  In this paper, we introduce adaptive neuron enhancement (ANE) method for the
best least-squares approximation using two-layer ReLU neural networks (NNs).
For a given function f(x), the ANE method generates a two-layer ReLU NN and a
numerical integration mesh such that the approximation accuracy is within the
prescribed tolerance. The ANE method provides a natural process for obtaining a
good initialization which is crucial for training nonlinear optimization
problems. Numerical results of the ANE method are presented for functions of
two variables exhibiting either intersecting interface singularities or sharp
interior layers.
