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Trajectory Data Analyses for Pedestrian Space-time Activity Study

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Published on: February 25, 2013

Sparse inference and active learning of stochastic differential equations from data.

Yunfei Huang¹, Youssef Mabrouk^2,3, Gerhard Gompper¹

¹Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Juelich, 52425, Juelich, Germany.

Scientific Reports

|December 15, 2022

Summary

This study introduces a Bayesian approach for directly inferring differential equations from data, enabling physical interpretation. An active learning method enhances the discovery of stochastic differential equations, improving model accuracy.

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Area of Science:

Computational Physics
Data Science
Applied Mathematics

Background:

Machine learning models often lack physical interpretability.
Existing methods struggle with complex dynamical systems.

Purpose of the Study:

To develop a method for direct inference of governing differential equations from experimental data.
To enhance the discovery of stochastic differential equations using active learning.

Main Methods:

Formulating differential equation inference as a linear inverse problem.
Employing a Bayesian framework with a Laplacian prior for sparse solutions.
Developing an active learning feedback loop for automated equation discovery.

Main Results:

Demonstrated superior accuracy and robustness for ordinary, partial, and stochastic differential equations.
Showcased active learning's ability to improve global model inference for systems with multiple energetic minima.

Conclusions:

The Bayesian approach facilitates physically interpretable models from data.
Active learning significantly advances automated discovery of complex dynamical systems.