JosephPB / n3jet

Neural networks for high precision scattering amplitudes

n3jet

Note: For use of the generaic NJet python interface see NJet_interface/ directory.

Neural Network NJet (n3jet) is a package to enable training and inference of neural networks using the NJet numerical matrix element calculation package. The package presented here accompanies the paper arXiv:2002.07516.

Specifically, we aim to use neural networks as a multi-dimensional interpolation function for complex, high-multiplicity QCD processes at both leading order (LO) and next-to-leading order (NLO). NLO processes at these multiplicities are very computationally expensive to calculate and therefore by training network approximations, we aim to reduce this computational time by a factor ~ proportional to the ratio of the number of phase-space points used in inferences / the number of points required for training.

Here, we provide implementations for the processes e+e- -> <= 5 jets. In the case of NLO approximations, NJet calculates the virtual matrix correction and therefore we exploring approximating both these corrections explicitly and the NLO/LO k-factors in which the LO divergences have been normalised.

As can be seen in the paper, we test both the ability of a single network to approximate the entirety of uniformly sampled phase-space, as well as taking an ensemble approach based on the phase-space partitioning carried out during FKS subtraction. Implementations of both the single network and ensemble approach are provided here for ease of use and comparison.

Usage

Run:

pip install -e .

Requirements

This package was written in Python 2 since the current NJet interface is not Python 3 compatible, although this should also be Python 3 compatible.

The user is expected to have downloaded and installed NJet.

The requirements.txt should contain all remaining packages.

Note: Every file in this directory should be internally references with the only external reference pointing to you version of the NJet home directory. Please change this in: n3jet/utils/njet_run_functions.py.

Structure

The directory is structured as follows:

|-LO/
  |- single/
  |- fks_ensemble/
|-NLO/
  |- single/
  |- fks_ensemble/
|-models/
  |- model.py
  |- model_dataset.py
|-phase/
  |- ## functions for different phase-space sampling algorithms ##
|-utils/
  |- ## utility files for calling njet and data generation ##
|-tests/
  |- ## test scripts for datasets ##

Interfacing with NJet

n3jet is designed to enable data generation suitable for machine learning models from NJet through a Python interface. Therefore, this package requires NJet to be installed, although does not require the use of additional package linkings.

Note: Every file in this directory should be internally references with the only external reference pointing to you version of the NJet home directory. Please change this in: n3jet/utils/njet_run_functions.py.

Most of the functions interfacing with NJet have been taken and adapted from the NJet/blha/njeyt.py and NJet/examples/runtests.py scripts and many of the relevant functions appear in n3jets/utils/njet_run_functions.py.

Data generation

We offer several methods of data generation:

• explicit 2/3 jet sampling parameterised by jet energy and angles with default uniform sampling although this can be altered (see n3jet/phase/phase_space.py)
• uniform sampling across the whole of phase-space with RAMBO with a single global cut using the JADE algorithm (see n3jet/phase/rambo_while.py)
• uniform sampling over two regions separated by another JADE cut allowing for e.g. the creation of divergent and non-divergent region datasets (see n3jet/phase/rambo_piecewise_balance.py)

Note:. To make generting LO data according to the second point easier you can use the n3jet/LO/single/LO_datasets.py script with the appropriate flags, while NLO data can be done using: n3jet/NLO/NLO_datasets.py.

Models

The models directory contains machine learning models which are all written in Keras.

Models are written as classes which include all the necessary functions for data processing, allowing the user to process data without training a model as well as just having to call model.fit() if the class was initialised with the desired data.

The default model is a three hidden layer, fully connected model, however, the baseline_model() function can easily be changed and substituted for training alternatives.

Single network models

Generating data and training networks on uniformly sampled data can be done using n3jet/LO/single/LO_datasets_models.py, while the equivalent for NLO can be achieved by using n3jet/NLO/NLO_datasets_modles.py.

FKS inspired ensemble

TODO

• Update README for new package details