Upgrades of Genetic Programming for Data-Driven Modeling of Time Series.

Area of Science:

• Engineering
• Scientific Computing
• Data Science

Background:

• Time series data is prevalent but challenging to interpret and model in scientific and engineering disciplines.
• Genetic programming (GP) offers powerful data-driven knowledge extraction capabilities.

Purpose of the Study:

• To enhance symbolic regression (SR) via GP for improved time series analysis.
• To extract interpretable mathematical models that reveal underlying generative mechanisms, not just for prediction.

Main Methods:

• Proposed several upgrades and refinements to GP, including knowledge representation, genetic operators, and fitness functions.
• Leveraged GP's ability to incorporate prior scientific knowledge and physical constraints.
• Applied to various time series modeling tasks, including autoregressive systems, PDEs, dimensionless quantities, and delayed differential equations.

Main Results:

• Demonstrated improved explorative capabilities of GP for time series investigation.
• Successfully identified models for complex systems, including those with hysteretic behavior and time delays.
• Validated the developed tools through systematic numerical tests and real-world experimental data.

Conclusions:

• The enhanced GP-based SR tools provide a robust framework for empirical time series modeling.
• The approach facilitates the discovery of physically meaningful equations from experimental signals.
• This work advances the ability to model and understand complex dynamic systems through automated equation discovery.