Efficient Tensor Network Low-Rank Approximation for Solving High-Dimensional PDEs
Abstract
Tensor networks (TNs) were introduced more than 30 years ago to solve high-dimensional many-body quantum problems. In the past decade, methods involving TNs have been utilized across a rapidly growing and diverse range of application domains, far beyond the initial focus on quantum problems. TNs decompose high-dimensional functions into sparsely interconnected, lower-dimensional functions and can break the curse of dimensionality in many application areas, including solving high-dimensional partial differential equations (PDEs). However, the computational cost of solving nonlinear PDEs on low-rank tensor manifolds can exceed that of solving the full-order model for a large class of problems. This issue is the primary barrier to adopting TNs for a large class of computational science and engineering problems because reducing the computational cost is the primary reason low-rank approximations are utilized.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 06, 2025
- Source ID
- FA95502510039
Entities
People
- Hessam Babaee
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Pittsburgh