Pareto-based optimization of sparse dynamical systems.

Area of Science:

• Physical Sciences
• Computational Science
• Chemical Engineering

Background:

• Sparse data-driven approaches approximate physical laws using parsimonious equations.
• Existing methods often rely on pre-defined libraries of basis functions, which can be difficult to optimize.
• Discovering optimal basis functions is crucial for promoting sparsity but challenging to determine a priori.

Purpose of the Study:

• To develop an alternative data-driven approach that optimizes the library of functions itself while enforcing sparsity.
• To evaluate model robustness using both goodness-of-fit and residual distribution analysis.
• To demonstrate the application of this method for deriving microkinetic equations from experimental data.

Main Methods:

• Implementing a novel approach that optimizes the library of functions alongside sparsity.
• Utilizing a multi-objective genetic algorithm (NSGA-II) to generate a Pareto front of optimal models.
• Assessing model performance based on fit quality and statistical properties of residuals.

Main Results:

• Successfully optimized the library of functions, leading to sparser and more accurate governing equations.
• Demonstrated robustness by analyzing the statistical distribution of residuals against data noise.
• Generated a set of optimal models via NSGA-II, providing a systematic approach to model selection.

Conclusions:

• The proposed method offers a powerful alternative to fixed library approaches in sparse data-driven modeling.
• This technique effectively derives microkinetic equations from experimental data, advancing scientific discovery.
• Optimizing the function library alongside sparsity provides a more comprehensive and robust model discovery process.