L. Ruby Leung

Aniruddha Bora, Khemraj Shukla, Shixuan Zhang et al.

Numerical simulation for climate modeling resolving all important scales is a computationally taxing process. Therefore, to circumvent this issue a low resolution simulation is performed, which is subsequently corrected for bias using reanalyzed data (ERA5), known as nudging correction. The existing implementation for nudging correction uses a relaxation based method for the algebraic difference between low resolution and ERA5 data. In this study, we replace the bias correction process with a surrogate model based on the Deep Operator Network (DeepONet). DeepONet (Deep Operator Neural Network) learns the mapping from the state before nudging (a functional) to the nudging tendency (another functional). The nudging tendency is a very high dimensional data albeit having many low energy modes. Therefore, the DeepoNet is combined with a convolution based auto-encoder-decoder (AED) architecture in order to learn the nudging tendency in a lower dimensional latent space efficiently. The accuracy of the DeepONet model is tested against the nudging tendency obtained from the E3SMv2 (Energy Exascale Earth System Model) and shows good agreement. The overarching goal of this work is to deploy the DeepONet model in an online setting and replace the nudging module in the E3SM loop for better efficiency and accuracy.

Aniruddha Bora, Shixuan Zhang, Khemraj Shukla et al.

Coarse resolution, imperfect parameterizations, and uncertain initial states and forcings limit Earth-system model (ESM) predictions. Traditional bias correction via data assimilation improves constrained simulations but offers limited benefit once models run freely. We introduce an operator-learning framework that maps instantaneous model states to bias-correction tendencies and applies them online during integration. Building on a U-Net backbone, we develop two operator architectures Inception U-Net (IUNet) and a multi-scale network (M\&M) that combine diverse upsampling and receptive fields to capture multiscale nonlinear features under Energy Exascale Earth System Model (E3SM) runtime constraints. Trained on two years E3SM simulations nudged toward ERA5 reanalysis, the operators generalize across height levels and seasons. Both architectures outperform standard U-Net baselines in offline tests, indicating that functional richness rather than parameter count drives performance. In online hybrid E3SM runs, M\&M delivers the most consistent bias reductions across variables and vertical levels. The ML-augmented configurations remain stable and computationally feasible in multi-year simulations, providing a practical pathway for scalable hybrid modeling. Our framework emphasizes long-term stability, portability, and cadence-limited updates, demonstrating the utility of expressive ML operators for learning structured, cross-scale relationships and retrofitting legacy ESMs.

Benedikt Barthel Sorensen, Alexis Charalampopoulos, Shixuan Zhang et al.

Due to the rapidly changing climate, the frequency and severity of extreme weather is expected to increase over the coming decades. As fully-resolved climate simulations remain computationally intractable, policy makers must rely on coarse-models to quantify risk for extremes. However, coarse models suffer from inherent bias due to the ignored "sub-grid" scales. We propose a framework to non-intrusively debias coarse-resolution climate predictions using neural-network (NN) correction operators. Previous efforts have attempted to train such operators using loss functions that match statistics. However, this approach falls short with events that have longer return period than that of the training data, since the reference statistics have not converged. Here, the scope is to formulate a learning method that allows for correction of dynamics and quantification of extreme events with longer return period than the training data. The key obstacle is the chaotic nature of the underlying dynamics. To overcome this challenge, we introduce a dynamical systems approach where the correction operator is trained using reference data and a coarse model simulation nudged towards that reference. The method is demonstrated on debiasing an under-resolved quasi-geostrophic model and the Energy Exascale Earth System Model (E3SM). For the former, our method enables the quantification of events that have return period two orders longer than the training data. For the latter, when trained on 8 years of ERA5 data, our approach is able to correct the coarse E3SM output to closely reflect the 36-year ERA5 statistics for all prognostic variables and significantly reduce their spatial biases.

Paul A. Ullrich, Elizabeth A. Barnes, William D. Collins et al.

Machine learning (ML) is a revolutionary technology with demonstrable applications across multiple disciplines. Within the Earth science community, ML has been most visible for weather forecasting, producing forecasts that rival modern physics-based models. Given the importance of deepening our understanding and improving predictions of the Earth system on all time scales, efforts are now underway to develop forecasting models into Earth-system models (ESMs), capable of representing all components of the coupled Earth system (or their aggregated behavior) and their response to external changes. Modeling the Earth system is a much more difficult problem than weather forecasting, not least because the model must represent the alternate (e.g., future) coupled states of the system for which there are no historical observations. Given that the physical principles that enable predictions about the response of the Earth system are often not explicitly coded in these ML-based models, demonstrating the credibility of ML-based ESMs thus requires us to build evidence of their consistency with the physical system. To this end, this paper puts forward five recommendations to enhance comprehensive, standardized, and independent evaluation of ML-based ESMs to strengthen their credibility and promote their wider use.

Julian R. Rice, Karthik Balaguru, Fadia Ticona Rollano et al.

Storm surge is one of the deadliest hazards posed by tropical cyclones (TCs), yet assessing its current and future risk is difficult due to the phenomenon's rarity and physical complexity. Recent advances in artificial intelligence applications to natural hazard modeling suggest a new avenue for addressing this problem. We utilize a deep learning storm surge model to efficiently estimate coastal surge risk in the United States from 900,000 synthetic TC events, accounting for projected changes in TC behavior and sea levels. The derived historical 100-year surge (the event with a 1% yearly exceedance probability) agrees well with historical observations and other modeling techniques. When coupled with an inundation model, we find that heightened TC intensities and sea levels by the end of the century result in a 50% increase in population at risk. Key findings include markedly heightened risk in Florida, and critical thresholds identified in Georgia and South Carolina.