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Updated: Feb 4, 2026

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps

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Published on: February 9, 2017

Identifying stochastic dynamics from non-sequential data (DyNoSeD).

Zhixin Lu¹, Łukasz Kuśmierz¹, Stefan Mihalas^1,2

¹Allen Institute, 615 Westlake Ave. N, Seattle, Washington 98109, USA.

Chaos (Woodbury, N.Y.)

|February 2, 2026

Summary

This summary is machine-generated.

We developed DyNoSeD, a novel framework for inferring stochastic dynamics from non-sequential data. This method overcomes limitations of standard time-series analysis for unordered, restricted-region measurements.

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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.