FlowSDE: a flow-matching-based SDE framework for predicting state transitions

Area of Science:

• Complex Systems Dynamics
• Computational Neuroscience
• Statistical Physics

Background:

• Stochastic differential equations (SDEs) model diverse phenomena, from chemical reactions to neural dynamics.
• Identifying critical state transitions in complex systems is crucial for understanding their behavior.
• Traditional early warning signals can be unreliable under non-stationary or noisy conditions.

Purpose of the Study:

• To introduce FlowSDE, a novel framework for learning SDEs and modeling non-equilibrium dynamics.
• To identify critical state transitions and capture system evolution using data-driven representations.
• To enhance the accuracy and robustness of transition prediction in complex systems.

Main Methods:

• Utilizing a flow-matching-based SDE learning framework (FlowSDE).
• Integrating conditional flow matching with physical constraints to model system dynamics.
• Comparing FlowSDE with traditional early warning signals (variance, lag-1 autocorrelation) in epileptor models.

Main Results:

• FlowSDE accurately uncovers latent transition points and predicts transitions in various dynamical systems.
• The framework captures mean-field potentials and provides data-driven representations of system evolution.
• FlowSDE demonstrates robustness and superior performance compared to traditional methods, especially under non-stationary or noisy conditions.

Conclusions:

• FlowSDE provides an interpretable, flexible, and robust method for characterizing and forecasting complex dynamics.
• The framework has broad applications in neuroscience and other fields requiring analysis of critical transitions.
• This approach offers improved accuracy and reliability for understanding and predicting system state changes.