Curriculum learning for data-driven modeling of dynamical systems.

Area of Science:

• Complex systems modeling
• Machine learning applications
• Dynamical systems theory

Background:

• Predicting complex system temporal behavior is crucial but hindered by inaccessible or computationally expensive governing equations.
• Data-driven modeling using machine learning, particularly deep neural networks, is common but often overlooks model generalizability and data impact.
• Existing approaches frequently rely on prior physics knowledge, limiting broader applicability.

Purpose of the Study:

• To systematically apply curriculum learning for enhanced data-driven modeling of complex dynamical systems.
• To investigate the impact of training data quantity and structure on model generalizability and long-term prediction accuracy.
• To leverage ergodic theory and entropy for informed dataset design in machine learning models.

Main Methods:

• Implementation of a curriculum learning strategy, organizing training data from simple to complex samples.
• Application of ergodic theory to determine sufficient data for a priori model guarantees.
• Utilizing dataset entropy as a complexity metric for informed training set design.

Main Results:

• Curriculum learning significantly improves model generalizability and convergence for complex dynamical systems.
• Analysis of training set structure and quantity, guided by ergodic theory, impacts long-term prediction fidelity.
• Informed dataset design based on entropy analysis enhances model performance and provides insights into data requirements.

Conclusions:

• Curriculum learning offers a systematic approach to improve data-driven modeling of complex dynamical systems.
• Dataset design, informed by complexity metrics like entropy and theoretical insights, is critical for effective machine learning models.
• This work provides a framework for guaranteeing faithful physical system models and optimizing data selection for improved generalizability.