# Calibrating subgrid parametrizations of single-column ocean models via simulation-based inference

arXiv: https://arxiv.org/abs/2609.13242 · HTML: https://mlsanity.com/paper/2609.13242/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 23 references that are in the map.
- First posted on arXiv 3 Sep 2026.

## Builds on (most cited first, 9 of 9)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations](https://mlsanity.com/paper/1709.00037/) (2017)
- [Truncated proposals for scalable and hassle-free simulation-based inference](https://mlsanity.com/paper/2210.04815/) (2022)
- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [Ensemble Kalman Methods: A Mean Field Perspective](https://mlsanity.com/paper/2209.11371/) (2022)
- [Effortless, Simulation-Efficient Bayesian Inference using Tabular Foundation Models](https://mlsanity.com/paper/2504.17660/) (2025)
- [The Ensemble Kalman Inversion Race](https://mlsanity.com/paper/2511.15853/) (2025)

## Abstract (arXiv)

Subgrid parametrizations of vertical mixing in ocean models depend on free coefficients that cannot be measured directly and must be calibrated against high-fidelity references such as large-eddy simulations (LES). Existing approaches return point estimates and leave the associated uncertainty unquantified, a limitation when the inverse problem is ill-posed or when distinct parameter configurations fit the data comparably well. Simulation-based inference (SBI) addresses exactly this: given a prior and access to the simulator, it approximates the full posterior over parameters without requiring a tractable likelihood, at a cost set by the number of simulator evaluations. We apply it to texttttunax, a JAX-based single-column ocean model, to calibrate the coefficients of its k--varepsilon closure. A blockwise PCA summary statistic compresses the simulator output along the depth axis while preserving its forcing--horizon--variable structure, making inference tractable at modest budgets. We compare neural posterior estimation and its sequential variants against a recent training-free approach built on a tabular foundation model. The latter recovers informative posteriors from a few hundred simulator calls, outperforming the trained estimators at every budget considered.