Information-driven transitions in projections of underdamped dynamics

Area of Science:

• Dynamical systems theory
• Information theory
• Statistical physics

Background:

• Low-dimensional representations are crucial for understanding complex systems.
• Underdamped systems are prevalent in various scientific fields.
• Current methods for model reduction may not fully capture system dynamics.

Purpose of the Study:

• To develop an optimal low-dimensional model for underdamped systems using information projections.
• To investigate the emergence of transitions in model parameters during information minimization.
• To assess the implications of these findings for general inference approaches.

Main Methods:

• Utilizing information projections to construct dynamical models.
• Analyzing spatial trajectories of paradigmatic underdamped systems.
• Minimizing information loss to identify optimal model parameters.

Main Results:

• An optimal model was derived that maximally preserves information from observed spatial trajectories.
• A discontinuous transition in optimal model parameters was observed, driven by information loss minimization.
• The findings highlight fundamental properties of effective dynamical representations.

Conclusions:

• Information projections offer a powerful tool for creating accurate low-dimensional models.
• The observed discontinuous transition presents challenges and insights for inference methods.
• This work has broad implications for fields including biophysics and dimensionality reduction.