Earth Observation (EO) data analysis has been significantly revolutionized by deep learning (DL), with applications typically limited to grid-like data structures. Graph Neural Networks (GNNs) emerge as an important innovation, propelling DL into the non-Euclidean domain. Naturally, GNNs can effectively tackle the challenges posed by diverse modalities, multiple sensors, and the heterogeneous nature of EO data. To introduce GNNs in the related domains, our review begins by offering fundamental knowledge on GNNs. Then, we summarize the generic problems in EO, to which GNNs can offer potential solutions. Following this, we explore a broad spectrum of GNNs' applications to scientific problems in Earth systems, covering areas such as weather and climate analysis, disaster management, air quality monitoring, agriculture, land cover classification, hydrological process modeling, and urban modeling. The rationale behind adopting GNNs in these fields is explained, alongside methodologies for organizing graphs and designing favorable architectures for various tasks. Furthermore, we highlight methodological challenges of implementing GNNs in these domains and possible solutions that could guide future research. While acknowledging that GNNs are not a universal solution, we conclude the paper by comparing them with other popular architectures like transformers and analyzing their potential synergies.

Precipitation nowcasting (up to a few hours) remains a challenge due to the highly complex local interactions that need to be captured accurately. Convolutional Neural Networks rely on convolutional kernels convolving with grid data and the extracted features are trapped by limited receptive field, typically expressed in excessively smooth output compared to ground truth. Thus they lack the capacity to model complex spatial relationships among the grids. Geometric deep learning aims to generalize neural network models to non-Euclidean domains. Such models are more flexible in defining nodes and edges and can effectively capture dynamic spatial relationship among geographical grids. Motivated by this, we explore a geometric deep learning-based temporal Graph Convolutional Network (GCN) for precipitation nowcasting. The adjacency matrix that simulates the interactions among grid cells is learned automatically by minimizing the L1 loss between prediction and ground truth pixel value during the training procedure. Then, the spatial relationship is refined by GCN layers while the temporal information is extracted by 1D convolution with various kernel lengths. The neighboring information is fed as auxiliary input layers to improve the final result. We test the model on sequences of radar reflectivity maps over the Trento/Italy area. The results show that GCNs improves the effectiveness of modeling the local details of the cloud profile as well as the prediction accuracy by achieving decreased error measures.

Deep generative models are increasingly used to gain insights in the geospatial data domain, e.g., for climate data. However, most existing approaches work with temporal snapshots or assume 1D time-series; few are able to capture spatio-temporal processes simultaneously. Beyond this, Earth-systems data often exhibit highly irregular and complex patterns, for example caused by extreme weather events. Because of climate change, these phenomena are only increasing in frequency. Here, we proposed a novel GAN-based approach for generating spatio-temporal weather patterns conditioned on detected extreme events. Our approach augments GAN generator and discriminator with an encoded extreme weather event segmentation mask. These segmentation masks can be created from raw input using existing event detection frameworks. As such, our approach is highly modular and can be combined with custom GAN architectures. We highlight the applicability of our proposed approach in experiments with real-world surface radiation and zonal wind data.

Existing adversarially trained models typically perform inference on test examples independently from each other. This mode of testing is unable to handle covariate shift in the test samples. Due to this, the performance of these models often degrades significantly. In this paper, we show that simple adaptive batch normalization (BN) technique that involves re-estimating the batch-normalization parameters during inference, can significantly improve the robustness of these models for any random perturbations, including the Gaussian noise. This simple finding enables us to transform adversarially trained models into randomized smoothing classifiers to produce certified robustness to $\ell_2$ noise. We show that we can achieve $\ell_2$ certified robustness even for adversarially trained models using $\ell_{\infty}$-bounded adversarial examples. We further demonstrate that adaptive BN technique significantly improves robustness against common corruptions, while often enhancing performance against adversarial attacks. This enables us to achieve both adversarial and corruption robustness for the same classifier.