Learning Prognostic Variables for AI Convective Parameterizations via Symbolic Distillation
Abstract
Hybrid AI-physics climate modeling aims to improve coarse (~100km-resolution) Earth system models by learning to parameterize subgrid processes from high-fidelity data. However, this so far mostly involves local-in-time, diagnostic parameterizations, in which the subgrid state depends only on the current coarse state with no memory of previous states, which is unrealistic for processes such as convection that have intrinsic persistence. To address this, we enhance local-in-time parameterizations by learning prognostic variables that compactly carry important, additional past information where no explicit sub-grid information is available. First we compress past information into a low-dimensional latent space using an autoencoder, which then informs a neural network trained to parameterize targeted subgrid-scale processes. We then replace the autoencoder with symbolic equations that govern the time evolution of the latent variables, yielding additional prognostic memory variables that can be integrated alongside the resolved atmospheric state. We evaluate this approach on two systems: the Lorenz-96 model (online) and surface precipitation from high-resolution atmospheric simulations (offline). A forced multivariate linear ordinary differential equation recovers most of the added value achieved by the autoencoder-based approach in both experiments. Benchmarked against diagnostic parameterizations without memory, our memory-informed approach improves climate statistics and temporal structure, including a realistic diurnal cycle of tropical land precipitation.
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BibTeX
@misc{schonfeld2026learning,
title = {{Learning Prognostic Variables for AI Convective Parameterizations via Symbolic Distillation}},
author = {Jurij Schönfeld and Tom Beucler and Julien Savre and Steven Sherwood and Veronika Eyring},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24882},
eprint = {2609.24882},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24882},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Learning Prognostic Variables for AI Convective Parameterizations via Symbolic Distillation
AU - Jurij Schönfeld
AU - Tom Beucler
AU - Julien Savre
AU - Steven Sherwood
AU - Veronika Eyring
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24882
UR - https://arxiv.org/abs/2609.24882
AB - Hybrid AI-physics climate modeling aims to improve coarse (~100km-resolution) Earth system models by learning to parameterize subgrid processes from high-fidelity data. However, this so far mostly involves local-in-time, diagnostic parameterizations, in which the subgrid state depends only on the current coarse state with no memory of previous states, which is unrealistic for processes such as convection that have intrinsic persistence. To address this, we enhance local-in-time parameterizations by learning prognostic variables that compactly carry important, additional past information where no explicit sub-grid information is available. First we compress past information into a low-dimensional latent space using an autoencoder, which then informs a neural network trained to parameterize targeted subgrid-scale processes. We then replace the autoencoder with symbolic equations that govern the time evolution of the latent variables, yielding additional prognostic memory variables that can be integrated alongside the resolved atmospheric state. We evaluate this approach on two systems: the Lorenz-96 model (online) and surface precipitation from high-resolution atmospheric simulations (offline). A forced multivariate linear ordinary differential equation recovers most of the added value achieved by the autoencoder-based approach in both experiments. Benchmarked against diagnostic parameterizations without memory, our memory-informed approach improves climate statistics and temporal structure, including a realistic diurnal cycle of tropical land precipitation.
ER -