Pranav Jain

I am a CS PhD student at University of Southern California , advised by Prof. Oded Stein and Prof. Krishna Garikipati . My research lies at the intersection of physics-based simulation, scientific machine learning, geometry processing, and numerical analysis.

My research interests include:

• Physics-based simulation: Developing numerical methods for PDE-governed systems, including fluids and processes on curved surfaces.
• Scientific machine learning: Studying neural PDE solvers with an emphasis on convergence, accuracy, stability, and reliability.
• Mesh- and grid-free methods: Exploring continuous simulation techniques that avoid fixed discretizations and handle complex geometries.
• Optimal transport for simulation: Investigating transport-based formulations for representing physical evolution and designing new algorithms.

Broadly, my goal is to develop mesh/grid-free simulation methods for complex geometries while establishing a clearer understanding of their accuracy and convergence.

I am currently looking for research internships for Summer 2027! If you have any open positions and feel that my profile fits your vacancy, please do reach out!