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From ecology to atmospheric sciences, many academic disciplines deal withdata characterized by intricate spatio-temporal complexities, the modeling ofwhich often requires specialized approaches. Generative models of these dataare of particular interest, as they enable a range of impactful downstreamapplications like simulation or creating synthetic training data. Recent workhas highlighted the potential of generative adversarial nets (GANs) forgenerating spatio-temporal data. A new GAN algorithm COT-GAN, inspired by thetheory of causal optimal transport (COT), was proposed in an attempt to bettertackle this challenge. However, the task of learning more complexspatio-temporal patterns requires additional knowledge of their specific datastructures. In this study, we propose a novel loss objective combined withCOT-GAN based on an autoregressive embedding to reinforce the learning ofspatio-temporal dynamics. We devise SPATE (spatio-temporal association), a newmetric measuring spatio-temporal autocorrelation by using the deviance ofobservations from their expected values. We compute SPATE for real andsynthetic data samples and use it to compute an embedding loss that considersspace-time interactions, nudging the GAN to learn outputs that are faithful tothe observed dynamics. We test this new objective on a diverse set of complexspatio-temporal patterns: turbulent flows, log-Gaussian Cox processes andglobal weather data. We show that our novel embedding loss improves performancewithout any changes to the architecture of the COT-GAN backbone, highlightingour model's increased capacity for capturing autoregressive structures. We alsocontextualize our work with respect to recent advances in physics-informed deeplearning and interdisciplinary work connecting neural networks with geographicand geophysical sciences.

SPATE-GAN: Improved Generative Modeling of Dynamic Spatio-Temporal Patterns with an Autoregressive Embedding Loss