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

Abstract

From ecology to atmospheric sciences, many academic disciplines deal with data characterized by intricate spatio-temporal complexities, the modeling of which often requires specialized approaches. Generative models of these data are of particular interest, as they enable a range of impactful downstream applications like simulation or creating synthetic training data. Recently, COT-GAN, a new GAN algorithm inspired by the theory of causal optimal transport (COT), was proposed in an attempt to improve generation of sequential data. However, the task of learning complex patterns over time and space requires additional knowledge of the specific data structures. In this study, we propose a novel loss objective combined with COT-GAN based on an autoregressive embedding to reinforce the learning of spatio-temporal dynamics. We devise SPATE (spatio-temporal association), a new metric measuring spatio-temporal autocorrelation. We compute SPATE for real and synthetic data samples and use it to compute an embedding loss that considers space-time interactions, nudging the GAN to learn outputs that are faithful to the observed dynamics. We test our new SPATE-GAN on a diverse set of spatio-temporal patterns: turbulent flows, log-Gaussian Cox processes and global weather data. We show that our novel embedding loss improves performance without any changes to the architecture of the GAN backbone, highlighting our model's increased capacity for capturing autoregressive structures.

AtmoDist: Self-supervised representation learning for atmospheric dynamics

“…Despite this, state-of-the-art methods can often provide valid whose statistics match those of the true fields. In the last years, in particular approaches based on GANs (Goodfellow et al, 2014) have become the de facto standard (e.g., Jiang et al, 2020; Stengel et al, 2020; Klemmer et al, 2022).…”

“…Despite this, state-of-the-art methods can often provide valid X hr whose statistics match those of the true fields. In the last years, in particular approaches based on GANs (Goodfellow et al, 2014) have become the de facto standard (e.g., Jiang et al, 2020;Stengel et al, 2020;Klemmer et al, 2022). Stengel et al (2020) recently applied GAN-based super-resolution to wind and solar data in North America, demonstrating physically consistent results that outperform competing methods.…”

“…Several GANs dedicated to geoscience applications have been proposed in the literature (e.g., Stengel et al, 2020; Zhu et al, 2020; Klemmer and Neill, 2021; Klemmer et al, 2022). Noteworthy is SPATE-GAN (Klemmer et al, 2022) that uses a custom metric for spatiotemporal autocorrelation and determines an embedding loss based on it.…”

“…Several GANs dedicated to geoscience applications have been proposed in the literature (e.g., Stengel et al, 2020; Zhu et al, 2020; Klemmer and Neill, 2021; Klemmer et al, 2022). Noteworthy is SPATE-GAN (Klemmer et al, 2022) that uses a custom metric for spatiotemporal autocorrelation and determines an embedding loss based on it. The authors demonstrate that this improves GAN performance across different datasets without changes to the neural network architecture of the generative model.…”

The Weisfeiler-Lehman Distance: Reinterpretation and Connection with GNNs

“…Note that COT has already found applications in mathematical finance (Glanzer et al, 2019;Backhoff-Veraguas et al, 2020) and in machine learning (Xu et al, 2020;Xu and Acciaio, 2022;Klemmer et al, 2022). As COT lies in the framework of Optimal Transport, multiple Sinkhorn algorithms have been proposed in the literature (Pichler and Weinhardt, 2022;Eckstein and Pammer, 2022) for accelerating computations.…”