Parameter and hidden-state inference in mean-field models from partial observations of finite-size neural networks

Fuente: arXiv
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Main Authors: Ratas, Irmantas, Pyragas, Kestutis
Format: Preprint
Published: 2026
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author Ratas, Irmantas
Pyragas, Kestutis
author_facet Ratas, Irmantas
Pyragas, Kestutis
contents We study large but finite neural networks that, in the thermodynamic limit, admit an exact low-dimensional mean-field description. We assume that the governing mean-field equations describing macroscopic quantities such as the mean firing rate or mean membrane potential are known, while their parameters are not. Moreover, only a single scalar macroscopic observable from the finite network is assumed to be measurable. Using time-series data of this observable, we infer the unknown parameters of the mean-field equations and reconstruct the dynamics of unobserved (hidden) macroscopic variables. Parameter estimation is carried out using the differential evolution algorithm. To remove the dependence of the loss function on the unknown initial conditions of the hidden variables, we synchronize the mean-field model with the finite network throughout the optimization process. We demonstrate the methodology on two networks of quadratic integrate-and-fire neurons: one exhibiting periodic collective oscillations and another displaying chaotic collective dynamics. In both cases, the parameters are recovered with relative errors below $1\%$ for network sizes exceeding 1000 neurons.
format Preprint
id arxiv_https___arxiv_org_abs_2602_09535
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Parameter and hidden-state inference in mean-field models from partial observations of finite-size neural networks
Ratas, Irmantas
Pyragas, Kestutis
Chaotic Dynamics
Data Analysis, Statistics and Probability
We study large but finite neural networks that, in the thermodynamic limit, admit an exact low-dimensional mean-field description. We assume that the governing mean-field equations describing macroscopic quantities such as the mean firing rate or mean membrane potential are known, while their parameters are not. Moreover, only a single scalar macroscopic observable from the finite network is assumed to be measurable. Using time-series data of this observable, we infer the unknown parameters of the mean-field equations and reconstruct the dynamics of unobserved (hidden) macroscopic variables. Parameter estimation is carried out using the differential evolution algorithm. To remove the dependence of the loss function on the unknown initial conditions of the hidden variables, we synchronize the mean-field model with the finite network throughout the optimization process. We demonstrate the methodology on two networks of quadratic integrate-and-fire neurons: one exhibiting periodic collective oscillations and another displaying chaotic collective dynamics. In both cases, the parameters are recovered with relative errors below $1\%$ for network sizes exceeding 1000 neurons.
title Parameter and hidden-state inference in mean-field models from partial observations of finite-size neural networks
topic Chaotic Dynamics
Data Analysis, Statistics and Probability
url https://arxiv.org/abs/2602.09535