Ruthvik Mukkamala

Global Challenge: Engineer the Tools of Scientific Discovery

Abstract:

Solving complex partial differential equations (PDEs) accurately and efficiently underpins progress in fields ranging from quantitative finance to structural engineering and infrastructure development. Traditional numerical solvers are computationally intensive and often struggle with high-dimensional or complex-geometry problems. Physics-Informed Neural Networks (PINNs) embed governing physical laws into neu- ral networks, yielding a data-efficient and physically consistent framework for solving both forward and inverse problems. This paper presents a comprehensive review of PINNs, their recent advancements, and applications in finance, construction, and en- gineering. We discuss novel architectures (including CNN- and RNN-based PINNs), improvements in activation functions and optimization strategies, techniques for high- dimensional PDEs, hybrid methods integrating PINNs with classical numerical solvers, and their ability to solve inverse problems. The paper also reviews real-world applica- tions (e.g., smart building energy management, traffic flow, structural health monitor- ing) and examines the ESG implications of deploying these models. Finally, we map the role of PINNs to global areas of excellence such as Infrastructure Innovation and Financial Inclusion.

Bio:

Ruthvik was an Applied Mathematics and Computer Science major at NYU. He was the founder and president of the NYU Robotics Club, which he created from the existing PolyBots club. He built the club into one of the largest collegiate robotics clubs in the country. He worked on quantitative research and development in finance, and will be working in quantitative finance in particular Applied AI/LLM research engineering.