This project is deprecated. Please refer to Zünis for the follow-up implementation.

NF

An implementation of importance sampling with normalizing flows based on (Müller et. al, 2019), implemented in Pytorch. A phase space generator based on "RAMBO on diet" (Plätzer, 2018) is included in order to be used with matrix elements generated by, for example, MadGraph 5.

Table of contents

• General info
• Technologies
• Setup
• Features
• Status

General info

Conventional adaptive importance sampling, like with the VEGAS algorithm, often fails when the integration variables are correlated, for example for a Gaussian double peak on the diagonal. Training normalizing flows via neural networks offers the possibility to generate a variable transformation which reduces the variance even in such cases.

Technologies

• Python - version >2.5
• PyTorch - version 1.6
• LHAPDF - version 6.3.0

Setup

Install the package using pip install . from inside the folder. Afterwards, the code can be run by importing the package directly!

Code Examples

Training a double peak:

from nisrep.normalizing_flows.manager import *

def camel(x):
    return torch.exp( -((x[:,0]-0.75)**2+(x[:,1]-0.75)**2)/(0.2**2))+torch.exp( -((x[:,0]-0.25)**2+(x[:,1]-0.25)**2)/(0.2**2))

n_flow=2

NF =  PWQuadManager(n_flow=n_flow)
NF.create_model(2,4, [3]*3)
optim = torch.optim.Adamax(NF._model.parameters(),lr=2e-3, weight_decay=1e-04) 
NF._train_variance_forward_seq(camel,optim,True, "./logs/tmp/",10000,300,0,True, True,preburn_time=50)

Afterwards, NF.best_model can be used for Monte-Carlo integration!

res, res_err=NF.integrate(f, nitn, neval)

If the function is a matrix element of collision event, the phase space generator module can be used to map the output of the model into the phase space:

from nisrep.PhaseSpace.flat_phase_space_generator import *

mass=100
my_PS_generator=FlatInvertiblePhasespace([mass]*2, [mass + 0.*i for i in range(4)],
                                            pdf=None,pdf_active=False)
momenta, wgt = my_PS_generator.generateKinematics_batch(E_cm, w,pT_mincut=0,
                                                            delR_mincut=0, rap_maxcut=-1,pdgs=[2,-1])

Take a look at the Demo Notebook

Features

• Neural importance sampling based on variance loss with linear and quadratic coupling cells
• Flat phase space generator for massive and massless 2 -> X processes, supporting PDFs as well as pT, del_r and rapidity cuts

To-do list:

• Inversion of the coupling cells and the phase space generator

Status

Project is: This project is deprecated. Please refer to Zünis for the follow-up implementation.