochastic differential equations.
  • Inferring these underlying stochastic differential equations from observational data is a significant challenge in analyzing complex systems.
  • Existing methods struggle to accurately capture the dynamics of networked systems from empirical data.

Purpose of the Study:

  • To introduce a novel Langevin graph network approach for learning hidden stochastic differential equations in complex networked systems.
  • To validate the efficacy of the proposed method against state-of-the-art techniques.
  • To apply the approach to real-world systems, including biological and physical phenomena.

Main Methods:

  • Development of a Langevin graph network architecture designed to infer stochastic differential equations.
  • Application of the network to simulated and real-world complex systems.
  • Comparative analysis against five leading inference methods.

Main Results:

  • The Langevin graph network approach significantly outperformed five state-of-the-art methods in inferring stochastic differential equations.
  • Inferred equations for bird flock movement closely matched the second-order Vicsek model, validating its applicability to physical systems.
  • The method successfully uncovered the governing equation for tau pathology diffusion in mouse brains, allowing for early prediction and revealing distinct dynamics.

Conclusions:

  • The Langevin graph network provides a powerful tool for learning interpretable stochastic dynamics in complex systems.
  • This approach offers unprecedented insights into phenomena such as flocking behavior and neurodegenerative disease progression.
  • The findings open new possibilities for the control and management of complex networked systems.