Learning brain dynamics via integral equations
Abstract: Modeling brain dynamics is a notoriously difficult problem, and relating such models to behavioral and cognitive characteristics is a fundamental objective of computational neurology. However, the brain presents long-range spatiotemporal relations that produce non-local complex dynamics. While the use of non-local equations to model the brain has a long history in computational approaches, deep learning models based on such equations have not appeared until very recently.
In this “Pillola di Ricerca” I will present a deep learning model based on integral equations, called Neural Integral Equation, and discuss its applications to the study of the brain. This model is essentially an approach to operator learning with potential applications that range from computational neurology, to physics and epidemiology, where the target of the optimization process is an integral operator.
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