Accelerating GMRES with Deep Learning in Real-Time

03/19/2021
by   Kevin Luna, et al.
13

GMRES is a powerful numerical solver used to find solutions to extremely large systems of linear equations. These systems of equations appear in many applications in science and engineering. Here we demonstrate a real-time machine learning algorithm that can be used to accelerate the time-to-solution for GMRES. Our framework is novel in that is integrates the deep learning algorithm in an in situ fashion: the AI-accelerator gradually learns how to optimizes the time to solution without requiring user input (such as a pre-trained data set). We describe how our algorithm collects data and optimizes GMRES. We demonstrate our algorithm by implementing an accelerated (MLGMRES) solver in Python. We then use MLGMRES to accelerate a solver for the Poisson equation – a class of linear problems that appears in may applications. Informed by the properties of formal solutions to the Poisson equation, we test the performance of different neural networks. Our key takeaway is that networks which are capable of learning non-local relationships perform well, without needing to be scaled with the input problem size, making them good candidates for the extremely large problems encountered in high-performance computing. For the inputs studied, our method provides a roughly 2× acceleration.

READ FULL TEXT

Authors

page 5

page 8

page 13

page 14

page 15

page 16

03/12/2021

Physics-Informed Deep-Learning for Scientific Computing

Physics-Informed Neural Networks (PINN) are neural networks that encode ...
04/29/2021

Distributed Multigrid Neural Solvers on Megavoxel Domains

We consider the distributed training of large-scale neural networks that...
05/13/2021

Informed Equation Learning

Distilling data into compact and interpretable analytic equations is one...
09/27/2021

Using neural networks to solve the 2D Poisson equation for electric field computation in plasma fluid simulations

The Poisson equation is critical to get a self-consistent solution in pl...
10/12/2021

A fast time domain solver for the equilibrium Dyson equation

We consider the numerical solution of the real time equilibrium Dyson eq...
12/15/2017

Study on a Poisson's Equation Solver Based On Deep Learning Technique

In this work, we investigated the feasibility of applying deep learning ...
04/01/2022

Deep neural networks for solving extremely large linear systems

In this paper, we study deep neural networks for solving extremely large...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.