Knowledge-Guided Machine Learning for Shape Parameter and Drag Coefficient Prediction of Falling Snowflakes

Abstract A novel knowledge-guided convolutional neural network (KGCNN) is presented in this work for the prediction of various three-dimensional shape parameters, drag coefficient, mass, and density of falling snowflakes. To compensate for the lack of extensive data on real snow, the neural network model is pretrained on images of synthetic snowflakes that are geometrically similar to real snowflakes. The model is then fine-tuned on real snowflake images from available datasets for effective drag coefficient prediction. Existing drag coefficient correlations are integrated into the final layer of the KGCNN to remove the burden of learning the relationship between the Reynolds number and drag coefficient from the model. The shape parameter outputs are also regularized by custom knowledge-guided loss functions to ensure physical interpretability and allow for simultaneous prediction of particle volume and density. Pretraining and custom loss functions were found to reduce normalized root-mean-square error (NRMSE) on mass by 11.8%. Integration of drag coefficient correlations reduced mass NRMSE by 30.1% over similar models directly predicting drag coefficient and outperformed existing physical correlations for snowflake drag coefficient. Predictions of shape parameters, volume, and density by the KGCNN were found to be consistent with experimental values. Significance Statement This work aims to provide a method of estimating the three-dimensional shape of snowflakes, as well as drag coefficient, mass, and density, from a single image of a falling snowflake. This method combines machine learning with existing knowledge of particle falling behavior for a more robust and accurate prediction than the individual parts could achieve alone. By combining this approach with high-quality cameras, properties of a given snow event can be estimated and used for the gathering of data for large-scale weather prediction and monitoring. Alternatively, the measured properties of a snow event could be used to predict local snowpack properties relevant to avalanches or vehicle mobility.