UNTANGLING COMPUTATION
Abstract
The proposed work addresses three major challenges arising as computational scientists and engineer tackle larger problems with ever larger computational resources. I: The need to divide problems over many computational nodes, possibly distributed across the world. II: The coupling of effects on different scales leads to highly ill-conditioned problems. III: The possibly exponential growth in the number of interactions among degrees of freedom. The proposed work follows three synergistic research thrusts. Thrust I develops randomized methods for almost communication-free parallel computation. It expresses the target problem as the sum of a vast number of miniature problems, randomly solves some of them individually, and averages the result. The bias of this estimator is then removed using novel bias corrections based on the bootstrap.Thrust II decouples ill-conditioned minimization problems into benign multi-agent games. It develops algorithms for solving the resulting games and applies them to challenging problems in computational mechanics.Thrust III develops a systematic approach for the targeted reduction of non-Gaussian data, based on sparse cumulant tensors. It further develops a calculus based on tensor decompositions that allows manipulating the resulting objects and computing statistically important quantities, such as conditionals or higher-order moments.Approved for Public Release
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jun 29, 2023
- Source ID
- N000142312545
Entities
People
- Florian Schaefer
Organizations
- Georgia Tech Research Corporation
- Office of Naval Research
- United States Navy