NNPDF
Encyclopedia
NNPDF is used to denote the parton distribution functions from the NNPDF Collaboration.
The NNPDF approach can be divided into four main steps
The set of
PDF sets (trained neural networks) provides a representation of the underlying PDF probability density, from which any statistical estimator can be computed
The NNPDF Collaboration strategy is summarized in this diagram:
The image below shows the gluon
at small-x from the the NNPDF1.0 analysis, available
through the LHAPDF interface
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NNPDF Parton Distributions
The NNPDF approach can be divided into four main steps
- The generation of a large (
) sample of Monte Carlo replicas of the original experimental data, in a way that central values, errors and correlations are reproduced with enough accuracy. - The training (minimization of the
) of a set of PDFs parametrized by neural networkArtificial neural networkAn artificial neural network , usually called neural network , is a mathematical model or computational model that is inspired by the structure and/or functional aspects of biological neural networks. A neural network consists of an interconnected group of artificial neurons, and it processes...
s on each of the above MC replicas of the data. PDFs are parametrized at the initial evolution scale
and then evolved to the experimental data scale 
by means of the DGLAPDGLAPDGLAP are the authors who first wrote the QCD evolution equation of the same name. DGLAP was first published in the western world by Altarelli and Parisi in 1977, hence DGLAP and its specialisations are sometimes still called Altarelli-Parisi equations...
equations. Since the PDF parametrization is redundant, the minimization strategy is based in genetic algorithmGenetic algorithmA genetic algorithm is a search heuristic that mimics the process of natural evolution. This heuristic is routinely used to generate useful solutions to optimization and search problems...
s - The neural net training is stopped dynamically before entering into the overlearning regime, that is, so that the PDFs learn the physical laws which underlie experimental data without fitting simultaneously statistical noise
- Once the training of the MC replicas has been completed, a set of statistical estimators can be applied to the set of PDFs, in order to assess the statistical consistency of our results. For example, the stability with respect PDF parametrization can be explicitly verified.
The set of
PDF sets (trained neural networks) provides a representation of the underlying PDF probability density, from which any statistical estimator can be computedThe NNPDF Collaboration strategy is summarized in this diagram:
The image below shows the gluon
Gluon
Gluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles....
at small-x from the the NNPDF1.0 analysis, available
through the LHAPDF interface
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NNPDF Parton Distributions
- NNPDF1.0 - arxiv:0808.1231
- NNPDF1.1
- NNPDF1.2
- NNPDF2.0: A global analysis of all relevant hard scattering data: DIS, Drell-Yan,
vector boson production and inclusive jets