Linear Model

This model was presented in Ref. CMMU25.

Model Repository: https://github.com/HEP-PBSP/wmin-model .

What is this model for?

This model is especially suitable for running bayesian fits. It can be used to:

  1. Bayesian PDF Fits with POD Parametrisation

  2. POD Basis Construction Generate a Proper Orthogonal Decomposition (POD) basis (see Ref. CMMU25 for details on what this is).

How to use this model

You can find installation instructions in the model repository.

Constructing a POD basis

The following is an example runcard that can be used to construct a POD basis:

meta:
title: POD basis
author: Lazy Person
keywords: ["POD basis", "wmin"]

# NNPDF Neural Net Architecture settings
replica_range_settings:
min_replica: 1
max_replica: 1000   # generate replicas numbered 1 to 1000


impose_sumrule: true
filter_sr_outliers: false   # whether to filter sum rules outliers

fitbasis: EVOL

nodes: [25, 20, 8]

activations: ["tanh", "tanh", "linear"]

initializer_name: "glorot_normal"
layer_type: "dense"


# Number of components to keep
Neig: 10

# theoryid used after SVD to evolve fit
theoryid: 40_000_000

actions_:
- write_pod_basis

This will generate max_replica - min_replica random initialisations of the n3fit Neural Network, that will then be reduced to Neig eigenvectors, which will be the basis elements. It can be run with the command:

wmin runcard.yaml

where wmin is the model-specific executable.

This basis should then be evolved, and the basis elements then need to be shifted by running:

python shift_lhapdf_members.py evolved_directory/postfit/evolved_directory

where the shift_lhapdf_members.py script can be found in the directory wmin-model/wmin/runcards and evolved_directory is the fit or POD basis directory that should have previously been evolved.

You can then follow Colibri’s analytic and bayesian workflows to run fits.