Prediction of thermodynamic parameters from simulated 2D dendritic morphology via machine learning.

The formation of dendritic patterns are controlled by various thermodynamic and kinetic factors. However, these parameters are usually determined through other more complicated characterization methods, while the shape characteristics from dendritic pattern itself is neglected. In this paper, we present a concept of predicting physical parameters from dendritic morphology via machine learning methods. Two model parameters from Kobayashi’s phase field model, namely the dimensionless latent heat and strength of anisotropy, are selected as labels for prediction.
We then performed a series of simulations with different parameter combinations, during which the whole solidification process is sampled as sequential images of 2D dendritic patterns. The
data set consists of around 10000 data points from different combination of dimensionless latent heat, strength of anisotropy and simulation time step. Several morphological features are
extracted from the images, concatenated with two labels and split into training and test data. Three machine learning models, namely Lasso Regression, Kernel Ridge Regression(KRR) and
Fully Connected Neural Network(FCNN), are trained via cross validation on the training data set and predict the parameters from test data. Comparison between predicted values and original labels of the test data show great predictive power regarding both parameters among all three models, but KRR produces more accurate predictions with smaller training sets. Moreover, results from Lasso regression build up a quantitative relation between dimensionless latent heat and some morphology characteristics. It is eventually shown that such quantitative equation coincides with the singular limit equation of Kobayashi’s model. As a conclusion, this work has demonstrated the viability of applying machine learning methods to predict thermodynamic and kinetic parameters directly from dendritic patterns.