Michael Pritchard

Sungduk Yu, Zeyuan Hu, Akshay Subramaniam et al.

Modern climate projections lack adequate spatial and temporal resolution due to computational constraints, leading to inaccuracies in representing critical processes like thunderstorms that occur on the sub-resolution scale. Hybrid methods combining physics with machine learning (ML) offer faster, higher fidelity climate simulations by outsourcing compute-hungry, high-resolution simulations to ML emulators. However, these hybrid ML-physics simulations require domain-specific data and workflows that have been inaccessible to many ML experts. As an extension of the ClimSim dataset (Yu et al., 2024), we present ClimSim-Online, which also includes an end-to-end workflow for developing hybrid ML-physics simulators. The ClimSim dataset includes 5.7 billion pairs of multivariate input/output vectors, capturing the influence of high-resolution, high-fidelity physics on a host climate simulator's macro-scale state. The dataset is global and spans ten years at a high sampling frequency. We provide a cross-platform, containerized pipeline to integrate ML models into operational climate simulators for hybrid testing. We also implement various ML baselines, alongside a hybrid baseline simulator, to highlight the ML challenges of building stable, skillful emulators. The data (https://huggingface.co/datasets/LEAP/ClimSim_high-res) and code (https://leap-stc.github.io/ClimSim and https://github.com/leap-stc/climsim-online) are publicly released to support the development of hybrid ML-physics and high-fidelity climate simulations.

Jaideep Pathak, Yair Cohen, Piyush Garg et al.

Storm-scale convection-allowing models (CAMs) are an important tool for predicting the evolution of thunderstorms and mesoscale convective systems that result in damaging extreme weather. By explicitly resolving convective dynamics within the atmosphere they afford meteorologists the nuance needed to provide outlook on hazard. Deep learning models have thus far not proven skilful at km-scale atmospheric simulation, despite being competitive at coarser resolution with state-of-the-art global, medium-range weather forecasting. We present a generative diffusion model called StormCast, which emulates the high-resolution rapid refresh (HRRR) model-NOAA's state-of-the-art 3km operational CAM. StormCast autoregressively predicts 99 state variables at km scale using a 1-hour time step, with dense vertical resolution in the atmospheric boundary layer, conditioned on 26 synoptic variables. We present evidence of successfully learnt km-scale dynamics including competitive 1-6 hour forecast skill for composite radar reflectivity alongside physically realistic convective cluster evolution, moist updrafts, and cold pool morphology. StormCast predictions maintain realistic power spectra for multiple predicted variables across multi-hour forecasts. Together, these results establish the potential for autoregressive ML to emulate CAMs -- opening up new km-scale frontiers for regional ML weather prediction and future climate hazard dynamical downscaling.

Ankur Mahesh, William Collins, Boris Bonev et al.

Studying low-likelihood high-impact extreme weather events in a warming world is a significant and challenging task for current ensemble forecasting systems. While these systems presently use up to 100 members, larger ensembles could enrich the sampling of internal variability. They may capture the long tails associated with climate hazards better than traditional ensemble sizes. Due to computational constraints, it is infeasible to generate huge ensembles (comprised of 1,000-10,000 members) with traditional, physics-based numerical models. In this two-part paper, we replace traditional numerical simulations with machine learning (ML) to generate hindcasts of huge ensembles. In Part I, we construct an ensemble weather forecasting system based on Spherical Fourier Neural Operators (SFNO), and we discuss important design decisions for constructing such an ensemble. The ensemble represents model uncertainty through perturbed-parameter techniques, and it represents initial condition uncertainty through bred vectors, which sample the fastest growing modes of the forecast. Using the European Centre for Medium-Range Weather Forecasts Integrated Forecasting System (IFS) as a baseline, we develop an evaluation pipeline composed of mean, spectral, and extreme diagnostics. Using large-scale, distributed SFNOs with 1.1 billion learned parameters, we achieve calibrated probabilistic forecasts. As the trajectories of the individual members diverge, the ML ensemble mean spectra degrade with lead time, consistent with physical expectations. However, the individual ensemble members' spectra stay constant with lead time. Therefore, these members simulate realistic weather states, and the ML ensemble thus passes a crucial spectral test in the literature. The IFS and ML ensembles have similar Extreme Forecast Indices, and we show that the ML extreme weather forecasts are reliable and discriminating.

Ankur Mahesh, William Collins, Boris Bonev et al.

In Part I, we created an ensemble based on Spherical Fourier Neural Operators. As initial condition perturbations, we used bred vectors, and as model perturbations, we used multiple checkpoints trained independently from scratch. Based on diagnostics that assess the ensemble's physical fidelity, our ensemble has comparable performance to operational weather forecasting systems. However, it requires orders of magnitude fewer computational resources. Here in Part II, we generate a huge ensemble (HENS), with 7,424 members initialized each day of summer 2023. We enumerate the technical requirements for running huge ensembles at this scale. HENS precisely samples the tails of the forecast distribution and presents a detailed sampling of internal variability. HENS has two primary applications: (1) as a large dataset with which to study the statistics and drivers of extreme weather and (2) as a weather forecasting system. For extreme climate statistics, HENS samples events 4$σ$ away from the ensemble mean. At each grid cell, HENS increases the skill of the most accurate ensemble member and enhances coverage of possible future trajectories. As a weather forecasting model, HENS issues extreme weather forecasts with better uncertainty quantification. It also reduces the probability of outlier events, in which the verification value lies outside the ensemble forecast distribution.

Scott A. Martin, Noah Brenowitz, Dale Durran et al.

Accurate long-range weather forecasting remains a major challenge for AI models, both because errors accumulate over autoregressive rollouts and because reanalysis datasets used for training offer a limited sample of the slow modes of climate variability underpinning predictability. Most AI weather models are autoregressive, producing short lead forecasts that must be repeatedly applied to reach subseasonal-to-seasonal (S2S) or seasonal lead times, often resulting in instability and calibration issues. Long-timestep probabilistic models that generate long-range forecasts in a single step offer an attractive alternative, but training on the 40-year reanalysis record leads to overfitting, suggesting orders of magnitude more training data are required. We introduce long-range distillation, a method that trains a long-timestep probabilistic "student" model to forecast directly at long-range using a huge synthetic training dataset generated by a short-timestep autoregressive "teacher" model. Using the Deep Learning Earth System Model (DLESyM) as the teacher, we generate over 10,000 years of simulated climate to train distilled student models for forecasting across a range of timescales. In perfect-model experiments, the distilled models outperform climatology and approach the skill of their autoregressive teacher while replacing hundreds of autoregressive steps with a single timestep. In the real world, they achieve S2S forecast skill comparable to the ECMWF ensemble forecast after ERA5 fine-tuning. The skill of our distilled models scales with increasing synthetic training data, even when that data is orders of magnitude larger than ERA5. This represents the first demonstration that AI-generated synthetic training data can be used to scale long-range forecast skill.

Kushagra Pandey, Jaideep Pathak, Yilun Xu et al.

Diffusion models achieve state-of-the-art generation quality across many applications, but their ability to capture rare or extreme events in heavy-tailed distributions remains unclear. In this work, we show that traditional diffusion and flow-matching models with standard Gaussian priors fail to capture heavy-tailed behavior. We address this by repurposing the diffusion framework for heavy-tail estimation using multivariate Student-t distributions. We develop a tailored perturbation kernel and derive the denoising posterior based on the conditional Student-t distribution for the backward process. Inspired by $γ$-divergence for heavy-tailed distributions, we derive a training objective for heavy-tailed denoisers. The resulting framework introduces controllable tail generation using only a single scalar hyperparameter, making it easily tunable for diverse real-world distributions. As specific instantiations of our framework, we introduce t-EDM and t-Flow, extensions of existing diffusion and flow models that employ a Student-t prior. Remarkably, our approach is readily compatible with standard Gaussian diffusion models and requires only minimal code changes. Empirically, we show that our t-EDM and t-Flow outperform standard diffusion models in heavy-tail estimation on high-resolution weather datasets in which generating rare and extreme events is crucial.

Stathi Fotiadis, Noah Brenowitz, Tomas Geffner et al.

Conditioning diffusion and flow models have proven effective for super-resolving small-scale details in natural images.However, in physical sciences such as weather, super-resolving small-scale details poses significant challenges due to: (i) misalignment between input and output distributions (i.e., solutions to distinct partial differential equations (PDEs) follow different trajectories), (ii) multi-scale dynamics, deterministic dynamics at large scales vs. stochastic at small scales, and (iii) limited data, increasing the risk of overfitting. To address these challenges, we propose encoding the inputs to a latent base distribution that is closer to the target distribution, followed by flow matching to generate small-scale physics. The encoder captures the deterministic components, while flow matching adds stochastic small-scale details. To account for uncertainty in the deterministic part, we inject noise into the encoder output using an adaptive noise scaling mechanism, which is dynamically adjusted based on maximum-likelihood estimates of the encoder predictions. We conduct extensive experiments on both the real-world CWA weather dataset and the PDE-based Kolmogorov dataset, with the CWA task involving super-resolving the weather variables for the region of Taiwan from 25 km to 2 km scales. Our results show that the proposed stochastic flow matching (SFM) framework significantly outperforms existing methods such as conditional diffusion and flows.

Tom Beucler, Pierre Gentine, Janni Yuval et al.

Projecting climate change is a generalization problem: we extrapolate the recent past using physical models across past, present, and future climates. Current climate models require representations of processes that occur at scales smaller than model grid size, which have been the main source of model projection uncertainty. Recent machine learning (ML) algorithms hold promise to improve such process representations, but tend to extrapolate poorly to climate regimes they were not trained on. To get the best of the physical and statistical worlds, we propose a new framework - termed "climate-invariant" ML - incorporating knowledge of climate processes into ML algorithms, and show that it can maintain high offline accuracy across a wide range of climate conditions and configurations in three distinct atmospheric models. Our results suggest that explicitly incorporating physical knowledge into data-driven models of Earth system processes can improve their consistency, data efficiency, and generalizability across climate regimes.

Griffin Mooers, Jens Tuyls, Stephan Mandt et al.

While cloud-resolving models can explicitly simulate the details of small-scale storm formation and morphology, these details are often ignored by climate models for lack of computational resources. Here, we explore the potential of generative modeling to cheaply recreate small-scale storms by designing and implementing a Variational Autoencoder (VAE) that performs structural replication, dimensionality reduction, and clustering of high-resolution vertical velocity fields. Trained on ~6*10^6 samples spanning the globe, the VAE successfully reconstructs the spatial structure of convection, performs unsupervised clustering of convective organization regimes, and identifies anomalous storm activity, confirming the potential of generative modeling to power stochastic parameterizations of convection in climate models.

Tom Beucler, Michael Pritchard, Pierre Gentine et al.

Data-driven algorithms, in particular neural networks, can emulate the effect of sub-grid scale processes in coarse-resolution climate models if trained on high-resolution climate simulations. However, they may violate key physical constraints and lack the ability to generalize outside of their training set. Here, we show that physical constraints can be enforced in neural networks, either approximately by adapting the loss function or to within machine precision by adapting the architecture. As these physical constraints are insufficient to guarantee generalizability, we additionally propose to physically rescale the training and validation data to improve the ability of neural networks to generalize to unseen climates.

Tom Beucler, Stephan Rasp, Michael Pritchard et al.

Artificial neural-networks have the potential to emulate cloud processes with higher accuracy than the semi-empirical emulators currently used in climate models. However, neural-network models do not intrinsically conserve energy and mass, which is an obstacle to using them for long-term climate predictions. Here, we propose two methods to enforce linear conservation laws in neural-network emulators of physical models: Constraining (1) the loss function or (2) the architecture of the network itself. Applied to the emulation of explicitly-resolved cloud processes in a prototype multi-scale climate model, we show that architecture constraints can enforce conservation laws to satisfactory numerical precision, while all constraints help the neural-network better generalize to conditions outside of its training set, such as global warming.

Yevgeniy Vorobeychik, Michael Pritchard

We propose a framework for cyber risk assessment and mitigation which models attackers as formal planners and defenders as interdicting such plans. We illustrate the value of plan interdiction problems by first modeling network cyber risk through the use of formal planning, and subsequently formalizing an important question of prioritizing vulnerabilities for patching in the plan interdiction framework. In particular, we show that selectively patching relatively few vulnerabilities allows a network administrator to significantly reduce exposure to cyber risk. More broadly, we have developed a number of scalable approaches for plan interdiction problems, making especially significant advances when attack plans involve uncertainty about system dynamics. However, important open problems remain, including how to effectively capture information asymmetry between the attacker and defender, how to best model dynamics in the attacker-defender interaction, and how to develop scalable algorithms for solving associated plan interdiction games.