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In this paper, we propose an adaptive group Lasso deep neural network forhigh-dimensional function approximation where input data are generated from adynamical system and the target function depends on few active variables or fewlinear combinations of variables. We approximate the target function by a deepneural network and enforce an adaptive group Lasso constraint to the weights ofa suitable hidden layer in order to represent the constraint on the targetfunction. We utilize the proximal algorithm to optimize the penalized lossfunction. Using the non-negative property of the Bregman distance, we provethat the proposed optimization procedure achieves loss decay. Our empiricalstudies show that the proposed method outperforms recent state-of-the-artmethods including the sparse dictionary matrix method, neural networks with orwithout group Lasso penalty.

Adaptive Group Lasso Neural Network Models for Functions of Few Variables and Time-Dependent Data