Development of the VGF Crystal Growth Recipe: Intelligent Solutions of Ill‐Posed Inverse Problems using Images and Numerical Data

Development of the Vertical Growth Freeze crystal growth process is a typical example of solving the ill‐posed inverse problem, which violates one or more of Hadamard's well‐posedness criteria of solution existence, uniqueness, and stability. In this study, different data‐driven approaches are used to solve inverse problems: Reduced Order Modelling method of Proper Orthogonal Decomposition with Inverse Distance weighting (ROM POD InvD), an approximation method of Kriging and Artificial Neural Networks (ANN) employing images, combination of images and numerical data and solely numerical data, respectively. The ≈200 training data are generated by Computational Fluid Dynamics (CFD) simulations of the forward problem. Numerical input data are related to the temperatures and coordinates in 10 characteristic monitoring points in the melt and crystal, while the image input data are related to the interface shape and position. Using the random mean squared error as a criterion, the Kriging method based on images and numerical data and the ANN method based on numerical data are able to capture the system behavior more accurately, in contrast to the ROM POD InvD method, which is based solely on images.