  We present a method for training a deep neural network containing sinusoidal
activation functions to fit to time-series data. Weights are initialized using
a fast Fourier transform, then trained with regularization to improve
generalization. A simple dynamic parameter tuning method is employed to adjust
both the learning rate and regularization term, such that stability and
efficient training are both achieved. We show how deeper layers can be utilized
to model the observed sequence using a sparser set of sinusoid units, and how
non-uniform regularization can improve generalization by promoting the shifting
of weight toward simpler units. The method is demonstrated with time-series
problems to show that it leads to effective extrapolation of nonlinear trends.
