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Related Experiment Video

Updated: Sep 20, 2025

Quantifying Learning in Young Infants: Tracking Leg Actions During a Discovery-learning Task

Quantifying Learning in Young Infants: Tracking Leg Actions During a Discovery-learning Task

Published on: June 1, 2015

Learning emergent partial differential equations in a learned emergent space.

Felix P Kemeth¹, Tom Bertalan¹, Thomas Thiem²

¹Department of Chemical and Biomolecular Engineering, Whiting School of Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD, 21218, USA.

Nature Communications

|June 10, 2022

Summary

This summary is machine-generated.

We developed a novel method to learn effective evolution equations for complex agent systems. This approach uses manifold learning to find emergent coordinates and neural networks to derive partial differential equations (PDEs) describing system dynamics and bifurcations.

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Area of Science:

Complex Systems Science
Computational Neuroscience
Applied Mathematics

Background:

Large systems of interacting agents often lack clear spatial coordinates for modeling.
Describing collective dynamics and bifurcations in such systems is challenging.
Existing methods struggle to derive effective evolution laws from time-series data.

Purpose of the Study:

To develop a data-driven approach for learning effective evolution equations in systems of interacting agents.
To identify emergent spatial coordinates for complex dynamical systems.
To apply machine learning for discovering partial differential equations (PDEs) that capture system behavior.

Main Methods:

Utilized manifold learning to extract emergent coordinates from time-series data.
Employed neural networks to learn partial differential equations (PDEs) in these emergent coordinates.
Demonstrated the approach on coupled normal form oscillators and Hodgkin-Huxley-like neurons.

Main Results:

Successfully learned effective evolution equations for complex agent systems.
The derived PDEs accurately reproduced system dynamics.
Captured collective bifurcations as system parameters were varied.
Integrated data-driven coordinate extraction with machine learning for PDE identification.

Conclusions:

The proposed method effectively integrates automatic coordinate extraction with machine learning for discovering emergent PDEs.
This approach provides a powerful tool for understanding and modeling complex interacting systems.
Applicable to diverse fields including physics, neuroscience, and engineering.