Jakob Buehler L&S Math & Physical Sciences
TENSOR NETWORK METHODS FOR FLUID PDES IN COMPLEX GEOMETRIES
Partial differential equations (PDEs) are the mathematical language scientists use to describe a great variety of physical system, from ocean currents to fusion plasmas. Solving them on a computer becomes prohibitively expensive as problems grow in size and dimension, creating a major bottleneck across science and engineering. Tensor networks are a promising new class of methods that can reduce this cost by exploiting hidden structure in PDE solutions, but so far tensor network techniques have mostly been tried on simple box-shaped domains. The main goal of this project is to extend these methods to more realistic, curved geometries, specifically, the cross-sections of tokamaks, the donut-shaped devices used to confine plasma in fusion energy research. This research systematically compares several tensor representations on these domains to determine which are most viable in practice. The potential benefit of success is a powerful new computational tool for fusion simulation and, more broadly, a bridge between today’s tensor network methods and the complex geometries that appear throughout real-world physics and engineering.
Message To Sponsor
Thank you so much for your generosity! This is my first real research experience, and it's something I wouldn't be able to pursue without your support. What excites me most about this project is that it sits at the intersection of a lot of things I'm interested in: theory, applied mathematics, and computation all combined to solve a real physical problem. I'm grateful for the chance to spend the summer fully focused on it, and I look forward to sharing what comes of it.