Data-driven mean-field within whole-brain models

Abstract: Mean-field models provide a link between microscopic neuronal activity and macroscopic brain dynamics. Their derivation depends on simplifying assumptions, such as all-to-all connectivity, limiting their biological realism. To overcome this, we introduce a data-driven framework in which a multi-layer perceptron (MLP) learns the macroscopic dynamics directly from simulations of a network of spiking neurons. The network connection probability serves here as a new parameter, inaccessible to purely analytical treatment, which is validated against ground truth analytical solutions. Through bifurcation analysis on the trained MLP, we demonstrate the existence of new cusp bifurcation that systematically reshapes the system's phase diagram in a degenerate manner with synaptic coupling. By integrating this data-driven mean-field model into a whole-brain computational framework, we show that it extends beyond the macroscopic emergent dynamics generated by the analytical model. For validation, we use simulation-based inference on synthetic functional magnetic resonance imaging (fMRI) data and demonstrate accurate parameter recovery for the novel mean-field model, while the current state-of-the-art models lead to biased estimates. This work presents a flexible and generic framework for building more realistic whole-brain models, bridging the gap between microscale mechanisms and macroscopic brain recordings.