Discovering how ice crystals grow using neural ODEs and symbolic regression

Depositional ice growth strongly influences the evolution and lifetime of ice-containing clouds on Earth and Mars, yet its physics remain uncertain because the earliest stages of ice-crystal growth cannot be directly observed and are sparsely sampled in laboratory settings. Here, we use physics-informed machine learning to learn the functional dependence of unknown physics in the depositional ice growth model from limited observations. By optimizing against mass growth time series from 290 ice crystals grown in a levitation diffusion chamber, we identify a modified capacitance growth model that more accurately captures observed early-stage growth. The resulting functional form, retrieved using symbolic regression, outperforms existing parameterizations and generalizes well to independent measurements from the AIDA Aerosol and Cloud Chamber. Our data-efficient learning framework provides an improved representation of depositional ice growth and offers a pathway to infer unresolved physical processes in other systems that are sparsely observed.