Identifying stochastic dynamics from non-sequential data (DyNoSeD)

Area of Science:

• * Computational Biology
• * Systems Biology
• * Data Science

Background:

• * Inferring stochastic dynamics is crucial for understanding complex systems.
• * Standard time-series methods fail with unordered, non-sequential data, common in real-world applications.
• * Limited state-space sampling further complicates dynamic system identification.

Purpose of the Study:

• * Introduce DyNoSeD (Identifying Dynamics from Non-Sequential Data), a first-principles framework.
• * Enable dynamical parameter inference from non-sequential data by minimizing Fokker-Planck residuals.
• * Provide robust methods for system identification even with restricted or unordered data.

Main Methods:

• * Developed two complementary routes: a local route for region-restricted data and a global route using kernel Stein discrepancy.
• * Utilized Fokker-Planck equation residuals for parameter inference.
• * Applied gradient-based optimization for general non-affine parameterizations.

Main Results:

• * Established conditions for parameter uniqueness and derived sensitivity analysis for affine dynamics.
• * Successfully recovered parameters for a stochastic Lorenz system using both local and global routes.
• * Identified a gene-regulatory network interaction matrix from unordered steady-state samples using the global route.

Conclusions:

• * DyNoSeD offers two novel, first-principles routes for system identification from non-sequential data.
• * The framework effectively links data, density, and stochastic dynamics.
• * DyNoSeD provides a powerful tool for analyzing complex systems with limited or non-sequential measurements.