Scalable Accelerated Algorithms for Exascale Simulation and Optimization/Deep Learning
Abstract
The goal of our research has been the development of new scalable accelerated algorithms to enable exascale computing with the aim of dramatically increasing the scale and size of solvable problems in the synergistic domains of (i) simulation and optimization of physical systems, and (ii) training deep neural networks. Towards this goal, we have devised new classes of first-order methods with an eye towards applying these methods to general nonlinear systems arising from numerical simulation of physical processes and also to deep neural networks. While first-order methods have lower complexity per iteration by orders of magnitude compared to second-order or other information-intensive schemes, they suffer from much slower convergence. The main research challenge lies in developing first-order methods (FOMs) with improved convergence rates and making them competitive with second-order methods. In order to accelerate the convergence rate of FOMs, we have been developing fast scalable preconditioners that can be implemented on next-generation exascale platforms to enable numerical simulation of complex physical phenomena at unprecedented speed and accuracy, as well as the real-time solution of ever-larger and more complex deep learning applications. Our aim as always has been to apply our designed algorithms to large-scale simulation and optimization problems of direct interest to the Air Force. More specifically, we have studied nonlocal and nonlinear optical responses associated with surface-plasmon excitations in metallic nanostructures. The combination of fast accurate simulations accounting for nonlocality and nonlinearity with deep learning can provide engineers and scientists with physics-based tools to optimize the performance of nanoplasmonic devices including spectroscopy, lasers, biosensors, super-resolution imaging, and antennas.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 13, 2022
- Accession Number
- AD1230528
Entities
People
- Robert Freund
Organizations
- Massachusetts Institute of Technology