Physics-informed neural networks for subject-specific recovery of travelling-wave structure in resting-state fMRI

Resting-state BOLD fluctuations show reproducible spatiotemporal propagation that is not accounted for by conventional zero-lag functional connectivity. Travelling wave analyses based on phase gradients or statistical decomposition have problems when multiple wave generators overlap or when wave origins have to be localized. This work introduces a wave-informed physics-informed neural network that represents the parcellated BOLD signal as a superposition of seven spatially extended damped travelling wave generators, each periodically re-excited at its own characteristic frequency and fixed at initialization to one of the seven canonical Schaefer resting-state networks. A soft anatomical prior derived from each subject's diffusion-tensor structural connectivity is included to encode the hypothesis that white-matter pathways constrain wave direction. The pipeline is validated on synthetic data by three simulation studies, creating the operating envelope, and then applied to 41 cognitively normal participants of the ADNI 3 cohort. A within-subject ablation showed that mean alignment between recovered wave directions and underlying white matter geometry increased by a small but statistically detectable amount when using the structural prior (one-sidedWilcoxon signed-rank, p = 0.026), with exploratory network-level effects most evident in the visual, dorsal-attention, and salience/ventral-attention networks. The contribution is a network-anchored parametric inverse method returning subject-specific propagation descriptors from short resting-state scans.