Discovering How Ice Crystals Grow Using NODE's and Symbolic Regression

Depositional ice growth is an important process for atmospheric cloud formation, 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 growth rate of ice 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 (NODEs) are a recently developed machine learning method that can be used to learn the derivative of a hidden state. Here we explore how NODE's can be used to evaluate model structural uncertainty in depositional ice growth models by optimizing against experimental measurements. We find a functional form for the depositional ice growth model that best fits 307 mass time series of ice crystals grown in a levitation diffusion chamber. We use symbolic regression to derive a closed form equation for the function learned by the NODE model.