Self-adaptive deep neural network: Numerical approximation to functions and PDEs. (arXiv:2109.02839v2 [math.NA] UPDATED)

Designing an optimal deep neural network for a given task is important and
challenging in many machine learning applications. To address this issue, we
introduce a self-adaptive algorithm: the adaptive network enhancement (ANE)
method, written as loops of the form train, estimate and enhance. Starting with
a small two-layer neural network (NN), the step train is to solve the
optimization problem at the current NN; the step estimate is to compute a
posteriori estimator/indicators using the solution at the current …

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