Optimization of depth-graded multilayer structure for x-ray optics using machine learning

Abstract

We present a general machine-learning-based approach to solve the inverse design problem of depth-graded multilayer structures (so-called supermirrors) for x-ray optics. Our model uses Monte Carlo tree search (MCTS) with policy gradient in combination with a reflectivity simulation. MCTS is an iterative design method that showed competitive efficiency in materials design and discovery problems. A policy gradient algorithm with a neural network was added to optimize the tree expansion. The policy gradient is a reinforcement learning method that optimizes parametrized policies toward an expected return using gradient descent. This approach is applied to design a depth-graded multilayer structure that maximizes mean reflectivity in an angular range for Cu Kα radiation by selecting the optimal thickness and material for each layer in the structure. Mean reflectivity of 0.80 was achieved in an angular range of 0.45–0.55°. Alternating materials are selected from a predetermined set of materials. We confirmed that the policy gradient enhances the efficiency of MCTS. This approach can be applied autonomously on several x-ray applications without any parameter tuning or pre-available data.