# Calibration of a neural network ocean closure for improved mean state and variability

arXiv: https://arxiv.org/abs/2604.06398 · HTML: https://mlsanity.com/paper/2604.06398/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 93 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Builds on (most cited first, 11 of 11)

- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [A posteriori learning for quasi-geostrophic turbulence parametrization](https://mlsanity.com/paper/2204.03911/) (2022)
- [Iterative Ensemble Kalman Methods: A Unified Perspective with Some New Variants](https://mlsanity.com/paper/2010.13299/) (2020)
- [Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods](https://mlsanity.com/paper/2104.03384/) (2021)
- [Adaptive regularisation for ensemble Kalman inversion](https://mlsanity.com/paper/2006.14980/) (2020)
- [Online Calibration of Deep Learning Sub-Models for Hybrid Numerical Modeling Systems](https://mlsanity.com/paper/2311.10665/) (2023)
- [The Ensemble Kalman Inversion Race](https://mlsanity.com/paper/2511.15853/) (2025)
- [Adjoint-based online learning of two-layer quasi-geostrophic baroclinic turbulence](https://mlsanity.com/paper/2411.14106/) (2024)
- [Nesterov Acceleration for Ensemble Kalman Inversion and Variants](https://mlsanity.com/paper/2501.08779/) (2025)
- [NORi: An ML-Augmented Ocean Boundary Layer Parameterization](https://mlsanity.com/paper/2512.04452/) (2025)

## Abstract (arXiv)

Global ocean models exhibit biases in the mean state and variability, particularly at coarse resolution, where mesoscale eddies are unresolved. To address these biases, parameterization coefficients are typically tuned ad hoc. Here, we formulate parameter tuning as a calibration problem using Ensemble Kalman Inversion (EKI). We optimize parameters of a neural network parameterization of mesoscale eddies in two idealized ocean models at coarse resolution. The calibrated parameterization reduces errors by factors of 1.7-3.3 in the time-averaged fluid interfaces and their variability compared to the unparameterized model, depending on the metric and configuration. The EKI method is robust to noise in time-averaged statistics arising from chaotic ocean dynamics. Furthermore, we propose an efficient calibration protocol that bypasses integration to statistical equilibrium by carefully choosing an initial condition. These results demonstrate that systematic calibration can substantially improve coarse-resolution ocean simulations and provide a practical pathway for reducing biases in global ocean models.