https://doi.org/10.1140/epjs/s11734-025-02112-x
Regular Article
Data-driven identification of macroscopic dynamics with implicit equation-free sampling and Gaussian process regression: for the example of an integrate-and-fire neural network
1
Institute of Mathematics, University of Rostock, Rostock, Germany
2
Laboratory of Mathematics and Informatics (ISCE), Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece
3
Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Università degli Studi di Napoli Federico II, Naples, Italy
a
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Received:
30
September
2025
Accepted:
16
December
2025
Published online:
12
January
2026
We investigate a data-driven approach to derive low-dimensional macroscopic models of complex systems with only high-dimensional microscopic descriptions available. This is achieved by sampling of the macroscopic behaviour at selected points using an implicit equation-free approach with appropriate initialisation of the microscopic system. This enables subsequent data-driven identification of the macroscopic dynamics with Gaussian process regression. We demonstrate the technique on a high-dimensional neural network of integrate-and-fire neurons. A numerical bifurcation analysis of the obtained macroscopic model is performed, showing both stable and unstable branches. The appropriate sampling using the implicit equation-free approach avoids grid distortion and prevents spurious states as well as other artefacts.
In memory of Hermann Haken.
© The Author(s) 2026
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