Environmental spatio-temporal processes are governed by complex dynamical interactions across multiple scales and multiple processes. Often the time scales or multi-process complexity of such processes preclude the effective specification of a specific mechanism in which to motivate the model, particularly in low-order and stochastic representations. It is particularly challenging to specify parameterizations for nonlinear dynamic spatio-temporal models (DSTMs) that are simultaneously useful scientifically, efficient computationally, and allow for proper uncertainty quantification. We describe a recent approach that utilizes a deep convolutional neural network to learn the kernel mapping function in a computationally efficient state-dependent integro-difference equation (IDE) DSTM. The most important aspect of this work is that it demonstrates remarkable “transfer learning” potential – i.e., it can predict a geophysical system quite different than the one that produced the data on which it was trained. However, this approach does not learn the functional form of the relevant dynamics. Recently, there has been interest in several academic communities to use data-driven discovery methods to learn the fundamental dynamical mechanisms present in data. These approaches have shown promise in simulations of low-dimensional systems without a great deal of noise in observation or process or missing data. Here, we present a statistical spatio-temporal dynamics discovery approach that accommodates noisy observations and stochastic dynamics.