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Neural Networks for Singular Perturbations
(2024)SAM Research ReportWe prove deep neural network (DNN for short) expressivity rate bounds for solution sets of a model class of singularly perturbed, elliptic two-point boundary value problems, in Sobolev norms, on the bounded interval (−1,1). We assume that the given source term and reaction coefficient are analytic in [−1,1]. We establish expression rate bounds in Sobolev norms in terms of the NN size which are uniform with respect to the singular perturbation ...Report