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Here, we develop a mathematical theory for noisy linear recurrent neural networks (lRNNs) within the reservoir computing framework and demonstrate their effectiveness in constructing autonomous in silico replicas \u2013 digital\u2010twins \u2013 of brain activity. We show that the Laplace\u2010transform poles of high\u2010dimensional inferred lRNNs directly encode the spectral properties of observed systems and are linked to the kernels of auto\u2010regressive models. Notably, our approach enables accurate recovery of the system's linear spectrum even when observations undergo conventional preprocessing, including band\u2010pass filtering pipelines commonly used in neural recordings and resting\u2010state fMRI. In these regimes, established techniques such as dynamic mode decomposition often produce spurious spectral estimates. Applying our framework to resting\u2010state fMRI, we successfully predict and decompose BOLD activity into spatiotemporal modes in a low\u2010dimensional latent state space confined around a single equilibrium point. The inferred lRNNs provide interpretable signatures that differentiate subjects and brain areas, supporting biologically meaningful clustering. This flexible digital\u2010twin framework opens the door to virtual experiments and computationally efficient real\u2010time adaptive learning, offering a promising avenue for personalized medicine and intervention\u00a0strategies.<\/jats:p>","DOI":"10.1002\/advs.202517234","type":"journal-article","created":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T22:40:01Z","timestamp":1773960001000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Linearizing and Forecasting: A Reservoir Computing Route to Digital Twins of the Brain"],"prefix":"10.1002","volume":"13","author":[{"given":"Gabriele","family":"Di Antonio","sequence":"first","affiliation":[{"name":"\u201cEnrico Fermi\u201d Research Center \u2010 CREF Rome Italy"},{"name":"Natl. 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