Linearizing and forecasting: a reservoir computing route to digital twins of the brain

Exploring the dynamics of a complex system, such as the human brain, poses significant challenges due to inherent uncertainties and limited data. In this study, we enhance the capabilities of noisy linear recurrent neural networks (lRNNs) within the reservoir computing framework, demonstrating their effectiveness in creating autonomous in silico replicas - digital-twins - of brain activity. Our findings reveal that the poles of the Laplace transform of high-dimensional inferred lRNNs are directly linked to the spectral properties of observed systems and to the kernels of auto-regressive models. Applying this theoretical framework to resting-state fMRI, we successfully predict and decompose BOLD signals into spatiotemporal modes of a low-dimensional latent state space confined around a single equilibrium point. lRNNs provide an interpretable proxy for clustering among subjects and different brain areas. This adaptable digital-twin framework not only enables virtual experiments but also offers computational efficiency for real-time learning, highlighting its potential for personalized medicine and intervention strategies.