Simple equations rival neural networks for predicting monsoon rainfall

Symbolic distillation yields interpretable formulas that capture 85% of neural network skill while using a thousand times fewer parameters, revealing that moisture and instability compete rather than combine.

Big Tech

Savannah L. Ferretti · Jane W. Baldwin · Michael S. Pritchard · Tom Beucler

University of California, Irvine · NVIDIA Corporation · University of Lausanne

Research Digest·12 November 2026·3 min read

Illustration: Simple equations rival neural networks for predicting monsoon rainfall

In one line

Symbolic distillation discovered interpretable equations for monsoon precipitation that explain 1.5 times more variance than a standard buoyancy diagnostic.

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An idea this paper builds on

mechanistic interpretabilityThe study of how neural networks compute through internal circuits, features, and causal interventions, rather than just input-output behavior.131 papers →

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Forecasting monsoon rainfall is difficult because it depends on complex interactions of temperature and moisture throughout the lower atmosphere. Current simple models, which combine moisture and instability into a single number, miss important details.

Researchers used a two-step process called symbolic distillation. First, a neural network, a computer model loosely inspired by the brain, learned which vertical layers matter most for rainfall. Then, symbolic regression searched for simple math formulas that fit the network's insights.

The best equation explained about one and a half times more rainfall variation than the standard method and was about a thousand times simpler than the neural network. It revealed that moisture and instability act as opposing controls, with the heaviest rain when the lower free troposphere is humid.

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Concepts

symbolic distillation symbolic regression integration kernel learning knowledge distillation mechanistic interpretability chain of thought