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-2749554191000 Proposal for FY2021 Laboratory Directed Research and Development FundsTitle: Universal Monte Carlo Event GeneratorTopic: Advancing High Performance ComputingLead Scientist or Engineer:Wally melnitchoukPhone:(757) 692 6881Email:wmelnitc@Date:May 31, 2020 (revised August 7, 2020)Department/Division:Theory CenterOther Personnel:Pawel Ambrozewicz, Michelle Kuchera, Yaohang Li, Raghu Ramanujan, Nobuo Sato Mentor (if needed)Proposal Term:From: 10/2018Through: 09/2021If continuation, indicate year (2nd/3rd): 3rdDivision Budget AnalystJianwei QiuPhone:(757) 692 6026Email:jqiu@This document and the material and data contained herein were developed under the sponsorship of the United States Government. Neither the United States nor the Department of Energy, nor the Thomas Jefferson National Accelerator Facility, nor their employees, makes any warranty, express or implied, or assumes any liability or responsibility for accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use will not infringe privately owned rights. Mention of any product, its manufacturer, or suppliers shall not, nor it is intended to imply approval, disapproval, or fitness for any particular use. A royalty-free, non-exclusive right to use and disseminate same for any purpose whatsoever, is expressly reserved to the United States and the Thomas Jefferson National Accelerator Facility.AbstractDuring the first two years of this project, we have developed a machine learning (ML) based universal Monte Carlo event generator (UMCEG) which can reliably represent particle distributions at the event level, agnostic of theoretical assumptions about femtometer scale physics. After exploring many different ML prototypes for the UMCEG, we have identified an optimal ML strategy that shows great promise for constructing a faithful data compactification utility, making it possible to convert the vast amount of data produced in high-statistics experiments, such as those at Jefferson Lab and the future EIC, into a small-scale and easily accessed UMCEG. In this proposal, we plan to develop the missing building blocks needed to complete the full analysis chain required for QCD studies, namely, the event-level folding and unfolding ML algorithms, and physics extraction tools tailored to inclusive and semi-inclusive electron-hadron scattering. Summary of ProposalDescription of ProjectIn Years 1 and 2 we had proposed to develop a universal Monte Carlo event generator using ML that was agnostic of theoretical assumptions about the microscopic nature of particle interactions. We have to date identified an optimal design for the ML architecture, which has allowed us to mimic particle production using synthetic data generated by the Pythia MCEG, as well as real data from Jefferson Lab experiments. Our results indicate that the construction of an ML-based UMCEG, viewed as a data compactification tool, is for the first time viable. Such a device will allow the large quantities of experimental data, typically stored on tapes, to be synthesized into a relatively small and easily accessed data regeneration ML tool, that can then be used by QCD scientists to interpret the underlying femtometer scale physics. Having established the feasibility of building such an event generator, in Year 3 we propose to develop two additional building blocks that will be needed to finalize our ML infrastructure, and apply the technology to the analysis of real JLab data. * Folding and unfolding tools using ML: Since detector-level event samples are subject to distortions induced by the detector itself (smearing, bin migration, etc.), an “unfolding” procedure is needed to correct them to vertex-level event samples. Currently all unfolding procedures require applying the corrections at the histogram level, tailored to specific channels and observables of interest. However, this poses a limitation on exploring additional representations of the data which may not have been conceived of during the time of the original data analysis. Furthermore, future analyses of the data are limited as additional data representations or observables would require the processing of detector-level events with new, dedicated unfolding procedures. A novel way to avoid such limitations is to carry out the unfolding procedure directly at the event level, which can in practice only be done in the context of ML. Moreover, using ML it is possible to train neural networks to map vertex-level events into detector-level events, which we will shall refer to as the “folding procedure”. We have performed preliminary tests of such folding and unfolding tools using (semi-realistic) toy distortions, as well as more realistic distortions with the BNL developed package eic_smear [1], that performs fast smearing to introduce detector resolution effects, and obtained promising results (see Approaches/Methods section below). An additional complication for electron-nucleon scattering is the need to account for radiative QED effects. These effects can be viewed as a second layer of (un)folding, and we plan to develop a dedicated (un)folding procedure specifically for QED effects. For Year 3, we therefore propose to develop the folding tools using ML and integrate them with our UMCEG.* Physics extraction tools: Once the UMCEG is fully trained, a natural step will be to use it to extract physical observables, such as cross sections and structure functions. We plan to develop dedicated ML extraction tools tailored to inclusive and semi-inclusive electron-nucleon scattering, integrated with our UMCEG. The completion and integration of such extraction tools will realize our final goal of obtaining data for QCD studies, free of theory bias introduced during the complex process of converting detector-level events into physical objects such as Born-level structure functions.* Application to JLab data: While our ultimate goal is to build the UMCEG at the vertex level, which requires the development of folding algorithms, the UMCEG at the detector level is already available as a data compactification utility for applications to real data. To that end, we have engaged with experimental colleagues from Jefferson Lab Hall B to train the UMCEG using detector-level samples for two types of processes: (i) detector-level inclusive scattering training, and (ii) exclusive particle production in p p +?. Our preliminary results indicate that the detector-level particle distributions generated by the trained UMCEG can reproduce the experimental data very well. We plan to continue these studies, improving the results by incorporating the folding procedure and including additional channels. This will help us disseminate across the JLab community our R & D for building a theory-agnostic UMCEG for the Jefferson Lab 12 GeV and future EIC physics programs.* Dissemination and public release of ML algorithms: We plan to develop comprehensive documentation on publicly accessible web pages, with detailed explanations of the developed algorithms and step-by-step tutorials available. In addition, we plan to organize a dedicated mini-lecture and tutorial training session, where the ML developers will guide participants in learning how to use and train our UMCEG on data. To summarize, in Year 3 we plan to finalize the main objectives that were initiated in Years 1 and 2, by developing event-level unfolding tools using ML, as well as dedicated physics extraction tools integrated within our analysis chain. We further plan to continue the study of applying our ML technology to real data from Jefferson Lab experiments. The completion of this project will define a new paradigm for analyzing experimental data using ML, and will help realize the full potential of the scientific programs at the Jefferson Lab 12 GeV and future EIC facilities.Expected ResultsWhile the application of the (un)folding procedure at the event level is applicable to any type of reaction, we will focus on electron-nucleon scattering as the most relevant process for the Jefferson Lab 12 GeV and future EIC programs. The main strategy for developing the (un)folding procedure is through the use of generational adversarial networks (GANs) [2], which have found tremendous success recently in industrial applications, such as generating near-realistic images, as well as in music and videos. Motivated by these developments, we have carried out preliminary studies by training ML algorithms at the event level with semi-realistic detector effects, and have confirmed the feasibility of our proposed approach. We plan to use existing calibrated detector simulators based on Geant4 [3] to train our inverse mappers to convert realistic detector-level events into vertex-level events. To test the reliability of our (un)folding algorithms, we plan to work on closure tests by using synthetic data generated from the Pythia MCEG [4]. This will allow us to assess the accuracy of the (un)folding procedure for transforming detector-level events, simulated in Geant4 and Pythia, into the original vertex-level Pythia samples. Similarly, we plan to incorporate electromagnetic effects as part of the (un)folding algorithm and validate the model's reliability via closure tests. Once the folding algorithms are in place, we plan to integrate them into our UMCEG prototypes and train the UMCEG directly using detector-level event samples. While the folding algorithms will be integrated within the UMCEG, the unfolding algorithms can be used in other applications, such as standard cross section reconstruction analyses. To complete our final goals, we will develop physics extraction tools using ML to extract from our trained UMCEG quantities such as inclusive and semi-inclusive structure functions. This will allow the completion of the full analysis chain, from detector-level events to physical observables for global QCD studies. In addition, we plan to work with experimental colleagues at JLab to train the GAN on real data, including (i) ep eX from JLab 6 GeV data, and (ii) exclusive p p+? data. Finally, we will make all the developed algorithms publicly available to the Jefferson Lab community, with detailed web documentation and tutorial sessions to training users to implement our ML algorithms.Proposal NarrativePurpose/GoalsBuild the first ever event-level (un)folding algorithm based on ML, transforming detector-level events into vertex-level events for electron-proton scattering using novel ML algorithms.Include QED radiative effects as part of a secondary layer for the (un)folding algorithm.Integrate the event-level folding algorithm with the UMCEG using data from Jefferson Lab experiments. Construct ML-based physics extraction tools tailored to inclusive and semi-inclusive deep-inelastic scattering.Apply the ML technology to real data from Jefferson Lab experiments.Publicly release our developed ML algorithms with documentation for the Jefferson Lab community. To facilitate this, we plan to organize tutorial sessions to teach users how to create and train their own UMCEG using ML.Approach/MethodsIn Years 1 and 2 we have developed a UMCEG using ML without taking into account detector effects or QED radiation. In Year 3 we plan to work on the missing blocks needed to finally pass the relevant observables into QCD global analysis frameworks, such as that used by the Jefferson Lab Angular Momentum (JAM) Collaboration, to perform the Bayesian inferences on quark and gluon structures. These outstanding components are: (1) the (un)folding procedure to take into account detector and QED effects, and (2) physics extraction algorithms tailored to inclusive and semi-inclusive eN scattering. In Fig. 1 we present our final sketch of an ML-enabled particle data analysis framework that is agnostic about theoretical interpretation of the underlying femtometer scale dynamics. Notice that there are 3 pairs of colored blocks: (i) UMCEG detector-level event discriminator, (ii) event-level folding generator-folding discriminator, and (iii) structure functions generator-cross section discriminator. Each of these corresponds to generator and discriminator for a particular GAN setup. While the algorithms for (i) have been already developed in Year 1, the GANs for (ii) and (iii) will be developed in Year 3. This is indicated by the orange lines in Fig. 1 as the missing blocks to be developed are indicated. In the following we discuss in detail how the missing blocks will be developed.(Un)folding tools using MLOur proposed (un)folding set of tools using ML is composed of two major components: (1) a detector simulator with QED effects that can faithfully map the vertex events into detector-level events, and (2) an event-level (un)folding GAN algorithm that mimics the detector simulator. The (un)folding GAN algorithm is trained as a deep neural network forward mapper by adversarial learning, as shown in the upper orange loop in Fig. 1. In contrast to ordinary GANs that receive noise as input, our GAN uses the vertex-level events as inputs and converts them into detector-level events. The folding discriminator ensures that the generated detector-level events are statistically consistent with the true detector-level events from the detector simulator by minimizing the Wasserstein loss and MMD loss. When successfully trained, the folding GAN generator is able to mimic the distortion at the event level induced on vertex-level events by the detector + QED effects.Fig. 1. Schematic overview of the full ML infrastructure to convert experimental information into the fundamental quark and gluon structures. The work associated with the current proposal is indicated by the orange lines.The folding GAN generator is then incorporated into the UMCEG GAN architecture in order to train the vertex-level UMCEG using directly detector-level event samples. We have obtained preliminary results for our proposed folding GAN generator. In Fig.2 we present GAN-based (un)folding for a toy event-level folding procedure that modifies the azimuthal angle distribution of the scattered electron in ep scattering in the lab frame. In this case, we have trained two GANs for folding and unfolding. After passing the undistorted events to the folding GAN, or the distorted events to the unfolding GAN, we obtain reasonably good agreement with the expected output distributions. Similarly, we have examined the folding procedure using eic_smear and found a relatively good performance for the trained folding GAN. We will investigate and develop more accurate and reliable (un)folding GANs in Year 3, and perform detailed statistical tests, such as multi-variate Kolmogorov-Simonov tests, to quantify the degree of compatibility of the outputs of the folding algorithms against the validation samples.Fig. 2. Illustration of GAN capabilities to mimic event-level folding and unfolding procedures. In a) and b) we consider toy folding tests for the azimuthal angle, ’, of the scattered electron in the ep lab frame. The input distribution in blue in a) transforms via a toy folding into the blue distribution in b). A GAN was trained at the event level to map the input samples from a) into the output samples in b). The orange distribution in b) is constructed from the output events from the GAN folding algorithm. Similarly, another GAN was trained to carry out the unfolding procedure. The orange distribution in a) is constructed from the output events of the GAN unfolding algorithm. In b) and c) we consider a more realistic detector smearing using eic_smear, and in c) and d) results obtained after training the GAN folding algorithm focusing on the outgoing electron energy, E'.Physics extraction toolsWe propose to build and train GAN models that generate structure functions for inclusive deep-inelastic scattering (DIS) and semi-inclusive DIS (SIDIS). The models generate the relevant structure functions as a function of the kinematic variables on which they depend.The trained GANs will generate synthetic stochastic values for the structure functions across kinematics spanning the feasible range admissible by the data uncertainties. In contrast to traditional approaches where neural networks are trained several times to match pseudodata generated from resampling, our GAN-based structure function generator learns the uncertainties directly during the training. This removes the need to perform training multiple times. The uncertainty quantification for the structure functions is then built into the trained models by construction.The training data or cross sections for the GANs are created using the UMCEG developed in Years 1 and 2. This work will therefore complete the ML-driven analysis cycle to provide structure functions to be studied in global QCD analyses, such as by the JAM Collaboration [5,6]. This is represented in the bottom half of the overview diagram in Fig.1. Dissemination and public release of ML algorithmsAn important element in the completion of the project Year 3 is the dissemination of our work to the public, in a form that can be easily reproduced and integrated with existing frameworks. A beneficial feature of our research is that all the algorithms have been developed in Python using state-of-the-art ML libraries, such as TensorFlow and Keras interfaces. At present, we have several publicly available repositories, but with limited documentation. In this proposal, we plan to synthesize our ODU-Davidson College-JLab collaborative work for dedicated web pages that give example codes with tutorials to guide users. We plan to consolidate the ML codes into a stand-alone package for public release, and collaborate with JLab’s CST division in order to develop coding infrastructure that will allow users to extend the project in future. The pages will be linked to repositories from which users can run codes and reproduce and validate our results. Some preliminary documentation is available at the following link: ResourcesFor Year 3 of the project, we request continued support for the ML collaborators at ODU and Davidson College, as well as for the dedicated postdoc recently hired in the Jefferson Lab Theory Center. In particular, we request support for 2 graduate students (6 months each) at ODU, 1 undergraduate student (summer 2021) at Davidson College, and summer salaries for Prof. Yaohang Li (ODU, 1 month), Prof. Michelle Kuchera (Davidson, 1/4 month) and Prof. Raghu Ramanuja (Davidson, 1/4 month). We also request support for a CS staff member (5% FTE) from JLab's CST division for public release software development.For computational needs, this project requires the use of GPU-enabled nodes in the JLab computing farm servers.This project requires the use of office space in the Theory Center at JLab.Anticipated Outcomes/ResultsEvent-level (un)folding tools Q1: Develop the (un)folding for inclusive DIS without QED corrections. Q2: Develop the (un)folding for SIDIS without QED corrections. Q3: Develop the (un)folding for inclusive DIS and SIDIS with QED corrections. Q4: Combine the folding GAN with the UMCEG for DIS.Physics extraction tools Q1: Develop the GAN for DIS structure functions. Q2: Develop the GAN for SIDIS (pT-integrated) structure functions. Q3: Develop the GAN for SIDIS (pT-differential) structure functions. Q4: Combine the extraction tools with the UMCEG.UMCEG application to JLab data Q2: Finalize the GAN training at the detector level for DIS and p p+? data. Q4: Train the GAN for p p+? with the unfolding procedure.Web documentation and open source Q1: Web documentation for Years 1 and 2 GAN UMCEG prototypes and code release. Q2: Deploy the trained UMCEG as a web application for interactive use and as a downloadable model with an intuitive API for physicists to utilize in their analyses. Q3: Organize a set of mini-lectures and tutorials, where the ML developers will guide participants in learning how to use and train the UMCEG on data. Q4: Finalize the web documentation for the work carried out in Year 3 and public software release.Accomplishments in Previous YearsThe FAT-GANIn Fig. 3 we illustrate the schematic architecture of the feature-augmented and transformed (FAT) GAN (or “FAT-GAN”). Feature augmentation is a procedure whereby the generated four-vector components are combined in multiple ways to better capture all possible correlations among the particle momenta, and improve the sensitivity of the discriminator [7]. The use of transformed features in place of original features allows a significant simplification for the training, as the generation of non-physical phase space can be more easily avoided. Both the UMCEG and its discriminator are implemented as deep fully-connected neural networks, optimized by a maximum mean discrepancy (MMD) loss and a standard Wasserstein loss during training.Fig. 3. Architecture of the inclusive FAT-GAN event generator. All colored boxes are designed with fully connected NNs. Feature augmentation and transformation (FAT) is designed to transform variables, such as the beam axis momenta, to help avoid non-physical events, and augment the feature space to increase the discriminator's sensitivity. The MMD layer employs a kernel-based two-sample test to measure the distance between the distributions of GAN-generated and Pythia events. The MMD loss and the standard Wasserstein loss are combined for the FAT-GAN training.We have trained the FAT-GAN on inclusive ep scattering samples generated from Pythia. In Fig. 4 we present a detailed comparison of the electron momentum distributions generated from Pythia and from the UMCEG. We in addition simulate the Bjorken scaling variable xbj and the four-momentum transfer squared Q2, which were not included in the feature augmentation set, and are thus genuine predictions of the UMCEG. This suggests that the UMCEG can indeed be used to produce other kinds of observables, that were not conceived of during the data analysis stage or included in the original features list.Fig. 4. Comparison of distributions of the scattered electron's kinematic variables from Pythia (black histograms) and the trained UMCEG FAT-GAN (red histograms), including the three-momentum components (px, py, pz), transverse momentum pT = px2+ py2 , energy E (all in GeV), polar scattering angle and azimuthal angle (in radians), along with distributions for the Bjorken variable xbj and four-momentum transfer squared, Q2 (in GeV2), which were not part of the FAT set. At the bottom of each panel the Pythia to FAT-GAN ratios are shown, with the uncertainty indicated in yellow. A further analysis is shown in Fig.5, which compares reduced cross section data for inclusive ep DIS from HERA [8] with predictions from Pythia8 and from the UMCEG (trained on Pythia8 samples), in bins of xbj across several orders of magnitude in Q2. Note that the UMCEG has been deliberately trained using only 1M Pythia8 events, which gives the rather noisy cross sections at some kinematics. Since there is no limitation in generating samples from a trained UMCEG, we have made predictions for the HERA data using 100M UMCEG events. Interestingly, the UMCEG can provide relatively stable predictions in regions where the training samples give somewhat noisy and unstable predictions. This indicates that the UMCEG can be trained with a smaller number of samples and yet is able to learn the underlying law that governs the particle production. Once the global and local patterns of the underlying law are learned, the UMCEG is able to produce unbiased samples representing the phase space. This novel aspect of the UMCEG is one of the highlighted features of GANs in ML known as “super-resolution”, where images with lower resolution can be transformed into images with much higher resolution [9]. We have also explored the possibility to train the UMCEG with two particles, suited for SIDIS studies. In this case, the UMCEG has been trained on charged pions along with the scattered electrons. In Fig. 6 we present kinematic distributions for the electron and charged pions. We stress that none of these distributions were included in the features set, so that these are therefore actual predictions of the trained UMCEG. In particular, the transverse momentum of the produced hadron, phT, is computed in the Breit frame, while any transverse momenta that entered the UMCEG feature space are all in the ep center of mass frame. While the SIDIS UMCEG generally shows good agreement with Pythia, some regions of kinematics still require more training, as is evident in Fig. 6. Nevertheless, our FAT-GAN based UMCEG shows rather promising results for the application to our ML technology to SIDIS. Thus far we have presented results from the UMCEG trained on Pythia8. In the remained of this section we examine the feasibility of training the UMCEG directly using detector-level events.Inclusive ep from JLab 6 GeV Hall B data: We have obtained from Prof. Larry Weinstein and Dr. Florian Hauenstein at ODU samples of fully inclusive detector-level events from the 6 GeV CLAS e1f run on a proton target [11]. In Fig. 7 we present the corresponding momentum distributions of the scattered electron. In contrast to Fig. 4, we can observe that the training detector-level samples produce distributions that are not smooth, such as the azimuthal angle distribution of the scattered electron. The results confirm that even in the presence of detector effects the UMCEG can capture relatively well the kinematic distributions.Fig. 5. Reduced neutral current ep reduced cross sections predicted from Pythia8 and the UMCEG (trained on Pythia events) at HERA kinematics [8]. A sample of 1M Pythia8 events was used to produce the cross sections and train the UMCEG. The UMCEG predictions were generated from 100M samples, showing stability of the UMCEG in regions of phase space where the training samples display noisy and unstable cross sections.Fig. 6. Comparison of the xbj, Q2 (in GeV2), z and phT (in GeV) distributions for pion production in SIDIS generated from Pythia (blue histograms) and from the FAT-GAN UMCEG (orange histograms). The agreement between the training data and UMCEG is slightly worse here relative to the DIS case in Fig. 4 because of increased complexity in learning more features from SIDIS data.Exclusive p p+??data from CLAS g11 run: We have initiated a collaboration with Dr. Marco Battaglieri and Dr. Viktor Mokeev from Hall B to explore the usage of the UMCEG as a data compactification tool for exclusive p p+??events. Since the initial state real photon energy changes event by event, we have included as part of the generator features the momentum for the incoming photon. In Fig. 8, we present our preliminary results for training the UMCEG with the exclusive events. As indicated, the UMCEG is capable of capturing relatively well the particles' invariant mass distributions. We expect that by improving our existing GAN technology by allowing a longer time for the training, as well utilizing the “FAT-free” architectures to be discussed below, we will be able to generate nearly indistinguishable distributions and make the UMCEG a state-of-the-art data compactification utility. We conclude that the FAT-GAN based UMCEG has enormous potential in various applications relevant for JLab physics. On the other hand, the full power of GAN-enabled ML methodologies for building UMCEGs has not yet been fully explored. In the next sections, we describe current progress in improving the technology of UMCEG beyond the FAT-GAN approach.Fig. 7. As in Fig.4, but with actual JLab 6 GeV data from Hall B instead of simulated Pythia data.Fig. 8. As UMCEG training on p p+??data from the CLAS g11 run [10]. The experimental data provides the reconstructed missing mass for the process p p+X out of which the ??momentum is reconstructed. Here M(A,B) represents the invariant mass of the A+B system. S-dependent UMCEGAn important extension of the UMCEG is the inclusion of the center of mass energy, S, of the reaction, so that the particle production is not fixed to a particular energy. The ability to include the S dependence has enormous interest in both theory and experiment. From a theoretical perspective, the energy S is one of the features that gives a solid understanding of the QCD evolution equations. The theoretical framework is designed to have universal properties that separate intrinsic hadronic features, such as PDFs and fragmentation functions, and short-distance perturbatively calculable and S-dependent coefficients to describe the reaction. From an experimental point of view, there is a need to have a reliable MCEG for detector studies and simulation for future experiments. Fig. 9. Architecture of the inclusive FAT-GAN event generator, as in Fig.3, but enhanced by allowing the energy dependence of the reaction to be part of the UMCEG training. In Fig. 9 we present the schematics for the S dependent UMCEG architecture. Due to technical difficulties in implementing the architecture in the presence of both S input and the MMD, we have carried out preliminary tests without the MMD layer using inclusive DIS samples from five different incident electron energies: 10, 20, 30, 40 and 50 GeV. In order to test if the UMCEG is indeed learning the energy dependence of the event samples we have examined the sensitivity of the latent variables in the hidden layers using the t-Distributed Stochastic Neighbor Embedding (t-SNE) [12]. In Fig. 10 we present the t-SNE principal 2D projections from three select hidden layers. As one can see from the first layers of the UMCEG, the t-SNE projection of the latent variables displays a clear distinguishable pattern for different incident energies. As the layers becomes deeper, one expects that the discrimination pattern becomes blurry since the knowledge extract by the GAN is becoming more abstract, which is precisely the behavior observed in Fig. 10. This confirms that our UMCEG architecture is indeed learning the center of mass energy of the initial state reaction. In Fig. 11 we present predictions for the kinematic distributions for different energies. As one can see the S enabled UMCEG can reproduce relatively well the xbj and Q2 distributions in regions where the statistics are higher. The tail regions however are more difficult to learn. We expect that the inclusion the MMD layer as well the use of the FAT-free architecture to be used in the next section along with longer training will significantly improve the predictions for the kinematic distributions.Fig. 10. 2D t-SNE visualization of latent variables in the second, fifth, and final hidden layers for the five trained beam energies E = 10, 20, 30, 40 and 50 GeV, and one extrapolated beam energy of 60 GeV.Fig. 11. Predictions for the kinematical variables Q2 (in GeV2) and xbj from Pythia (top row) and from the trained UMCEG (bottom row) for different incident electron energies E from 25 GeV to 45 GeV. The histograms at the bottom of the panels show the ratios of the UMCEG to Pythia results for each of the incident energies.Fig. 12. Predictions Comparison of the kinematic distributions for pion production in SIDIS, as in Fig.6, but including also the FAT-free GAN architecture (green histograms).The FAT-free UMCEGIn Fig.3 we presented the architecture of the FAT-GAN based UMCEG [7]. One of the limitations of the FAT-GAN is that one needs to design the feature augmentation set in order to obtain a maximal training performance. An alternative approach is to avoid using human intervention to design the augmentation feature set and allow the model detect all important and hidden features. This can be achieved by first creating an input layer composed of permutations among the particles momentum variables. This layer is then passed to a convolutional layer in the discriminator, and its output (feature map) fed to a fully connected neural network [13]. These changes can be implemented in the architecture in Fig.3, leaving the rest of the architecture intact. The new architecture fully utilizes the deep-learning capabilities in ML, and replaces the feature engineering UMCEG into a pure AI-enabled algorithm for the UMCEG. In Fig.12 we present the results for the kinematic distributions after training the UMCEG on SIDIS event samples generated by Pythia. We also compare the results with the pure FAT-GAN based UMCEG, and find relatively good agreement overall. Since the architecture is significantly more complex, it is expected that by adjusting the hyper-parameters of the architecture and allowing for a much longer training time, the FAT-free GAN UMCEG will reach the same level of precision as the FAT-GAN UMCEG architecture.Fig. 13. Schematic of the dual GAN architecture for the UMCEG.The dual GANFinally, we present another novel extension of the ML architecture for the UMCEG that admits the possibility of generating fully exclusive final states, as opposed to the previous versions where the UMCEG was trained as either a one-particle or two-particle inclusive UMCEG, or as a generator for the exclusive case p p+ ??events. In Fig.13 we present the schematics of such an architecture based on two sets of GANs. We design the exclusive final state production as a joint conditional probability distribution where the first GAN generates a given final state particle multiplicities followed by a secondary GAN that produces the corresponding particle momenta. By construction the dual GAN is designed to handle the discrete nature of multiplicities information in a given event and continuous nature of the particles momenta. As in the original FAT-based UMCEG, our dual GAN is designed also to preserve physical constraints such as on-shell condition for all final state particles as well as energy momentum conservation.In Fig.14 we present the comparison of the multiplicity probabilities inferred by the GAN against those from Pythia. As once can notice, for most cases there is a good agreement between Pythia and GAN while for particles with lower rates the GAN requires more training and training samples. While the complete study of the dual-GAN architecture is still in progress, we present in Fig.15 the total invariant mass W= (e+p?e')2 distribution. We can see a relatively good agreement between Pythia and the dual GAN give confidence that the UMCEG it is learning the gross features of the full final state well. We leave for Year 3 a continuation of the dual-GAN development as well as the integration with the FAT-free and S dependent designs.Fig. 14. Comparison between the particle multiplicities (probabilities) for various final states (photons, leptons, hadrons) generated from Pythia (black squares) and the GAN (red triangles).Fig. 15. Comparison of the hadronic final state mass W distributions generated from Pythia (black histograms) and from the dual GAN (red histograms, with uncertainty in yellow). The bottom panel shows the ratio of the dual GAN to Pythia results, with uncertainties given by the yellow envelope.Budget ExplanationFor Year 3, we request funding to support the ongoing collaboration with ML scientists from ODU and Davidson College, as well as fractional FTE support for the Jefferson Lab staff scientists and postdocs involved in this project. We plan the following division of labor for the requested funding: Folding and unfolding tools using ML: This work will be led by Prof. Yaohang Li from ODU, working with his PhD student, Yasir Alanazi, and Jefferson Lab LDRD postdoc Dr. Pawel Ambrozewicz. Physics extraction tools: This development will be led by Prof. Michelle Kuchera and Prof. Raghu Ramanuja from Davidson College, working with a computer science PhD student (to be hired through ODU) and a Davidson undergraduate student. Application to JLab data: Prof. Yaohang Li and PhD student Yasir Alanazi will work together with Jefferson Lab experimental physicists from Hall B to implement and train the UMCEG for inclusive DIS & exclusive p p+ ? and related channels. Dissemination and public release of ML algorithms: All members of the collaboration will help to compile specific documentation for the projects, with open source codes for the developed algorithms along with tutorials. We request funding to partially support a CS staff member to build the ML-based event generator software for public release. These efforts will be led by Dr. Wally Melnitchouk and Dr. Nobuo Sato from JLab.Dr. Melnitchouk and Dr. Sato will oversee and monitor the progress of the project on a weekly basis to ensure the timely completion of the deliverables.The planned allocation of the requested funds will be similar to that in previous years: $32.1k for ODU to fund 1 month summer salary for Dr. Li + 2 graduate students. ODURF has agreed to waive the indirect costs on the subcontract. $25.2k for Davidson College for ? month summer salaries each for Dr. Kuchera and Dr. Ramanujan (for ? month total) + 1 undergraduate student. Included in this will be funds (~ $2k) to cover travel for one PI + student to JLab for one week to work with the JLab and ODU collaborators. For the JLab staff scientists, we request 100% FTE for Dr. Ambrozewicz (postdoc), 5% FTE for Dr. Sato, 5% FTE for a CS staff member from the CST Division, and 5% FTE for Dr. Melnitchouk. $5k to support Dr. Ambrozewicz's travel to conference to present the results of this research, and for partial support of the organization of tutorial sessions for hands-on training of users for creating their own UMCEG using ML. Total ($k)151,296184,819222,497All budget numbers include estimated burden and overheads.Funds UseYear 1FY19(actual)Year 2FY20(Estimate)Year 3FY21(Estimate)Staff (FTE) / $k0.65 / 76,3341.15 / 103,9431.15 / 116,705M&H ($k)2,7072.6603,612Facilities ($k)21,57526,79534,150Travel ($k)5,0005,0005,000Subcontracts ($k)37,72546,42163,030Supplies ($k)10,63500References[1] EIC-Smear Package, .[2] I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A.Courville and Y.Bengio, Generative adversarial nets, Proceedings of NIPS'14, p. 2672 (2014).[3] S. Agostinelli et al., GEANT4: A simulation toolkit, Nucl. Instrum. Meth. A 506, 250 (2003).[4] T. Sjostrand, S. Mrenna and P. Z. Skands, A brief introduction to PYTHIA 8.1, Comput. Phys. Commun. 178, 852 (2008).[5] J. J. Ethier, N. Sato and W. Melnitchouk, First simultaneous extraction of spin-dependent PDFs and FFs from a global QCD analysis, Phys. Rev. Lett. 119, 132001 (2017).[6] N. Sato, C. Andres, J. J. Ethier and W. Melnitchouk, Strange quark suppression from a simultaneous Monte Carlo analysis of PDFs and FFs, Phys. Rev. D 101, 074020 (2020).[7] Y. Alanazi, N. Sato, T. Liu, R. E. McClellan, W. Melnitchouk, M. Kuchera, E.Pritchard, M. Robertson, R. Strauss, L. Velasco, and Y. Li, Simulation of electron-proton scattering events by a feature-augmented and transformed generative adversarial network (FAT-GAN), arXiv:2001.11103 (2020).[8] H. Abramowicz et al., Combination of measurements of inclusive deep-inelastic $e^\pm p$ scattering cross sections and QCD analysis of HERA data, Eur. Phys. J. C 75, 580 (2015).[9] C. Ledig, L. Theis, F. Huszar, J. Caballero, A. P. Aitken, A. Tejani, J. Totz, Z. Wang and W. Shi, Photo-realistic single image super-resolution using a generative adversarial network, arXiv:1609.04802 (2016).[10] M. Battaglieri et al., Photoproduction of pi+ pi- meson pairs on the proton, Phys. Rev. D 80, 072005 (2009).[11] F. Hauenstein, L. Weinstein et al., CLAS e1f measurement on a proton target, private communication (2020).[12] L. Van der Maaten and G. Hinton, Visualizing data using t-SNE, J. of Machine Learning Research 9, 2579 (2008).[13] M. Mirza and S. Osindero, Conditional generative adversarial nets, arXiv:1411.1784 (2014). ................
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