Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in such data, limiting their ability to capture stochastic dynamics accurately. We investigate this underestimation in detail and propose a straightforward solution: by including an explicit additional noise regularization in the loss function, we are able to learn a model that accurately captures the diffusion component of the data. We demonstrate our results on a conceptual model system that highlights the improved latent neural SDE's capability to model stochastic bistable dynamics.

Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate models can enhance their generalizability and numerical stability. In this paper, we introduce projected neural differential equations (PNDEs), a new method for constraining neural differential equations based on projection of the learned vector field to the tangent space of the constraint manifold. In tests on several challenging examples, including chaotic dynamical systems and state-of-the-art power grid models, PNDEs outperform existing methods while requiring fewer hyperparameters. The proposed approach demonstrates significant potential for enhancing the modeling of constrained dynamical systems, particularly in complex domains where accuracy and reliability are essential.

Ocean dynamics plays a crucial role in driving global weather and climate patterns. Accurate and efficient modeling of ocean dynamics is essential for improved understanding of complex ocean circulation and processes, for predicting climate variations and their associated teleconnections, and for addressing the challenges of climate change. While great efforts have been made to improve numerical Ocean General Circulation Models (OGCMs), accurate forecasting of global oceanic variations for multi-year remains to be a long-standing challenge. Here, we introduce ORCA (Oceanic Reliable foreCAst), the first data-driven model predicting global ocean circulation from multi-year to decadal time scales. ORCA accurately simulates the three-dimensional circulations and dynamics of the global ocean with high physical consistency. Hindcasts of key oceanic variables demonstrate ORCA's remarkable prediction skills in predicting ocean variations compared with state-of-the-art numerical OGCMs and abilities in capturing occurrences of extreme events at the subsurface ocean and ENSO vertical patterns. These results demonstrate the potential of data-driven ocean models for providing cheap, efficient, and accurate global ocean modeling and prediction. Moreover, ORCA stably and faithfully emulates ocean dynamics at decadal timescales, demonstrating its potential even for climate projections. The model will be available at https://github.com/OpenEarthLab/ORCA.

Climate change exacerbates extreme weather events like heavy rainfall and flooding. As these events cause severe losses of property and lives, accurate high-resolution simulation of precipitation is imperative. However, existing Earth System Models (ESMs) struggle with resolving small-scale dynamics and suffer from biases, especially for extreme events. Traditional statistical bias correction and downscaling methods fall short in improving spatial structure, while recent deep learning methods lack controllability over the output and suffer from unstable training. Here, we propose a novel machine learning framework for simultaneous bias correction and downscaling. We train a generative diffusion model in a supervised way purely on observational data. We map observational and ESM data to a shared embedding space, where both are unbiased towards each other and train a conditional diffusion model to reverse the mapping. Our method can be used to correct any ESM field, as the training is independent of the ESM. Our approach ensures statistical fidelity, preserves large-scale spatial patterns and outperforms existing methods especially regarding extreme events and small-scale spatial features that are crucial for impact assessments.

Accurate and high-resolution Earth system model (ESM) simulations are essential to assess the ecological and socio-economic impacts of anthropogenic climate change, but are computationally too expensive. Recent machine learning approaches have shown promising results in downscaling ESM simulations, outperforming state-of-the-art statistical approaches. However, existing methods require computationally costly retraining for each ESM and extrapolate poorly to climates unseen during training. We address these shortcomings by learning a consistency model (CM) that efficiently and accurately downscales arbitrary ESM simulations without retraining in a zero-shot manner. Our foundation model approach yields probabilistic downscaled fields at resolution only limited by the observational reference data. We show that the CM outperforms state-of-the-art diffusion models at a fraction of computational cost while maintaining high controllability on the downscaling task. Further, our method generalizes to climate states unseen during training without explicitly formulated physical constraints.

Recent studies have shown that deep learning (DL) models can skillfully predict the El Ni\~no-Southern Oscillation (ENSO) forecasts over 1.5 years ahead. However, concerns regarding the reliability of predictions made by DL methods persist, including potential overfitting issues and lack of interpretability. Here, we propose ResoNet, a DL model that combines convolutional neural network (CNN) and Transformer architectures. This hybrid architecture design enables our model to adequately capture local SSTA as well as long-range inter-basin interactions across oceans. We show that ResoNet can robustly predict ESNO at lead times between 19 and 26 months, thus outperforming existing approaches in terms of the forecast horizon. According to an explainability method applied to ResoNet predictions of El Ni\~no and La Ni\~na events from 1- to 18-month lead, we find that it predicts the Ni\~no3.4 index based on multiple physically reasonable mechanisms, such as the Recharge Oscillator concept, Seasonal Footprint Mechanism, and Indian Ocean capacitor effect. Moreover, we demonstrate that for the first time, the asymmetry between El Ni\~no and La Ni\~na development can be captured by ResoNet. Our results could help alleviate skepticism about applying DL models for ENSO prediction and encourage more attempts to discover and predict climate phenomena using AI methods.

Historical records of climate fields are often sparse due to missing measurements, especially before the introduction of large-scale satellite missions. Several statistical and model-based methods have been introduced to fill gaps and reconstruct historical records. Here, we employ a recently introduced deep-learning approach based on Fourier convolutions, trained on numerical climate model output, to reconstruct historical climate fields. Using this approach we are able to realistically reconstruct large and irregular areas of missing data, as well as reconstruct known historical events such as strong El Ni\~no and La Ni\~na with very little given information. Our method outperforms the widely used statistical kriging method as well as other recent machine learning approaches. The model generalizes to higher resolutions than the ones it was trained on and can be used on a variety of climate fields. Moreover, it allows inpainting of masks never seen before during the model training.

Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states, remains challenging. We propose stabilized neural differential equations (SNDEs), a method to enforce arbitrary manifold constraints for neural differential equations. Our approach is based on a stabilization term that, when added to the original dynamics, renders the constraint manifold provably asymptotically stable. Due to its simplicity, our method is compatible with all common neural differential equation (NDE) models and broadly applicable. In extensive empirical evaluations, we demonstrate that SNDEs outperform existing methods while broadening the types of constraints that can be incorporated into NDE training.

The accurate representation of precipitation in Earth system models (ESMs) is crucial for reliable projections of the ecological and socioeconomic impacts in response to anthropogenic global warming. The complex cross-scale interactions of processes that produce precipitation are challenging to model, however, inducing potentially strong biases in ESM fields, especially regarding extremes. State-of-the-art bias correction methods only address errors in the simulated frequency distributions locally at every individual grid cell. Improving unrealistic spatial patterns of the ESM output, which would require spatial context, has not been possible so far. Here, we show that a post-processing method based on physically constrained generative adversarial networks (cGANs) can correct biases of a state-of-the-art, CMIP6-class ESM both in local frequency distributions and in the spatial patterns at once. While our method improves local frequency distributions equally well as gold-standard bias-adjustment frameworks, it strongly outperforms any existing methods in the correction of spatial patterns, especially in terms of the characteristic spatial intermittency of precipitation extremes.

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.