  The boundary control problem is a non-convex optimization and control problem
in many scientific domains, including fluid mechanics, structural engineering,
and heat transfer optimization. The aim is to find the optimal values for the
domain boundaries such that the enclosed domain adhering to the governing
equations attains the desired state values. Traditionally, non-linear
optimization methods, such as the Interior-Point method (IPM), are used to
solve such problems.
  This project explores the possibilities of using deep learning and
reinforcement learning to solve boundary control problems. We adhere to the
framework of iterative optimization strategies, employing a spatial neural
network to construct well-informed initial guesses, and a spatio-temporal
neural network learns the iterative optimization algorithm using policy
gradients. Synthetic data, generated from the problems formulated in the
literature, is used for training, testing and validation. The numerical
experiments indicate that the proposed method can rival the speed and accuracy
of existing solvers. In our preliminary results, the network attains costs
lower than IPOPT, a state-of-the-art non-linear IPM, in 51\% cases. The overall
number of floating point operations in the proposed method is similar to that
of IPOPT. Additionally, the informed initial guess method and the learned
momentum-like behaviour in the optimizer method are incorporated to avoid
convergence to local minima.
