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.

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.

NGoetz/NF

NF