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

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 K alpha 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 degrees. 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.