Classification and spatiotemporal correlation of dominant fluctuations in complex dynamical systems.

Area of Science:

• Complex Systems Analysis
• Data-Driven Physics
• Multiscale Modeling

Background:

• Complex systems exhibit emergent behaviors from local rearrangements, challenging traditional analysis methods.
• Existing strategies often require system-specific knowledge and lack transferability.
• Understanding local event propagation is crucial for predicting collective phenomena.

Purpose of the Study:

• To present a general, transferable, and agnostic analysis approach for complex dynamical systems.
• To enable detection, classification, and spatiotemporal correlation of local fluctuations.
• To provide insights into system physics without prior knowledge.

Main Methods:

• Utilizing a bivariate combination of Local Environments and Neighbors Shuffling (LENS) and Time-Smooth Overlap of Atomic Positions (TSOAP).
• Analyzing trajectories of constitutive units from simulations or experimental data.
• Focusing on abstract concepts of local fluctuations and their spatiotemporal correlations.

Main Results:

• Demonstrated detection of local fluctuations in multibody dynamical systems.
• Successfully classified fluctuations and correlated them in space and time.
• Revealed insights into the emergence and propagation of local and collective phenomena.

Conclusions:

• The presented data-driven approach offers a general method for analyzing complex systems.
• Applicable to systems with unknown physics, from atomic to macroscopic scales.
• Provides a new perspective for studying diverse physical phenomena.