Learning Prognostic Variables for AI Convective Parameterizations via Symbolic Distillation
cs.LG, physics.ao-ph
Submitted: 2026-09-21
Updated: 2026-09-21
Code: https://github.com/DLRPA-EVA/schoenfeld26james
License: http://creativecommons.org/licenses/by/4.0/
The gist: Hybrid AI-physics climate modeling aims to improve coarse (100km-resolution) Earth system models by learning to parameterize subgrid processes from high-fidelity data.
Terminology
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.
Sources
- Simulating Atmospheric Processes in Earth System Models and Quantifying Uncertainties with Deep Learning Multi-Member and Stochastic Parameterizations
- A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling
- An Approach to Symbolic Regression Using Feyn
- Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl
- Adam: A Method for Stochastic Optimization
- SymTorch: Symbolic Distillation of Neural Networks
- climt-paraformer: Stable Emulation of Convective Parameterization using a Temporal Memory-aware Transformer
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