scholarly journals Application of a neural network to the sign problem via the path optimization method

2018 ◽  
Vol 2018 (2) ◽  
Author(s):  
Yuto Mori ◽  
Kouji Kashiwa ◽  
Akira Ohnishi
Keyword(s):  
Neural Network ◽  
Optimization Method ◽  
Path Optimization ◽  
Sign Problem

scholarly journals Path optimization in $0+1$D QCD at finite density

2019 ◽  
Vol 2019 (11) ◽  
Author(s):  
Yuto Mori ◽  
Kouji Kashiwa ◽  
Akira Ohnishi
Keyword(s):  
Neural Network ◽  
Quantum Chromodynamics ◽  
Gauge Theories ◽  
Chemical Potential ◽  
Optimization Method ◽  
Feedforward Neural Network ◽  
Path Optimization ◽  
Sign Problem ◽  
Gauge Fixing ◽  
Link Variable

Abstract We investigate the sign problem in $0+1$D quantum chromodynamics at finite chemical potential by using the path optimization method. The SU(3) link variable is complexified to the SL(3,$\mathbb{C}$) link variable, and the integral path is represented by a feedforward neural network. The integral path is then optimized to weaken the sign problem. The average phase factor is enhanced to be greater than 0.99 on the optimized path. Results with and without diagonalized gauge fixing are compared and proven to be consistent. This is the first step in applying the path optimization method to gauge theories.

scholarly journals Toward solving the sign problem with path optimization method

2017 ◽  
Vol 96 (11) ◽  
Author(s):  
Yuto Mori ◽  
Kouji Kashiwa ◽  
Akira Ohnishi
Keyword(s):  
Optimization Method ◽  
Path Optimization ◽  
Sign Problem

scholarly journals Path optimization method for the sign problem

2018 ◽  
Vol 175 ◽  
pp. 07043 ◽  
Author(s):  
Akira Ohnishi ◽  
Yuto Mori ◽  
Kouji Kashiwa
Keyword(s):  
Optimization Method ◽  
Singular Points ◽  
Path Optimization ◽  
Real Field ◽  
Integration Path ◽  
Flow Equations ◽  
The Neural Network ◽  
Sign Problem ◽  
Path Integral Method ◽  
The One

We propose a path optimization method (POM) to evade the sign problem in the Monte-Carlo calculations for complex actions. Among many approaches to the sign problem, the Lefschetz-thimble path-integral method and the complex Langevin method are promising and extensively discussed. In these methods, real field variables are complexified and the integration manifold is determined by the flow equations or stochastically sampled. When we have singular points of the action or multiple critical points near the original integral surface, however, we have a risk to encounter the residual and global sign problems or the singular drift term problem. One of the ways to avoid the singular points is to optimize the integration path which is designed not to hit the singular points of the Boltzmann weight. By specifying the one-dimensional integration-path as z = t +if(t)(f ϵ R) and by optimizing f(t) to enhance the average phase factor, we demonstrate that we can avoid the sign problem in a one-variable toy model for which the complex Langevin method is found to fail. In this proceedings, we propose POM and discuss how we can avoid the sign problem in a toy model. We also discuss the possibility to utilize the neural network to optimize the path.

Cable-path optimization method for industrial robot arms

2022 ◽  
Vol 73 ◽  
pp. 102245
Author(s):  
Shintaro Iwamura ◽  
Yoshiki Mizukami ◽  
Takahiro Endo ◽  
Fumitoshi Matsuno
Keyword(s):  
Industrial Robot ◽  
Optimization Method ◽  
Path Optimization ◽  
Robot Arms
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