Prediction of operating dynamics in floating-zone crystal growth using Gaussian mixture model

Data-driven automated control algorithm for floating-zone crystal growth derived by reinforcement learning

“…To validate the automated control of FZ crystal growth by the algorithm using PPO with GMM dynamics, we prepared datasets for training (𝐷 = {(𝒔 𝒕 * , 𝒂 𝒕 * ) 1 , (𝒔 𝒕 * , 𝒂 𝒕 * ) 2 , … , (𝒔 𝒕 * , 𝒂 𝒕 * ) 𝑁 }, where N is the number of training datasets) by use of an emulator program for FZ crystal growth with a given set of dynamics 34 . We prepared 12 datasets aiming to create an ideal crystal shape (𝑑 𝑡 𝑖𝑑𝑒𝑎𝑙 ) as shown in Fig.…”

“…Firstly, we constructed a prediction model for FZ crystal growth by GMM as we previously reported 34 . The number of Gaussian mixtures, which is a hyper-parameter of GMM, was set to 50.…”

Data-driven automated control algorithm for floating-zone crystal growth derived by reinforcement learning

“…Thus, it is necessary to predict the dynamics of FZ crystal growth from the operation trajectories. Due to the difficulty of acquiring numerous operation trajectories for FZ crystal growth, recently we proposed adaptation of the Gaussian mixture model (GMM) to predict the dynamics of FZ crystal growth, and demonstrated that GMM can precisely predict the operation trajectories from only five trajectories used for training 34 . In the present study, we constructed a control model by reinforcement learning using proximal policy optimization (PPO) and dynamics predicted by GMM.…”

“…The details of the training of GMM are described in Ref. 34 . In PPO, the parameterized policies function with parameter vector , which generates input values a t from the current state x t as a probability distribution, is iteratively optimized using a clipped surrogate objective instead of a policy gradient 35 – 37 .…”

“…To validate the automated control of FZ crystal growth by the algorithm using PPO with GMM dynamics, we prepared datasets for training ( , where N is the number of training datasets) by use of an emulator program for FZ crystal growth with a given set of dynamics 34 . We prepared 12 datasets aiming to create an ideal crystal shape as shown in Fig.…”