View source for NNPDF

{{Multiple issues|{{one source|date= November 2024}}
{{incomprehensible|date= November 2024}}}}{{Infobox software
| name                   = NNPDF
| logo                   = LogoNNPDF.png
| developer              = The NNPDF Collaboration
| latest release version = 4.0
| genre                  = [[Particle physics]]
| website                = {{URL|https://nnpdf.mi.infn.it/}}
}}

'''NNPDF''' is the acronym used to identify the [[parton distribution functions]] from the NNPDF Collaboration. {{Cn|date=November 2024}}NNPDF parton densities are 
extracted from global fits to data based on a combination of a [[Monte Carlo method]] for uncertainty estimation and the use of 
[[neural networks]] as basic interpolating functions.<ref>{{Cite book |last1=Miao |first1=Qinghai |url=https://books.google.com/books?id=sM4gEQAAQBAJ&dq=%22NNPDF%22+-wikipedia&pg=PA50 |title=Artificial Intelligence for Science (AI4S): Frontiers and Perspectives Based on Parallel Intelligence |last2=Wang |first2=Fei-Yue |date=2024 |publisher=Springer Nature |isbn=978-3-031-67419-8 |pages=50 |language=en}}</ref>

== Methodology ==
[[File:General-strategy-evol.jpg|thumb|The NNPDF Collaboration strategy is summarized in this diagram.]]
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 <math>\chi^2</math>) of a set of PDFs parametrized by [[artificial neural network|neural network]]s on each of the above MC replicas of the data. PDFs are parametrized at the initial evolution scale <math>Q^{2}_{0}</math> and then evolved to the experimental data scale <math>Q^2</math> by means of the [[DGLAP]] equations. Since the PDF parametrization is redundant, the minimization strategy is based in [[genetic algorithm]]s as well as gradient descent based minimizers.
* The neural network 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 the results. For example, the stability with respect PDF parametrization can be explicitly verified.

The set of <math>N_{rep}</math> PDF sets (trained neural networks) provides a representation of the underlying PDF probability density, from which   any statistical estimator can be computed.

== Example ==

The image below shows the [[gluon]] at small-x from  [https://arxiv.org/abs/0808.1231 the NNPDF1.0 analysis], available
through [http://projects.hepforge.org/lhapdf/ the LHAPDF interface]

<gallery widths=444px heights=300px>
File:Gluon log ref.jpg|The NNPDF1.0 gluon
</gallery>

== Releases ==
The NNPDF releases are summarised in the following table:
{| class="wikitable centered sortable" style="text-align: center;"
|-
! PDF set
! DIS data
! Drell-Yan data
! Jet data
! LHC data
! Independent param. of <math>s</math> and <math>\bar{s}</math>
! Heavy Quark masses
! NNLO
|-
| [http://projects.hepforge.org/lhapdf/ '''NNPDF4.0''']
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
|-
|-
| [http://projects.hepforge.org/lhapdf/ '''NNPDF3.1''']
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
|-
|-
| [http://projects.hepforge.org/lhapdf/ '''NNPDF3.0''']
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
|-
| [http://projects.hepforge.org/lhapdf/ '''NNPDF2.3''']
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
|-
| [http://projects.hepforge.org/lhapdf/ '''NNPDF2.2''']
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
|-
| [http://projects.hepforge.org/lhapdf/ '''NNPDF2.1''']
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{No}}
| {{Yes}}
| {{Yes}}
| {{Yes}}
|-
| [http://projects.hepforge.org/lhapdf/ '''NNPDF2.0''']
| {{Yes}}
| {{Yes}}
| {{Yes}}
| {{No}}
| {{Yes}}
| {{No}}
| {{No}}
|-
| [http://projects.hepforge.org/lhapdf/ '''NNPDF1.2''']
| {{Yes}}
| {{No}}
| {{No}}
| {{No}}
| {{Yes}}
| {{No}}
| {{No}}
|-
| [http://projects.hepforge.org/lhapdf/ '''NNPDF1.0''']
| {{Yes}}
| {{No}}
| {{No}}
| {{No}}
| {{No}}
| {{No}}
| {{No}}
|-
|}

All PDF sets are available through the LHAPDF interface and in the [http://nnpdf.mi.infn.it/for-users/ NNPDF webpage].

== References ==
{{reflist}}

==External links==
*[http://nnpdf.hepforge.org The NNPDF Collaboration homepage]
*[http://sophia.ecm.ub.es/nnpdf/nnpdf-driver.htm Download NNPDF Parton Distribution sets]
*[https://arxiv.org/abs/0808.1231 The NNPDF1.0 analysis]
*[https://arxiv.org/abs/hep-ph/0701127 The NNPDF Non-Singlet analysis]
*[https://link.springer.com/article/10.1140%2Fepjc%2Fs10052-017-5199-5 NNPDF3.1 release]
*[https://link.springer.com/article/10.1140%2Fepjc%2Fs10052-019-7197-2 NNPDF latest fitting code]
*[http://projects.hepforge.org/lhapdf/ The LHAPDF interface]

{{Authority control}}

[[Category:Computational particle physics]]
[[Category:Physics software]]