We introduce a distributed spatio-temporal artificial neural network architecture (DISTANA). It encodes mesh nodes using recurrent, neural prediction kernels (PKs), while neural transition kernels (TKs) transfer information between neighboring PKs, together modeling and predicting spatio-temporal time series dynamics. As a consequence, DISTANA assumes that generally applicable causes, which may be locally modified, generate the observed data. DISTANA learns in a parallel, spatially distributed manner, scales to large problem spaces, is capable of approximating complex dynamics, and is particularly robust to overfitting when compared to other competitive ANN models. Moreover, it is applicable to heterogeneously structured meshes.