Steady-State Control and Machine Learning of Large-Scale Deformable Mirror Models

We use Machine Learning (ML) and system identification validation approaches to estimate neural network models of large-scale Deformable Mirrors (DMs) used in Adaptive Optics (AO) systems. To obtain the training, validation, and test data sets, we simulate a realistic large-scale Finite Element (FE) model of a faceplate DM. The estimated models reproduce the input-output behavior of Vector AutoRegressive with eXogenous (VARX) input models and can be used for the design of high-performance AO systems. We address the model order selection and overfitting problems. We also provide an FE based approach for computing steady-state control signals that produce the desired wavefront shape. This approach can be used to predict the steady-state DM correction performance for different actuator spacings and configurations. The presented methods are tested on models with thousands of state variables and hundreds of actuators. The numerical simulations are performed on low-cost high-performance graphic processing units and implemented using the TensorFlow machine learning framework. The used codes are available online. The approaches presented in this paper are useful for the design and optimization of high-performance DMs and AO systems.