While optimization problems are ubiquitous in all domains of engineering, they are of critical importance to power systems engineers. A safe and economical operation of the power systems entails solving many optimization problems such as security-constrained unit commitment, economic dispatch, optimal power flow, optimal planning, etc. Although traditional optimization solvers and software have been successful so far in solving these problems, there is a growing need to accelerate the solution process. This need arises on account of several aspects of grid modernization, such as distributed energy resources, renewable energy, smart inverters, batteries, etc, that increase the number of decision variables involved. Moreover, the technologies entail faster dynamics and unpredictability, further demanding a solution speedup. Yet another concern is the growing communication overhead that accompanies this large-scale, high-speed, decision-making process. This thesis explores three different directions to address such concerns. The first part of the thesis explores the learning-to-optimize paradigm whereby instead of solving the optimization problems, machine learning (ML) models such as deep neural networks (DNNs) are trained to predict the solution of the optimization problems. The second part of the thesis also employs deep learning, but in a different manner. DNNs are utilized to model the dynamics of IEEE 1547.8 standard-based local Volt/VAR control rules, and then leverage efficient deep learning libraries to solve the resulting optimization problem. The last part of the thesis dives into the evolving field of quantum computing and develops a general strategy for solving stochastic binary optimization problems using variational quantum eigensolvers (VQE). / Doctor of Philosophy / A reliable and economical operation of power systems entails solving large-scale decision-making mathematical problems, termed as optimization problems. Modern additions to power systems demand an acceleration of this decision-making process while managing the accompanying communication overheads efficiently. This thesis explores the application of two recent advancements in computer science -- machine learning (ML) and quantum computing (QC), to address the above needs. The research presented in this thesis can be divided into three parts. The first part proposes replacing conventional mathematical solvers for optimization problems, with ML models that can predict the solutions to these solvers. Colloquially referred to as learning-to-optimize, this paradigm learns from a historical dataset of good solutions and extrapolates them to make new decisions in a fast manner, while requiring potentially limited data. The second part of the thesis also uses ML models, but differently. ML models are used to represent the underlying physical dynamics, and convert an originally challenging optimization problem into a simpler one. The new problem can be solved efficiently using popular ML toolkits. The third and final part of the thesis aims at accelerating the process of finding optimal binary decisions under constraints, using QC.

Objective Video Quality Assessment plays a vital role in visual processing systems and especially in the mobile communication field, some of the video applications boosted the interest of robust methods for quality assessment. Out of all existing methods for Video Quality Analysis, No-Reference (NR) Video Quality Assessment is the one which is most needed in situations where the handiness of reference video is not available. Our challenge lies in formulating and melding effective features into one model based on human visualizing characteristics. Our research work explores the tradeoffs between quality prediction and complexity of a system. Therefore, we implemented support vector regression algorithm as NR-based Video Quality Metric(VQM) for quality estimation with simplified input features. The features are obtained from extraction of H.264 bitstream data at the decoder side of the network. Our metric predicted with Pearson correlation coefficient of 0.99 for SSIM, 0.98 for PEVQ, 0.96 for subjective score and 0.94 for PSNR metric. Therefore in terms of prediction accuracy, the proposed model has good correlation with all deployed metrics and the obtained results demonstrates the robustness of our approach. In our research work, the proposed metric has a good correlation with subjective scores which concludes that proposed metric can be employed for real time use, since subjective scores are considered as true or standard values of video quality.

We explore the paradigm shift in quantum computing and quantum information science, emphasizing the synergy between hardware advancements and algorithm development. Only now have the recent advances in quantum computing hardware, despite a century of quantum mechanics, unveiled untapped potential, requiring innovative algorithms for full utilization. Project 1 addresses quantum applications in radiative reactions, overcoming challenges in many-fermion physics due to imaginary time evolution, stochastic methods like Monte Carlo simulations, and the associated sign problem. The methodology introduces the Electromagnetic Transition System and a general two-level system for computing radiative capture reactions. Project 2 utilizes Variational Quantum Eigensolver (VQE) to address the difficulties in adiabatic quantum computations, highlighting Singular Value Decomposition (SVD) in quantum computing. Results demonstrate an accurate ground state wavefunction match with only a 0.016% energy error. These projects advance quantum algorithm design, error mitigation, and SVD integration, showcasing quantum computing’s transformative potential in computational science.