Piecewise integrable neural network: An interpretable chaos identification framework

Area of Science:

• Computational physics
• Nonlinear dynamics
• Machine learning

Background:

• Artificial neural networks (ANNs) are powerful tools for modeling complex systems, including chaotic dynamics.
• However, the 'black box' nature of ANNs often hinders interpretability, limiting their application in scientific discovery.

Purpose of the Study:

• To develop an interpretable neural network framework for modeling chaotic dynamics.
• To recover the underlying differential equations and their integrals governing chaotic regimes.

Main Methods:

• Reframing chaotic dynamics into piecewise models using a novel neural network architecture.
• Implementing discontinuous formulations to define switching laws representative of bifurcation mechanisms.

Main Results:

• The proposed framework successfully recovers the system of differential equations describing the chaotic regime.
• The primitive (or integral) of the system was also recovered, providing deeper insights into the chaotic dynamics.

Conclusions:

• This interpretable neural network approach offers a new way to analyze and understand chaotic systems.
• The method bridges the gap between data-driven modeling and fundamental physical principles.