Discovering How Ice Crystals Grow Using Neural ODE's and Symbolic Regression

TL;DR

This paper employs Neural ODEs and symbolic regression to uncover and validate a new functional model for depositional ice crystal growth, enhancing understanding of cloud evolution processes.

Contribution

It introduces a novel approach combining Neural ODEs and symbolic regression to model and derive the physics of ice crystal growth from experimental data.

Findings

The derived model fits 290 ice crystal growth time series.

The new model includes terms proportional to ice crystal mass.

The model accurately reproduces early-stage ice growth in experiments.

Abstract

Depositional ice growth is an important process for cirrus cloud evolution, but the physics of ice growth in atmospheric conditions is still poorly understood. One major challenge in constraining depositional ice growth models against observations is that the early growth rates of ice crystals cannot be directly observed, and proposed models require assumptions about the functional dependence of physical processes that are still highly uncertain. Neural ordinary differential equations (NODE's) are a recently developed machine learning method that can be used to learn the derivative of an unknown function. Here we use NODE's to learn the functional dependence of unknown physics in the depositional ice growth model by optimizing against experimental measurements of ice crystal mass. We find a functional form for the depositional ice growth model that best fits 290 mass time series of ice crystals grown in a levitation diffusion chamber. We use symbolic regression to derive an equation for the function learned by the NODE model, which includes additional terms proportional to ice crystal mass in the capacitance growth model. We evaluate this functional form against experimental data sets from the AIDA Aerosol and Cloud Chamber, finding that our new proposed model for depositional ice growth accurately reproduces experimental results in the early stages of ice crystal growth.