Projects

My research, conducted under the supervision of Professor Pratik Chaudhari, investigates the fundamental limitations of generative models, particularly their inability to model systems exhibiting critical phenomena. By leveraging tools from statistical physics, specifically Renormalization Group (RG) and the Ising model, I aim to characterize where and why deep learning architectures fail to capture scale-invariant properties. My work is grounded in rigorous empirical validation; I have developed training pipelines for diffusion models, achieving high-fidelity performance on benchmarks like MNIST and CIFAR-10 to stress-test these theoretical boundaries. Final thesis is expected by June 2026.

Abstract: Time dependence plays a fundamental role in quantum mechanics, governing the evolution of physical systems across scales from atomic to macroscopic phenomena. Traditional approaches, such as Townsend's second edition of A Modern Approach to Quantum Mechanics, introduce time dependence through rigorous derivations of the time-dependent and time-independent Schrödinger equations. Meanwhile, emerging Al platforms like Gemini offer new pathways for interpreting, solving, and contextualizing quantum problems in real-world applications. This paper compares how time dependence is developed through Townsend's theoretical framework and Gemini's Al-generated modeling. I evaluate each method's strengths in technical accuracy, conceptual clarity, and relevance to practical systems such as particle confinement, free particles, and quantum computing. Finally, I will explore multiple artificial intelligence (Al) platforms such as Open Al's ChatGPT and Perplexity Al to discover the best platform for analyzing physical systems. Note that all Al platforms analyzed used are in the standard version, not a pro or advanced one. My findings highlight the complementary nature of rigorous formalism and accessible computational intuition, suggesting that hybrid learning models combining classical theory and Al-driven interpretation can better prepare students and researchers for advancing quantum technologies.

As part of a design optimization task, I was responsible for modifying a battery-powered jumping bunny toy to enhance its accessibility and usability for children developing fine motor skills. This involved replacing the original small on/off switch with a custom-design, 3D-printed button that was larger and more ergonomically suitable for users requiring assistive technologies. To do this, I carefully disassembled the original circuit, soldered the existing switch and wiring into the newly designed button mechanism, and subsequently restructured the electrical circuit to accommodate the new interface. In addition, I modified the embedded code to ensure proper functionality and responsiveness of the toy in response to the redesigned control input. This project emphasized user-centered design, rapid prototyping, and low-voltage hardware integration.

Abstract: In this paper, we will discuss the fundamentals of black holes, the physics behind their concept, the discoveries supporting their existence, and the different phenomena that result from their implications. Spacetime and the effects of gravity have long troubled astrophysicists and scientists. These concepts determine how the universe and matter inside of it function and react with each other. The concepts are also capable of being utilized in the pursuit of understanding the existence of perhaps the most powerful and yet still mysterious "things" in the universe. We will examine what a black hole consists of, as well as the development and formation of these

"rips" in spacetime and some of the primordial equations and solutions made to interpret them. In this paper, we have written an in-depth explanation of almost every known component of the different types of black holes. In addition, the first few detections of black holes will be explained and the evidence supporting their existence will be provided. To back up our descriptions with credible sources, the groundbreaking discoveries of important astrophysical figures, such as Paul Murdin and Andrea Ghez, will also be discussed. This paper is ultimately aimed at providing a comprehensive description of what a black hole is by exploring almost all conceivable characteristics that have been theorized, interpreted, and discovered.