Application of deep and reinforcement learning to boundary control problems

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.

AI Driven Near Real-time Locational Marginal Pricing Method: A Feasibility and Robustness Study

Accurate price predictions are essential for market participants in order to optimize their operational schedules and bidding strategies, especially in the current context where electricity prices become more volatile and less predictable using classical approaches. Locational Marginal Pricing (LMP) pricing mechanism is used in many modern power markets, where the traditional approach utilizes optimal power flow (OPF) solvers. However, for large electricity grids this process becomes prohibitively time-consuming and computationally intensive. Machine learning solutions could provide an efficient tool for LMP prediction, especially in energy markets with intermittent sources like renewable energy. The study evaluates the performance of popular machine learning and deep learning models in predicting LMP on multiple electricity grids. The accuracy and robustness of these models in predicting LMP is assessed considering multiple scenarios. The results show that machine learning models can predict LMP 4-5 orders of magnitude faster than traditional OPF solvers with 5-6\% error rate, highlighting the potential of machine learning models in LMP prediction for large-scale power models with the help of hardware solutions like multi-core CPUs and GPUs in modern HPC clusters.