A low-complexity neural network based approach for channel estimation was proposed recently, where assumptions on the channel model were incorporated into the design procedure of the estimator. Instead of using data from a measurement campaign as done in previous work, we evaluate the performance of the convolutional neural network (CNN) based channel estimator by using a reproducible mmWave environment of the DeepMIMO dataset. We further propose a neural network based predictor which is derived by starting from the linear minimum mean squared error (LMMSE) predictor. We start by deriving a weighted sum of LMMSE predictors which is motivated by the structure of the optimal MMSE predictor. This predictor provides an initialization (weight matrices, biases and activation function) to a feed-forward neural network based predictor. With a properly learned neural network, we show that it is possible to easily outperform the LMMSE predictor based on the Jakes assumption of the underlying Doppler spectrum in an reproducible indoor scenario of the DeepMIMO dataset.