# Retrofitting Earth System Models with Cadence-Limited Neural Operator Updates

arXiv: https://arxiv.org/abs/2512.03309 · HTML: https://mlsanity.com/paper/2512.03309/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 2 Dec 2025.

## Builds on (most cited first, 10 of 10)

- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2208.05419/) (2022)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [A non-intrusive machine learning framework for debiasing long-time coarse resolution climate simulations and quantifying rare events statistics](https://mlsanity.com/paper/2402.18484/) (2024)

## Built on by (most cited first, 1 of 1)

- [Probabilistic Predictions of Process-Induced Deformation in Carbon/Epoxy Composites Using a Deep Operator Network](https://mlsanity.com/paper/2512.13746/) (2025)

## Abstract (arXiv)

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.