SINDy-SA framework

SINDy-SA framework integrates global sensitivity analysis with the sparse identification of nonlinear dynamics (SINDy) to identify parsimonious mathematical models of dynamical systems from experimental data.

Key Features:

• Library construction: Constructs a library of potential terms for candidate dynamical equations.
• Sparse regression: Solves a sparse regression problem to eliminate terms with coefficients below a threshold.
• Global sensitivity analysis (SA): Ranks candidate terms by importance relative to a specified quantity of interest.
• Threshold elimination: Uses SA rankings to remove the need for manual selection of the SINDy threshold.
• Experimental settings: Allows formulation of various experimental settings to tailor analyses to specific contexts.
• Recalibration: Recalibrates each identified model to maintain accuracy across different scenarios.
• Model selection: Applies model selection techniques to identify the most parsimonious and effective models.

Scientific Applications:

• Dynamical system identification: Identification of parsimonious mathematical models for nonlinear dynamical systems from experimental datasets.
• Model discovery and validation: Discovery and validation of data-driven nonlinear models with improved robustness and interpretability.
• Comparative evaluation: Comparative studies against the original SINDy method to assess improvements in accuracy and interpretability.

Methodology:

Construct a library of candidate terms, solve a sparse regression problem to prune coefficients, apply global sensitivity analysis (SA) to rank terms relative to a quantity of interest and eliminate manual thresholding, recalibrate identified models, and perform model selection to choose parsimonious models.