Discovering a Model for Depositional Ice Growth from Observations Using Neural Ordinary Differential Equations and Symbolic Regression

Depositional ice growth is an important process for the growth and evolution of ice crystals in the atmosphere. Although several depositional ice growth models have been proposed, it has traditionally been challenging to constrain both the structural and parametric uncertainty of these models, particularly during the early stages of ice formation. Previous analyses of levitation diffusion chamber experiments and cloud chamber experiments require assumptions about the functional form and have focused on finding parameters to fit proposed models.

Building on recent developments in scientific machine learning, we propose a new approach using neural ordinary differential equations to analyze these experimental data sets that can directly learn the functional dependence of the depositional ice growth rate. We test this approach on synthetic data generated with a known functional dependence for ice growth. Our approach is able to accurately learn an underlying functional dependence for the saturation and temperature dependent deposition coefficient from Nelson and Baker, 2005.

However, applying this same method to measurements of >300 ice crystal mass times series in a levitation diffusion chamber and 48 adiabatic expansion experiments from AIDA indicates the capacitance model with a deposition coefficient functionally dependent on saturation and temperature cannot accurately reproduce all observations. We learn a saturation and temperature dependent modification to the capacitance growth model, which more accurately reproduces observations. We use symbolic regression to find an equation for this depositional ice growth model and evaluate the uncertainty in the derived functional form and parameter values using a deep ensemble method where we can simultaneously constrain parametric and structural uncertainty on depositional ice growth models.