Learning interpretable dynamics of stochastic complex systems from experimental data

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.