Research

As a particle phenomenologist with a strong focus on computation, my research sits halfway between the experimental and theoretical worlds, without fully belonging to either. In simpler terms, I use theoretical models to compute simulations that can then be tested by my experimentalist colleagues in the various experiments across the globe (most of them, actually, in Geneva (Switzerland)).

Of the wide world of particle physics, my work is primarily within the realm of Quantum Chromodynamics. My goal is to produce increasingly precise predictions with reliable and robust uncertainties which can then be meaningfully compared to the experiments. I am part of the NNPDF collaboration where we apply Machine Learning techniques to investigate the internal content of the proton.

On the computational side, my research involves Machine Learning, Monte Carlo simulations and hardware acceleration. They are all pieces of the same big puzzle: artificial intelligence is used to model the internal structure of the colliding protons, the theory of Quantum Chromodynamics allows us to model what happens after the collision. The resulting complicated integrals are then computed using Monte Carlo methods. These computations are very complex (and costly!) and thus the use of grid computing or GPUs becomes essential.

On this page you can read a bit more about what I do and also find an up to date list of all my papers, talks and open-sourced published software. My ORCiD number is 0000-0002-8061-1965.

If you want to check my contributions in iNSPIRE, you can use the following search string: find a cruz-martinez, j

Machine Learning and Artificial Intelligence

This scientific discipline uses automated learning to perform tasks without necessarily knowing the necessary explicit instructions. We use ML algorithms in order construct mathematical models which, based on sample data (commonly known as training data), are able to make prediction on data that the model has never seen. Nowadays machine learning techniques are widespread in the world of physics (jet tagging, model building, pdf determination, ...) and beyond (email filtering, computer vision, ...). Currently my main topic of research as part of N3PDF consist on the application of ML techniques to the determination of the internal structure of the proton.

The internal structure of the proton

One very important ingredient for the high energy physics program of the Large Hadron Collider (LHC) at CERN is the determination of the parton content of the proton. The internal structure of the proton in terms of quarks and gluons is given by the Parton Distribution Functions.

In the NNPDF collaboration we use Machine Learning techniques in order to determinate the aforementioned PDFs.

Some of our work on PDF determination has been featured in the cover of the European Physical Journal C.

Fixed-Order calculations in QCD

Fixed-order calculations in perturbative Quantum Chromodynamics (QCD) provides precise theoretical predictions for processes studied at the LHC and other high-energy colliders. These calculations help us understand how quarks and gluons interact and how their dynamics manifest in experimentally measurable quantities.

I have worked on some of the most precise calculations for the determination of the corrections due to Quantum Chromodynamics (QCD) effects to Higgs boson production on the gluon fusion and Vector Boson Fusion (VBF) production channels.

Numerical Calculations, Monte Carlo methods

State-of-the-art computations in High Energy Physics (HEP) require computing very complex multi-dimensional integrals numerically, as the analytical result is often not known. Monte Carlo algorithms are generally the option of choice be it in HEP applications or elsewhere, as the error of such algorithms does not grow with the number of dimensions.

Our aim is to improve the efficiency of widely used methods in order to enable more physics in less time. Some examples are our implementation of the Vegas algorithm in tensorflow (Vegasflow), PDFFlow or the distributed computing tool pyHepGrid.

New Hardware in High Energy Physics: GPUs and Quantum Computing

Very complicated calculations are also very costly in terms of computing resources. As a result physics at the frontier of knowledge require technologies at the frontier of software and hardware. I am also dedicated to adapt these very complicated calculations to hardware accelerators which have seen an amazing development during the last decades. With a focus on Graphical Processing Units (GPUs) with packages like Vegasflow or PDFFlow, we are also considering Field Programmable Gate Arrays (FPGAs) or, more recently, we are exploring the usage of quantum circuits as co-processor in order to accelerate calculation, such as the QPDF for PDF fitting using Variational Quantum Circuits.

Journal articles

TitleJournalArXiv
NNLOJET: a parton-level event generator for jet cross sections at NNLO QCD accuracy (2025) 2503.22804
NNPDFpol2.0: unbiased global determination of polarized PDFs and their uncertainties at next-to-next-to-leading order (2025) 2503.11814
Accelerating Berends-Giele recursion for gluons in arbitrary dimensions over finite fields (2025) 2502.07060
Fast interpolation grids for the Drell\textendash{Yan process}Eur. Phys. J. C (2025) 85, 4592501.13167
Parton distributions confront LHC Run II data: a quantitative appraisal (2025) 2501.10359
Combination of aN$^3$LO PDFs and implications for Higgs production cross-sections at the LHC (2024) 2411.05373
Hyperparameter optimisation in deep learning from ensemble methods: applications to proton structureMach. Learn. Sci. Tech. (2025) 6, 0250272410.16248
LO, NLO, and NNLO parton distributions for LHC event generatorsJHEP (2024) 09, 0882406.12961
The path to $\hbox {N^3\hbox {LO}$ parton distributions}Eur. Phys. J. C (2024) 84, 6592402.18635
Determination of the theory uncertainties from missing higher orders on NNLO parton distributions with percent accuracyEur. Phys. J. C (2024) 84, 5172401.10319
Photons in the proton: implications for the LHCEur. Phys. J. C (2024) 84, 5402401.08749
Intrinsic charm quark valence distribution of the protonPhys. Rev. D (2024) 109, L0915012311.00743
The LHC as a Neutrino-Ion ColliderEur. Phys. J. C (2024) 84, 3692309.09581
Determining probability density functions with adiabatic quantum computingQuantum Machine Intelligence (2025) 7, 52303.11346
Pineline: Industrialization of high-energy theory predictionsComput. Phys. Commun. (2024) 297, 1090612302.12124
Evidence for intrinsic charm quarks in the protonNature (2022) 608, 483--4872208.08372
Snowmass 2021 Whitepaper: Proton Structure at the Precision FrontierActa Phys. Polon. B (2022) 53, 12-A12203.13923
A data-based parametrization of parton distribution functionsEur. Phys. J. (2022) C82, 1632111.02954
An open-source machine learning framework for global analyses of parton distributionsEur. Phys. J. C (2021) 81, 9582109.02671
The path to proton structure at 1\% accuracy: NNPDF CollaborationEur. Phys. J. C (2022) 82, 4282109.02653
MadFlow: automating Monte Carlo simulation on GPU for particle physics processesEur. Phys. J. C (2021) 81, 6562106.10279
A comparative study of Higgs boson production from vector-boson fusionJHEP (2021) 11, 1082105.11399
Compressing PDF sets using generative adversarial networksEur. Phys. J. C (2021) 81, 5302104.04535
Future tests of parton distributionsActa Phys. Polon. B (2021) 52, 2432103.08606
Determining the proton content with a quantum computerPhys. Rev. D (2021) 103, 0340272011.13934
PDFFlow: Parton distribution functions on GPUComputer Physics Communications (2021) 264, 1079952009.06635
VegasFlow: accelerating Monte Carlo simulation across multiple hardware platformsComput. Phys. Commun. (2020) 254, 1073762002.12921
Towards hardware acceleration for parton densities estimationFrascati Phys. Ser. (2019) 69, 1-61909.10547
Towards a new generation of parton densities with deep learning modelsEur. Phys. J. (2019) C79, 6761907.05075
Report from Working Group 1CERN Yellow Rep. Monogr. (2019) 7, 1-2201902.04070
Second-order QCD effects in Higgs boson production through vector boson fusionPhys. Lett. (2018) B781, 672-6771802.02445
The HiggsTools handbook: a beginners guide to decoding the Higgs sectorJ. Phys. (2018) G45, 0650041711.09875
NNLO QCD corrections to Higgs boson production at large transverse momentumJHEP (2016) 10, 0661607.08817
Multi-variable integration with a variational quantum circuitQuantum Science and Technology (2024) 9, 035053
Higgs Production at NNLO in VBFActa Phys. Polon. Supp. (2018) 11, 277-284

Seminars and conferences

Invited SeminarUncovering New Laws of Nature at the EICQCD@LHC 2024NNPDF Collaboration MeetingInvited SeminarDIS2024NNLOJET Collaboration meetingNNPDF Collaboration meetingMilan Christmas Meeting 2023Collider Cross TalkPDF4LHC 2023Event generator' and N(n)LO codes' accelerationNNPDF Collaboration MeetingFPF Theory WorkshopLHCP11 2023HEP Theory SeminarQCD@LHC 2022QCD SeminarInvited seminarNNPDF Collaboration MeetingInvited seminar41th International Conference on High Energy Physics, ICHEP 2022Transversity 2022Invited seminarInvited seminar, Dalitz seriesThe 2021 International Workshop on the High Energy Circular Electron Positron ColliderInvited Seminar (virtual)25th International Conference on Computing in High-Energy and Nuclear Physics (vCHEP)PDF4LHC 2021Milano Joint Phenomenology SeminarInvited Seminar (virtual)HSF WLCG Virtual WorkshopGenerator Infrastructure and Tools Subgroup Meeting40th International Conference on High Energy Physics, ICHEPNNPDF Collaboration meetingArtificial Intelligence for Science, Industry and Society Symposium (AISIS 2019)James Stirling Memorial Conference \& PDF4LHCNNPDF Collaboration meetingQCD@LHC 2019NNLOJET Collaboration meetingNNPDF Collaboration meetingNNPDF Collaboration \& N3PDF Kickoff MeetingLoops and Legs in Quantum Field Theory 2018HiggsTools Final MeetingInternal SeminarStudent SeminarInvited SeminarHiggsTools Second Annual MeetingInternal SeminarStudent SeminarHiggsTools First Annual Meeting
titleconferencelocationdateslides
Challenges and developments in the determination of Parton Distribution Functions Cambridge University (UK)March 2025
PDF determination and the EIC: impact and opportunities Brookhaven National Lab (USA)November 2024 slides
PDF constraints from new data and expectations from future experiments Freiburg (Germany)October 2024 slides
State of the Code Morimondo (Italy)September 2024
Challenges and developments on PDF determination IFIC Valencia (Spain)September 2024 slides
Phenomenological implications of modern PDF determinations Grenoble (France)April 2024 slides
NNLO Grids in NNPDF from NNLOJET Milano (Italy)March 2024
Code status and data implementation updates towards NNPDF4.1 Amsterdam (The Netherlands)February 2024
Towards a framework for GPU event generation CERN, SwitzerlandDecember 2023 slides
Why are we still talking about PDFs? CERN, SwitzerlandDecember 2023
Implications of NNPDF4.0 for LHC physics CERN, SwitzerlandNovember 2023 slides
Towards a framework for GPU event generation CERN, SwitzerlandNovember 2023 slides
Status of the NNPDF framework and data implementation Gargnano, Lake Garda (Italy)September 2023
Physics with Muons at the FPF (SM pow) CERN, SwitzerlandSeptember 2023 slides
Recent results on PDF extractions Belgrade, SerbiaMay 2023 slides
NNPDF4.0 and the path to reliable uncertainties Brookhaven National Lab. (USA, Virtual)May 2023
Theory developments in PDF determination IJCLab Orsay, FranceNovember 2022 slides
NNPDF4.0 and the path to reliable uncertainties in PDF determination CERN, SwitzerlandNovember 2022 slides
GPU accelerated particle physics Nikhef, Amsterdam (The Netherlands)September 2022
Status of the NNPDF fitting framework and theory pipeline Gargnano, Lake Garda (Italy)September 2022
Facilitating GPU acceleration for Monte Carlo simulations Freiburg (Germany)July 2022
MadFlow: automating Monte Carlo simulation on GPU for particle physics Bologna (Italy)July 2022 slides
Machine Learning in PDF determination: NNPDF4.0 Pavia (Italy)May 2022 slides
Accelerating Monte Carlo simulations across hardware platforms USM/LMU Munich (Germany)May 2022
NNPDF4.0: the path to proton structure at 1\% accuracy Oxford (UK, Virtual)November 2021
GPU acceleration in High Energy Physics Nanjing (China, Virtual)November 2021 slides
Towards a GPU future for particle physics Monte Carlo simulations KIT Karlsruhe (Germany)June 2021
MadFlow: towards the automation of Monte Carlo simulation on GPU for particle physics VirtualMay 2021 slides
New studies from the NNPDF group VirtualMarch 2021 slides
Offloading Monte Carlo simulations to hardware accelerators Milan (Italy, Virtual)February 2021 slides
PDF determination with a quantum hardware IFIC Valencia (Spain)February 2021 slides
PDF/Vegas-Flow Virtual meetingNovember 2020 slides
VegasFlow and PDFFlow: accelerating Monte Carlo simulation across multiple devices (joint talk with M. Rossi) CERN (Virtual meeting)October 2020 slides
VegasFlow: accelerating Monte Carlo simulation across platforms Prague (Virtual meeting)August 2020 slides
Optimizing the hyperoptimization Amsterdam (The Netherlands)February 2020
Studying the parton content of the proton with deep learning models Ciudad de Mexico (Mexico)October 2019 slides
Methodological improvements in PDF determination Durham (UK)September 2019 slides
n3fit and hyperoptimization in the context of NNPDF 4.0 Varenna (Italy)August 2019
Towards a new generation of PDFs with deep learning models Buffalo, New York (USA)July 2019 slides
Numerical Integration with Neural Networks Zurich (Switzerland)May 2019
N3PDF studies of new methodologies Amsterdam (The Netherlands)February 2019
Recent developments within NNLOJET Gargnano, Lake Garda (Italy)September 2018 slides
NNLO corrections to VBF Higgs boson production St. Goar (Germany)May 2018
NNLO phenomenology with Antenna Subtraction Durham (UK)September 2017 slides
\phi^*_\eta observable for Higgs production Durham (UK)May 2017
Higgs phenomenology with antenna subtraction Durham (UK)February 2017
Higgs phenomenology with antenna subtraction Valencia (Spain)January 2017 slides
NNLO calculations for Higgs processes Granada (Spain)April 2016 slides
Renormalisation Scale Dependence as a Testing Ground for NNLO calculations Durham (UK)February 2016
Building and Playing with NNLO Monte Carlos Durham (UK)February 2016
NNLO predictions for Higgs production at LHC Freiburg (Germany)April 2015 slides

Academic open-sourced Software

titledescriptionsource
pyHepGridDistributed computing made easyZenodo (2019)
evolutionary kerasAn evolutionary algorithm implementation for KerasZenodo (2020)
vegasflowAccelerating Monte Carlo integrations across multiple hardware platformsZenodo (2020)
ekoSolves the DGLAP equations in Mellin space and produces evolution kernel operators (EKO)Zenodo (2020)
pdfflowFast device agnostic Parton Distribution Function interpolationZenodo (2020)
ganpdfsPDF (parton distribution functions) enhancement using Generative Adversarial NetworksZenodo (2021)
pycompressorPDF (parton distribution functions) compression frameworkZenodo (2021)
madflowAutomating event generation MC simulation on hardware accelerators.Zenodo (2021)
nnpdfAn open-source machine learning framework for global analyses of parton distributionsZenodo (2021)
pinekostreamlined high energy theory predictions for PDF fitting and beyondZenodo (2022)