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AmpSuite

Seismic amplitudes offer vital information about explosion source characteristics, including discrimination and yield estimation. To take advantage of this, we developed an interactive Python package to measure, control data quality, generate broad area propagation models and perform discrimination and estimate yield. Propagation models are essential in support of transportable yield and broad area discrimination. The key benefit of this package will be its ability to continuously integrate data and new techniques. The AmpSuite framework will provide standardized, repeatable, and accurate model generation and characterization routines. The capability is crucial for monitoring agencies tasked with rapid and high-quality seismic event characterization. The AmpSuite software includes a series of independent modules to perform: • Direct Phase Amplitude Measurement and Storage • Coda Envelope Measurement and Storage • Data Quality Control • New Propagation Model Developments • Seismic Discrimination and Analysis • Yield Estimation and supporting utility software. The AmpSuite software provides comprehensive solutions for monitoring agencies seeking to optimize model generation and event analysis within a contemporary Python framework. Stakeholders (AFTAC) have begun to move towards the Python language for scientific analysis as a new workforce emerges.

Alfaro, Richard↗

The role of AI in detecting and mitigating human errors in safety-critical industries: A review

For safety-critical industries, human error (HE) presents continual risks to system productivity, reliability and safety. Artificial intelligence (AI) and machine learning (ML) methods have emerged as promising approaches to understand, categorize and mitigate the risk of HE in safety-critical industries. Furthermore, this review offers an examination of the current landscape regarding the utilization of AI/ML with regards to HE in safety-critical industries, categorizing literature into descriptive modeling, predictive modeling, prescriptive modeling, and generative modeling techniques. Additionally, the review aims to provide insights regarding themes in literature, challenges, and future research directions. Findings of the review suggest that AI/ML methods can prove useful in addressing the HE problem across safety-critical industries.

42 ENGINEERING↗

Structural basis for a highly conserved RNA-mediated enteroviral genome replication

Abstract Enteroviruses contain conserved RNA structures at the extreme 5′ end of their genomes that recruit essential proteins 3CD and PCBP2 to promote genome replication. However, the high-resolution structures and mechanisms of these replication-linked RNAs (REPLRs) are limited. Here, we determined the crystal structures of the coxsackievirus B3 and rhinoviruses B14 and C15 REPLRs at 1.54, 2.2 and 2.54 Å resolution, revealing a highly conserved H-type four-way junction fold with co-axially stacked sA-sD and sB-sC helices that are stabilized by a long-range A•C•U base-triple. Such conserved features observed in the crystal structures also allowed us to predict the models of several other enteroviral REPLRs using homology modeling, which generated models almost identical to the experimentally determined structures. Moreover, our structure-guided binding studies with recombinantly purified full-length human PCBP2 showed that two previously proposed binding sites, the sB-loop and 3′ spacer, reside proximally and bind a single PCBP2. Additionally, the DNA oligos complementary to the 3′ spacer, the high-affinity PCBP2 binding site, abrogated its interactions with enteroviral REPLRs, suggesting the critical roles of this single-stranded region in recruiting PCBP2 for enteroviral genome replication and illuminating the promising prospects of developing therapeutics against enteroviral infections targeting this replication platform.

Biochemistry & Molecular Biology↗

Achieving balanced execution through runtime detection of performance variation

Systems, apparatuses, and methods for achieving balanced execution in a multi-node cluster through runtime detection of performance variation are described. During a training phase, performance counters and an amount of time spent waiting for synchronization is monitored for a plurality of tasks for each node of the multi-node cluster. These values are utilized to generate a model which correlates the values of the performance counters to the amount of time spent waiting for synchronization. Once the model is built, the values of the performance counters are monitored for a period of time at the start of each task, and these values are input into the model. The model generates a prediction of whether a given node is on the critical path. If the given node is predicted to be on the critical path, the power allocation of the given node is increased.

97 MATHEMATICS AND COMPUTING↗

A GPU‐Accelerated Generative Adversarial Model for Causal Inference

We develop a GPU-accelerated machine learning generative adversarial model designed to facilitate causal inferences from observational data. Our model's theoretical framework is conceptualized in a manner that is amenable to being operable and scalable for high-performance computing platforms. We leverage GPU acceleration to develop a parallel evolutionary algorithm to achieve large-scale parallel computation of the model within a now widely accessible computing platform. This capability both enhances computational speedup and efficiency and also extends the use of the model to a broader range of substantive research domains while maintaining the underlying theoretical properties of the model.

GPU↗

Evaluation of Leading Modes of Climate Variability in the CMIP Archives

The adequate simulation of internal climate variability is key for our understanding of climate as it underpins efforts to attribute historical events, predict on seasonal and decadal time scales, and isolate the effects of climate change. Here the skill of models in reproducing observed modes of climate variability is assessed, both across and within the CMIP3, CMIP5, and CMIP6 archives, in order to document model capabilities, progress across ensembles, and persisting biases. A focus is given to the well-observed tropical and extratropical modes that exhibit small intrinsic variability relative to model structural uncertainty. These include El Niño–Southern Oscillation (ENSO), the Pacific decadal oscillation (PDO), the North Atlantic Oscillation (NAO), and the northern and southern annular modes (NAM and SAM). Significant improvements are identified in models’ representation of many modes. Canonical biases, which involve both amplitudes and patterns, are generally reduced across model generations. For example, biases in ENSO-related equatorial Pacific sea surface temperature, which extend too far westward, and associated atmospheric teleconnections, which are too weak, are reduced. Stronger tropical expression of the PDO in successive CMIP generations has characterized their improvement, with some CMIP6 models generating patterns that lie within the range of observed estimates. For the NAO, NAM, and SAM, pattern correlations with observations are generally higher than for other modes and slight improvements are identified across successive model generations. Finally, for ENSO and PDO spectra and extratropical modes, changes are small compared to internal variability, precluding definitive statements regarding improvement.

54 ENVIRONMENTAL SCIENCES↗

Exploring the energy landscape of RBMs: reciprocal space insights into bosons, hierarchical learning and symmetry breaking

Deep generative models have become ubiquitous due to their ability to learn and sample from complex distributions. Despite the proliferation of various frameworks, the relationships among these models remain largely unexplored, a gap that hinders the development of a unified theory of AI learning. In this work, we address two central challenges: clarifying the connections between different deep generative models and deepening our understanding of their learning mechanisms. We focus on Restricted Boltzmann Machines (RBMs), a class of generative models known for their universal approximation capabilities for discrete distributions. By introducing a reciprocal space formulation for RBMs, we reveal a connection between these models, diffusion processes, and systems of coupled bosons. Our analysis shows that at initialization, the RBM operates at a saddle point, where the local curvature is determined by the singular values of the weight matrix, whose distribution follows the Marc̆enko-Pastur law and exhibits rotational symmetry. During training, this rotational symmetry is broken due to hierarchical learning, where different degrees of freedom progressively capture features at multiple levels of abstraction. This leads to a symmetry breaking in the energy landscape, reminiscent of Landau’s theory. This symmetry breaking in the energy landscape is characterized by the singular values and the weight matrix eigenvector matrix. We derive the corresponding free energy in a mean-field approximation. We show that in the limit of infinite size RBM, the reciprocal variables are Gaussian distributed. Our findings indicate that in this regime, there will be some modes for which the diffusion process will not converge to the Boltzmann distribution. To illustrate our results, we trained replicas of RBMs with different hidden layer sizes using the MNIST dataset. Our findings not only bridge the gap between disparate generative frameworks but also shed light on the fundamental processes underpinning learning in deep generative models.

97 MATHEMATICS AND COMPUTING↗

Diffusion model approach to simulating electron-proton scattering events

Generative artificial intelligence is a fast-growing area of research offering various avenues for exploration in high-energy nuclear physics. In this work, we explore the use of generative models for simulating electron-proton collisions relevant to experiments like the Continuous Electron Beam Accelerator Facility and the future Electron-Ion Collider (EIC). These experiments play a critical role in advancing our understanding of nucleons and nuclei in terms of quark and gluon degrees of freedom. The use of generative models for simulating collider events faces several challenges such as the sparsity of the data, the presence of global or eventwide constraints, and steeply falling particle distributions. In this work, we focus on the implementation of diffusion models for the simulation of electron-proton scattering events at EIC energies. Our results demonstrate that diffusion models can reproduce relevant observables such as momentum distributions and correlations of particles, momentum sum rules, and the leading electron kinematics, all of which are of particular interest in electron-proton collisions. Although the sampling process is relatively slow compared to other machine-learning architectures, we find diffusion models can generate high-quality samples. We foresee various applications of our work including inference for nuclear structure, interpretable generative machine learning, and searches of physics beyond the Standard Model. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Device Classification for Industrial Control Systems Using Predicted Traffic Features

To achieve a secure interconnected Industrial Control System (ICS) architecture, security practitioners depend on accurate identification of network host behavior. However, accurate machine learning based host identification methods depends on the availability of significant quantities of network traffic data, which can be difficult to obtain due to system constraints such as network security, data confidentiality, and physical location. In this work, we propose a network traffic feature prediction method based on a generative model, which achieves high host identification accuracy. Furthermore, we develop a joint training algorithm to improve host identification performance compared to separate training of the generative model and the classifier responsible for host identification.

97 MATHEMATICS AND COMPUTING↗

Neural Density Estimation and Uncertainty Quantification for ChemCam Spectra [Slides]

The ChemCam instrument of Curiosity uses laser-induced breakdown spectroscopy (LIBS). It fires a laser at target and vaporizes rock surfaces, creating a plasma. Three spectrographs divide the plasma light into wavelengths for chemical analysis: ultraviolet, violet, and visible near-infrared. Regression methods (SVR, PCR, CNN) have been employed for calibration (prediction of the elemental composition of samples); however, labeled ChemCam samples are limited. Here, we focus on unsupervised learning and employ generative models from ChemCam analysis. Further, we use labels (supervised) in combination to the generative model to compute uncertainties related to predictions. We report generative modeling can be successfully applied to model real-world data. Normalizing flow models can be efficiently constructed on latent spaces for fast downstream inference. Unsupervised and supervised learning can be combined to form an uncertainty quantification framework.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Data-Efficient Generation of Protein Conformational Ensembles with Backbone-to-Side-Chain Transformers

Excitement at the prospect of using data-driven generative models to sample configurational ensembles of biomolecular systems stems from the extraordinary success of these models on a diverse set of high-dimensional sampling tasks. Unlike image generation or even the closely related problem of protein structure prediction, there are currently no data sources with sufficient breadth to parametrize generative models for conformational ensembles. To enable discovery, a fundamentally different approach to building generative models is required: models should be able to propose rare, albeit physical, conformations that may not arise in even the largest data sets. Here, in this work, we introduce a modular strategy to generate conformations based on “backmapping” from a fixed protein backbone that (1) maintains conformational diversity of the side chains and (2) couples the side-chain fluctuations using global information about the protein conformation. Our model combines simple statistical models of side-chain conformations based on rotamer libraries with the now ubiquitous transformer architecture to sample with atomistic accuracy. Together, these ingredients provide a strategy for rapid data acquisition and hence a crucial ingredient for scalable physical simulation with generative neural networks.

36 MATERIALS SCIENCE↗

Deep generative molecular design reshapes drug discovery

Recent advances and accomplishments of artificial intelligence (AI) and deep generative models have established their usefulness in medicinal applications, especially in drug discovery and development. To correctly apply AI, the developer and user face questions such as which protocols to consider, which factors to scrutinize, and how the deep generative models can integrate the relevant disciplines. This review summarizes classical and newly developed AI approaches, providing an updated and accessible guide to the broad computational drug discovery and development community. We introduce deep generative models from different standpoints and describe the theoretical frameworks for representing chemical and biological structures and their applications. We discuss the data and technical challenges and highlight future directions of multimodal deep generative models for accelerating drug discovery.

59 BASIC BIOLOGICAL SCIENCES↗

Structured Neural Network Modeling for Developing Digital Twins Models of Hydropower Generation Units

Dynamic modeling is a key part in the development of digital twin (DT) for dynamic systems. This is true for hydropower systems, where whole system modeling including penstock, turbine and generators, etc is important in realizing actuate modeling for the real systems. On the other hand, in response to the large variations of the power demand due to increased penetration of renewables such as wind and solar, hydropower systems are now required to operate in a large power generation range. This situation triggers the nonlinear characteristics of the generation unit with respect to its models. As such, it is imperative to use data driven modeling such as neural networks to learn the nonlinear dynamics of the hydropower generation unit. To achieve this objective, this study constructs a modeling and learning algorithm integrated with multiple structured neural network models for the modeling of turbine shaft speed, penstock pressure, and generator power output based on the generator power control setpoint, field current, and field voltage. In addition, the study uses the hydropower data from Tacoma Public Utilities to train and validate the proposed neural network algorithm. The results have shown that this structured neural network modeling approach can learn the system dynamics effectively by using the real-time data collected from the hydropower system with the desired modeling results.

Wang, Hong↗

Discrete generative diffusion models without stochastic differential equations: A tensor network approach

Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard DMs, this is done by learning a “score function” that reverses the effect of adding diffusive noise to the distribution of interest. Here we consider the generalisation of DMs to lattice systems with discrete degrees of freedom, and where noise is added via Markov chain jump dynamics. We show how to use tensor networks (TNs) to efficiently define and sample such “discrete diffusion models” (DDMs) without explicitly having to solve a stochastic differential equation. We show the following: (i) by parametrising the data and evolution operators as TNs, the denoising dynamics can be represented exactly; (ii) the auto-regressive nature of TNs allows to generate samples efficiently and without bias; (iii) for sampling Boltzmann-like distributions, TNs allow to construct an efficient learning scheme that integrates well with Monte Carlo. We illustrate this approach to study the equilibrium of two models with non-trivial thermodynamics, the d = 1 constrained Fredkin chain and the d = 2 Ising model. Published by the American Physical Society 2025

Causer, Luke (ORCID:0000000194243473)↗

Observational Data for Next-Generation Climate Model Evaluation: Requirements, Considerations, and Best Practices

Climate model simulations are an important source of information about our planet’s climate system and also enable informed decision-making under different future scenarios. As a new archive of results from the next generation of climate models is anticipated to become available with the Coupled Model Intercomparison Project phase 7 (CMIP7), the need to develop efficient and robust methods to evaluate models is paramount. Observations are an integral part of model evaluation, providing a means to quantify and understand the degree to which climate models can faithfully reproduce Earth system processes. Such analysis is critical for constraining climate projections, identifying areas of focus for model development, and assisting analysts in deciphering the utility of models for specific applications. Observations of Earth system come from a diversity of sources, span different space–time domains, and are produced by different communities, and each dataset features different data structures and formats, metadata standards, and its own unique uncertainties. Uncertainties in an observational dataset may stem from gaps in temporal and spatial coverage, instrumentation errors, or assumptions in retrieval and processing methods. How then does one ensure that observational data are ready for use and utilized in the most appropriate way for robust, rapid, and routine climate model evaluation? The CMIP7 Model Benchmarking Task Team with input from the broader climate modeling, model evaluation, and observational data communities present a vision and considerations for best practices toward the optimal and appropriate use of observational data to support next-generation climate model evaluation.

Climate models↗

Search for vector-like leptons coupling to first- and second-generation Standard Model leptons in pp collisions at s = 13 TeV with the ATLAS detector

A search for pair production of vector-like leptons coupling to first- and second-generation Standard Model leptons is presented. The search is based on a dataset of proton-proton collisions at s$$ \sqrt{s} $$ = 13 TeV recorded with the ATLAS detector during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of 140 fb−1. Events are categorised depending on the flavour and multiplicity of leptons (electrons or muons), as well as on the scores of a deep neural network targeting particular signal topologies according to the decay modes of the vector-like leptons. In each of the signal regions, the scalar sum of the transverse momentum of the leptons and the missing transverse momentum is analysed. The main background processes are estimated using dedicated control regions in a simultaneous fit with the signal regions to data. No significant excess above the Standard Model background expectation is observed and limits are set at 95% confidence level on the production cross-sections of vector-like electrons and muons as a function of the vector-like lepton mass, separately for SU(2) doublet and singlet scenarios. The resulting mass lower limits are 1220 GeV (1270 GeV) and 320 GeV (400 GeV) for vector-like electrons (muons) in the doublet and singlet scenarios, respectively.

Aad, G↗

LLNL Kimberlina 1.2 NUFT Simulations June 2018 (v2)

This dataset contains the output 6,000, 3-dimensional reactive multi-phase flow and transport aquifer simulations of brine and CO2 leakage into a protective aquiver in California’s San Joaquin Valley and input data files detailing the geologic mesh, aquifer physical properties and CO2 and brine injection rates. This data set was generated as an ongoing effort with the US DOE National Risk Assessment Partnership (NRAP) to evaluate the effectiveness of monitoring techniques to detect brine and CO2 leakage from legacy wells into underground sources of drinking water overlaying a CO2 storage reservoir. Each simulation contains a unique set of input parameters, generated stochastically. The outputs consist of these upper three geologic layers (from top): the Etchegoin, Macoma-Chanac, Santa Margarita-McLure formations. These simulations span the several distances (1, 3 and 6 km or wells W31-0.2, W31-0.5 and W31-1.0, respectively) from the CO2 injector, initiated from bottom hole pressure and saturation to calculate wellbore leakage from the storage reservoir, with low and high regional groundwater gradients and wellbore leakage into 5 leaky nodes. The dataset includes 1,000 unique simulations for each distance, which each contain a unique aquifer heterogeneity, aquifer and caprock permeability, and two model generations are included with a high permeability (prod07) and hybrid permeability (prod09). The range of permeability distributions is listed in Table 1. Each model generation consists of 3,000 simulations. Included in the dataset are the leakage rates determined from 2D wellbore models which utilize the pressure and CO2 saturation from LBL's reservoir simulations, NUFT mesh files with distributed lithology, NUFT rocktab files which describe the material properties for the geologic layers and the NUFT input files and post-processed output 'ntab' files. Each ntab file contains spatial (rows) and temporal (columns) model output tables for each model cell, the locations (x,y,z) and dimensions for each cells (dx, dy, dz). Table 1. Permeability distribution ranges for prod07 and prod09 model generations Geologic Layer: Permeability Range (log10 m^2) prod07 prod09 Etchegoin -12.92 to -10.92 -13.70 to -11.44 Macoma-Chanac -12.72 to -10.72 -13.50 to -11.24 Santa Margarita-McLure -12.70 to -10.70 -13.48 to -11.22 The input files used to generate the model include which are included in the dataset are: Time series of CO2 leakage input into the model (ex: Q_brn.W31-0.2.sim1000.layers123.tab) Time series of CO2 leakage input into the model (ex: Q_CO2.W31-0.2.sim1000.layers123.tab) Physical properties of the aquifer materials detailing the aquifer porosity, solid density, partitioning coefficients, permeabilities and van-Genuchten parameters detailed in a NUFT rocktab file: (ex: sim1000.usnt.rocktab) Numerical mesh and geologic data assigned to each model cell detailed in a NUFT genmsh format (ex: sim1000.mesh_k16.prod07.trans.genmsh) The primary output parameters are: pH (use absolute value) Change in TDS (mg/kg) Change in Pressure (Pa) Change CO2 gas saturation (fraction range 0.0-1.0) for example, the directory /p/lscratchh/mansoor1/nrap/kimberlina/prod09/mainfiles/sim1000/W31- 0.2 contains: sim1000.W31-0.2.trans.pH.red.ntab sim1000.W31-0.2.no_bg.trans.TDS.red.ntab sim1000.W31-0.2.usnt.P.deltabg.red.ntab sim1000.W31-0.2.usnt.CO2_sat.deltabg.red.ntab Each row in the NTAB files consist of model output per numerical grid cell. Each output file contains 33 columns (variables), including the information of numerical records, geologic location and sizes and the simulated parameter values over time. The first 13 variables are about numerical records and relative geologic information for a simulation grid: 1. index: simulation index 2. i: the ith grid of x-axis 3. j: the ith grid of y-axis 4. k: the ith grid of z-axis 5. element_ref: element reference 6. nuft_ind: nuft index 7. x: grid location in the x axis direction 8. y: grid location in the y axis direction 9. z: grid location in the z axis direction 10. dx: grid length in the x axis direction 11. dy: grid length in the y axis direction 12. dz: grid length in the z axis direction 13. volume: volume of the simulation grid The remainder (14, 15, 16...) variables are the simulated parameter values over time, take Pressure as an example, are: 14. 0.0y: initial pressure per cell. 15. 10.0y: simulated pressure at the end of the 10th year. 16. 20.0y: simulated pressure at the end of the 20th year. ... (repeated for every 10 years until 200 years)... The model extends 10,000 m, 5,000 m and 1,411 m in the x,y and z dimensions, respectively. The mesh consists of 164,832 cells with mesh dimensions of 101 x 51 x 32 (nx, ny, nz), with cell dimensions ranging from 100 m laterally (along x and y-axis) and model layers are as designated in the z-axis: Layer 1: atmosphere (1e-30 m thick) Layer 2: upper caprock (10 m thick) Layers 3-13: Etchegoin (536.23 m thck) Layers 14-27: Macoma-Chanac (679.04 m thick) Layers 28-32: Santa Margarita-McLure (185.94 m thick) The wellbore is placed along node i=51, j=26, and extends vertically along 5 nodes from the top to the bottom of the model. Special instructions when extracting files: Each Gzip archive (ex: prod07.sim1000-sim00099.tar.gz) contains 100 simulations. Gzip archives should be transferred into base directories (ie. In Linux: mkdir prod07; mv prod07.*.tar.gz prod07/.) before extracting, or files will be overwritten. Each sub-simulation tree should have the following file structure pattern (using the linux 'tree' command): |-- prod07 | |-- sim0001 | |-- W31-0.2 | | |-- Q_brn.W31-0.2.sim0001.layers123.tab | | |-- Q_co2.W31-0.2.sim0001.layers123.tab | | |-- sim0001.W31-0.2.no_bg.trans.TDS.red.ntab | | |-- sim0001.W31-0.2.trans.pH.red.ntab | | |-- sim0001.W31-0.2.usnt.CO2_sat.deltabg.red.ntab | | |-- sim0001.W31-0.2.usnt.P.deltabg.red.ntab | |-- W31-0.5 | | |-- Q_brn.W31-0.5.sim0001.layers123.tab | | |-- Q_co2.W31-0.5.sim0001.layers123.tab | | |-- sim0001.W31-0.5.no_bg.trans.TDS.red.ntab | | |-- sim0001.W31-0.5.trans.pH.red.ntab | | |-- sim0001.W31-0.5.usnt.CO2_sat.deltabg.red.ntab | | |-- sim0001.W31-0.5.usnt.P.deltabg.red.ntab | |-- W31-1.0 | | |-- Q_brn.W31-1.0.sim0001.layers123.tab | | |-- Q_co2.W31-1.0.sim0001.layers123.tab | | |-- sim0001.W31-1.0.no_bg.trans.TDS.red.ntab | | |-- sim0001.W31-1.0.trans.pH.red.ntab | | |-- sim0001.W31-1.0.usnt.CO2_sat.deltabg.red.ntab | | |-- sim0001.W31-1.0.usnt.P.deltabg.red.ntab | |-- sim0001.mesh_k16.prod07.trans.genmsh Disclaimer This document was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes. Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the U.S. Department of Energy, National Nuclear Security Administration under Contract DE-AC52-07NA27344. This report was reviewed and released as LLNL-MI-753464.

aquifer↗

Unsupervised quantum circuit learning in high energy physics

Unsupervised training of generative models is a machine learning task that has many applications in scientific computing. Here, in this work, we evaluate the efficacy of using quantum circuit-based generative models to generate synthetic data of high energy physics processes. We use nonadversarial, gradient-based training of quantum circuit Born machines to generate joint distributions over two and three variables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗