The authors consider the case where the statistical behavior of environmental models must be learned in real time. In particular, they focus on learning such behavior predictively, as may be applicable in data compression, hypothesis testing or model identification, while statistical qualitative robustness for protection against outlier data is sought as well. They consider qualitatively robust predictive mappings of stochastic environmental models, where protection against outlier data is incorporated. They utilize digital representations of the models and deploy stochastic binary neural networks that are pre-trained to produce such mappings. The pre-training is implemented by a back propagating supervised learning algorithm which converges almost surely to the probabilities induced by the environment, under general ergodicity conditions.