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Machine Learning Meets High-Energy Nuclear Physics: From Pattern Recognition to Physics-Integrated Discovery

Xun Chen, Weiyao Ke, Yu-Gang Ma, Long-Gang Pang, Kai Zhou

arXiv:2610.12293v1hep-phcs.AIhep-lathep-thnucl-th

TL;DR

This review asks how AI can reduce the cost of high-fidelity calculations, extract more information from data, and connect historically separate areas of HENP. It surveys ML methods integrated with physical workflows and identifies a shift toward learned representations, uncertainty-aware inference, and physically validated generation. AI can make some previously intractable workflows feasible, but it does not remove the need for modeling assumptions and constraints.

  • Problem

    HENP faces the challenge of making costly calculations tractable, extracting information from existing and future data, and connecting sectors historically analyzed separately.

    Source: §IX · p. 32

  • Method

    The review synthesizes how learned representations, probabilistic ML, differentiable programming, and generative models enter HENP workflows under physical constraints and validation.

    Source: §IX · p. 31

  • Results

    The review identifies a shift toward learned representations, uncertainty propagation through inverse problems, and generative acceleration of simulation and sampling when constrained and validated against observables.

    Source: §IX · p. 31

  • Takeaways & Limitations

    AI can make previously intractable workflows feasible and expose hidden correlations, while making assumptions explicit through priors, likelihoods, constraints, and validation tests.

    Source: §IX · p. 32

    AI alone cannot solve the full-QCD sign problem, determine the QCD critical point, or infer neutron-star core composition without assumptions.

    Source: §IX · p. 32

Abstract

from arXiv · show

Machine learning (ML) in high-energy nuclear physics (HENP) is entering a new stage in which physical knowledge is incorporated more directly into data analysis, simulation, and physics inference. This mini-review focuses on developments that have matured in the past several years. Whereas earlier applications emphasized event classification, pattern recognition, and surrogate models for selected observables, recent work has moved toward physics-integrated workflows: calibrated Bayesian extraction of QCD matter properties, dense-matter equation-of-state inference from heavy-ion and neutron-star data, generative event modeling, neural unfolding of weak physical signals, differentiable inverse solvers, gauge-equivariant and diffusion-based lattice-field samplers, and neural reconstruction of model functions in holographic QCD. We survey recent applications of ML in heavy-ion collisions, neutron-star physics, lattice QFT, and holographic or continuum QCD. The emphasis is not on ML architectures alone, but on how they enter concrete physics workflows, how physical constraints such as symmetries, conservation laws, causality, thermodynamic stability, and topology are imposed, and how uncertainty quantification and validation determine whether an AI-assisted result can support a reliable physics conclusion.

I. INTRODUCTION

HENP uses complementary collision, neutron-star, lattice, and continuum approaches to probe QCD matter, but their computationally costly forward models make inference from finite, incomplete data challenging. This review surveys a shift toward physics-integrated ML workflows, where physical constraints, uncertainty quantification, and validation remain part of the analysis.

I. INTRODUCTION

  • HENP combines heavy-ion collisions, neutron-star observations, lattice QCD, and continuum or holographic approaches to study different regions and properties of strongly interacting QCD matter.These approaches provide complementary information about the phase diagram and real-time dynamics.Source: §I · p. 2
  • The review traces a shift from isolated classification and surrogate applications toward ML integrated into quantitative physics workflows, with stronger incorporation of physical knowledge, validation, and uncertainty quantification.The update focuses on developments that have matured enough to affect quantitative inference.Source: §I · pp. 2–3
  • Across these areas, forward models connect physical properties to observables, while inverse analyses use finite, incomplete, noisy, or high-dimensional data to constrain properties and viable theories.Repeated forward-model evaluations and uncertainty propagation can make the inference computationally expensive.Source: §I · p. 3
  • Reliable inference requires physical constraints such as symmetries, conservation laws, causality, stability, and topology to be checked alongside uncertainty quantification and validation.The review is weighted toward theory, simulation, and inference, and presents selected detector-facing examples rather than an exhaustive survey of experimental ML.Source: §I · pp. 2–4
  • Recent applications include calibrated inference, full-event modeling, and weak-signal reconstruction in heavy-ion physics; flexible EoS inference for neutron stars; and gauge-equivariant sampling in lattice QFT.Holographic and continuum approaches use ML to reconstruct model functions from boundary observables and propagate uncertainties into later predictions.Source: §I · p. 4

II. AI FOR HIC PHENOMENOLOGY STUDIES

In heavy-ion phenomenology, ML is moving beyond classification toward event representations, full-event generation, and reconstruction of weak signals. The review emphasizes that these tools must be tied to physical hypotheses and validated for their intended use.

A. Event representations and learned observables

  • PointNet treats collision events as unordered particle sets, while point-cloud and self-supervised transformer methods develop representations for centrality, EoS-related tasks, flow patterns, and downstream analyses [35] [36] [37] [38].This extends the approach beyond supervised classification of a few labels toward reusable, interpretable features.Source: A. Event representations and learned… · p. 5
  • Physics-informed neural networks encode thermodynamic identities and physical constraints in neural EoS parameterizations derived from first-principles lattice QCD input [39].Generative models also need validation beyond visual plausibility, including relevant correlations, parameter dependence, and uncertainty estimates.Source: A. Event representations and learned… · p. 5, B. Generative event models and fast… · p. 6

B. Generative event models and fast simulation

  • DiffHIC reproduces integrated and differential flow observables, higher-order correlations, and fluctuations, while HEIDi generates complete unordered hadron point-cloud events with momenta and species [40] [41] [42].The two approaches generate different event representations: two-dimensional spectra versus complete particle lists.Source: B. Generative event models and fast… · p. 5

C. Subtle signals identification from HICs

  • Jet-medium signals are embedded in an evolving, fluctuating soft background, motivating controlled inverse workflows that connect hard probes to medium properties with quantified uncertainty [46] [47] [48] [49] [50].ML has also been used to test jet classification robustness under background contamination and model variation.Source: C. Subtle signals identification from… · p. 6
  • Interpretable and self-attention approaches use final-state observables to infer initial-state deformation or nucleon correlations while addressing nuisance variations [51] [52] [53].A transformer without positional embedding respects particle-cloud permutation symmetry, and averaging learned features across events performed well for identifying short-range correlations.Source: C. Subtle signals identification from… · p. 6
  • Neural unfolding reconstructs a less-degraded CME signal from final-state information, mapping an experimentally accessible distribution toward a latent physical signal [54] [55].The study targets how interactions obscure initial charge separation.Source: C. Subtle signals identification from… · p. 6

D. Symbolic regression and interpretable model discovery

Symbolic regression searches for interpretable functional forms, while Bayesian inference uses statistical models and ML tools to constrain physical parameters from data. Across both, validation and uncertainty assessment are needed to establish whether the inferred results are trustworthy.

D. Symbolic regression and interpretable model discovery

  • Symbolic regression searches mathematical expressions for both functional form and numerical parameters, with methods including evolutionary search, sparse regression, and neural generation of equation skeletons [57].A useful result should be interpretable, generalize beyond its inference data, and pass independent physical consistency tests.Source: D. Symbolic regression and… · p. 7
  • The same SR equation skeleton describes measured multiplicities in kinematic intervals not used during inference, and its extracted parameters agree with an independent relation motivated by average transverse momentum [62].These cross-interval and independent-physics checks complement fit quality when assessing whether the structure captures useful physics.Source: D. Symbolic regression and… · p. 7
  • Current SR methods have underdeveloped uncertainty quantification, failure-rate characterization, and reporting of unsuccessful inferences, so compact expressions remain hypotheses requiring physical tests.The proposed checks include symmetries, dimensions, known limits, independent observables, and uncertainty estimates.Source: D. Symbolic regression and… · p. 7

III. BAYESIAN INFERENCE

  • Bayesian inference constrains parameters using data, while ML can accelerate forward calculations or estimate otherwise intractable likelihoods and posteriors.The methods address different computational bottlenecks and should be assessed using closure tests, posterior calibration, and computational cost, not sampling speed alone.Source: §III · pp. 8–9
  • Heavy-ion likelihoods are often approximated as multivariate Gaussian, but that assumption should be tested when uncertainties are non-Gaussian or observables have low statistics.The covariance may include experimental, finite-simulation, emulator, and model-discrepancy uncertainties.Source: §III · p. 8
  • GP emulators can reduce the cost of repeated heavy-ion model calculations, with PCA helping stabilize emulation of many correlated observables [70].The emulator is trained from representative full-model design points and must be validated against calculations not used for training.Source: §III · pp. 8–9

A. Bayesian extraction of the dense nuclear-matter EoS

Bayesian analysis uses heavy-ion data to constrain a density-dependent mean field and produce a posterior over dense nuclear-matter EoS functions. The review also connects this inference program to low-energy nuclear response and proposes hierarchical analyses across heavy-ion and neutron-star constraints.

A. Bayesian extraction of the dense nuclear-matter EoS

  • Heavy-ion data constrain a density-dependent mean field in transport-model calculations, yielding a posterior over dense nuclear-matter EoS functions rather than a class label [79].The analysis uses proton mean transverse kinetic energies and elliptic flows; Fig. 5 depicts the inference.Source: A. Bayesian extraction of the dense… · p. 9, Figure 5 · p. 9
  • Low-energy giant-dipole-resonance response was used to infer the isovector effective mass and neutron–proton effective-mass splitting from its energy-weighted sum rule and width [80].The BUU transport calculation propagates uncertain effective interactions through a forward model to measured response functions.Source: A. Bayesian extraction of the dense… · p. 9
  • Heavy-ion data and neutron-star observations probe different thermodynamic trajectories but overlapping dense-QCD theory space, motivating hierarchical analyses with separate nuisance parameters and validity ranges.The proposed inputs also include chiral effective theory, perturbative QCD, and lattice constraints; ML can accelerate forward maps and represent functional uncertainty.Source: A. Bayesian extraction of the dense… · p. 9

B. Transport properties of baryon-rich QCD matter

Bayesian analyses of baryon-rich matter constrain transport properties, but their posteriors depend on emulator quality and the assumed dynamical framework. Jet, heavy-flavor, and quarkonium studies extend these workflows while exposing limits from prior dependence, observable tension, and model assumptions.

B. Transport properties of baryon-rich QCD matter

  • The (3 + 1)D hybrid-model analysis favored increasing specific shear viscosity with µB up to about 0.4 GeV and a larger bulk-viscosity peak at √sNN = 19.6 GeV than at 7.7 or 200 GeV [82].It also constrained average initial-state rapidity loss using Au–Au observables across beam energies.Source: B. Transport properties of baryon-rich… · p. 10
  • Emulator closure tests found that heterogeneous-uncertainty-aware emulators recovered planted parameters more accurately, while high-posterior training points reduced information loss by roughly two orders of magnitude [84].Different GP implementations could yield substantially different posterior widths despite reasonable conventional prediction errors.Source: B. Transport properties of baryon-rich… · p. 10
  • Transport posteriors remain framework-dependent: an independent analysis weakly constrained µB dependence, and a preliminary baryon-diffusion extraction covered only one collision energy and two centrality classes [85].The preliminary study calls for broader parameter variation, closure tests, and more rapidity-dependent observables.Source: B. Transport properties of baryon-rich… · p. 10

C. Bayesian jet tomography and ML-assisted jet analysis

  • Jet closure tests reproduced marginalized mean quark/gluon energy losses across parametrizations, but steeply falling spectra limited full-distribution reconstruction and left results partly prior-sensitive [90].The analyses supported an approximately universal energy-loss description and found a gluon-to-quark ratio somewhat above naive Casimir scaling.Source: C. Bayesian jet tomography and… · p. 11, Figure 6 · p. 11
  • A GP-assisted calibration found high-pT hadrons and jets broadly compatible but lower-pT hadrons favored another region, tracing tension mainly to qhat's parton-energy dependence [94].Such disagreement among observable posteriors can expose model limitations in different kinematic regions.Source: C. Bayesian jet tomography and… · p. 11
  • A nonparametric information-field prior for qhat(T) reduces functional-parametrization bias by letting data constrain sensitive temperature regions while leaving weakly probed regions prior-dominated [95] [96].The global analysis found pronounced temperature dependence of qhat/T^3.Source: C. Bayesian jet tomography and… · p. 11
  • Jet-substructure classifiers found substantial medium-discrimination information in soft, infrared- and collinear-unsafe features, much of which underlying-event fluctuations and background subtraction obscure.Sparse regression produced simpler observables approximating the neural classifier and more accessible to theoretical calculations.Source: C. Bayesian jet tomography and… · p. 11

D. Open heavy flavor and quarkonium

  • Bayesian heavy-flavor analyses jointly constrained 2πTDs and qhat/T^3, finding a non-monotonic qhat/κ that departs substantially from the naive expectation qhat/κ = 2 [99].Other studies calibrated D-meson RAA and v2 to constrain heavy-quark transport alongside the effective coupling governing the QCD EoS [98] [100].Source: D. Open heavy flavor and quarkonium · p. 12

E. Bayesian constraints on initial-state and pre-equilibrium dynamics

Bayesian studies of early collision dynamics compare initial-state models, impose causality, and account for model discrepancy and model-choice uncertainty. Nuclear-structure analyses use Bayesian and neural inference for small-x inputs, neutron skins, and deformation, with several results still restricted to simulations or closure tests.

E. Bayesian constraints on initial-state and pre-equilibrium dynamics

  • Replacing parametric initial conditions with SMASH transport-generated profiles changed posterior constraints on η/s in Pb–Pb collisions, showing that initial-state modeling couples to extracted QGP properties.The study reported tighter constraints on early-time dynamics with transport-generated initial conditions.Source: E. Bayesian constraints on… · p. 12
  • Causality restrictions shifted initial-condition and bulk-viscosity posteriors in Au–Au flow analyses, and disfavored statistically acceptable parameter sets that violated causality.Fig. 7 reports that acausal regimes significantly bias bulk viscosity; the restriction excludes initial acausal energy fractions above 10^-4 in one comparison.Source: E. Bayesian constraints on… · p. 12, Figure 7 · p. 13
  • Model-discrepancy modeling absorbed a significant portion of hadron-spectrum and flow mismatch into a Gaussian-process discrepancy term, broadening inferred η/s and initial-state entropy deposition.The analysis also left early-time shear-stress initialization less constrained, indicating substantial theoretical uncertainty from pre-equilibrium modeling.Source: E. Bayesian constraints on… · pp. 12–13
  • An IP-Glasma–hydrodynamics–transport analysis used transfer learning and Bayesian model averaging, and available data did not statistically favor temperature-dependent over constant shear viscosity after accounting for model complexity [108] [109].Model averaging propagated uncertainty associated with the hydrodynamic-to-hadronic transition.Source: E. Bayesian constraints on… · p. 13

F. Bayesian and machine-learning constraints on the nuclear initial state: from partonic structure to nuclear shape

  • For the Balitsky–Kovchegov initial condition, HERA data favored an anomalous dimension close to unity, and the posterior was propagated through nonlinear evolution to proton–proton and future electron–ion predictions [110].A GP emulator and MCMC sampler enabled uncertainty propagation beyond a best-fit determination.Source: F. Bayesian and machine-learning… · p. 13
  • A joint proton-and-lead J/ψ photoproduction analysis remained difficult to describe without an additional normalization factor, revealing tension in the assumed nuclear small-x model [111].Principal-component GP emulators were refined with training points selected from an intermediate posterior.Source: F. Bayesian and machine-learning… · p. 13
  • The neutron-skin analysis inferred Pb nuclear structure jointly with collision parameters and identified correlations between neutron skin and initial entropy-deposition parameters [119].Its result was translated into a constraint on the slope of the nuclear symmetry energy.Source: F. Bayesian and machine-learning… · p. 14
  • Neural posterior estimation reconstructed nuclear deformation from simulated initial-state information, but had not yet extracted it from final-state experimental data; detailed correlations and clustering remain less developed.Multiple events were needed to suppress event-by-event fluctuations, and quadrupole deformation was reconstructed more accurately than the weaker β4 signal.Source: F. Bayesian and machine-learning… · p. 14

IV. HIC EXPERIMENTS WITH AI

AI methods are being incorporated into heavy-ion measurement chains, from jet-background correction and unfolding to online event selection and reconstruction. Their utility depends on performance under realistic backgrounds, detector conditions, and latency constraints.

A. Jet Quenching Classification, Background Subtraction, and Unfolding

  • ML momentum regression improved resolution over area-based subtraction, especially for low-pT jets, while high-dimensional OmniFold used up to 18 correlated observables to improve jet-substructure unfolding in simulation.Data application of the regression still requires validation against background and fragmentation mismodeling.Source: A. Jet Quenching Classification,… · pp. 14–15
  • DeepSub denoises full-event jet images and reproduces key jet observables at the sub-percent to percent level, outperforming existing subtraction techniques.A DNN trained on LBT quenched jets also reduced momentum-prediction bias versus Area-based and Constituent Subtraction methods.Source: A. Jet Quenching Classification,… · p. 15
  • Neural estimators of initial jet energy reduce final-energy selection bias and suggest event-by-event jet tomography, but inferred production geometry remains dependent on the training quenching model.LSTM predictions also correlated strongly with true energy loss in Jewel photon-jet samples and were validated with Delphes detector simulations.Source: A. Jet Quenching Classification,… · p. 15

1. Machine Learning-Based Online Triggers for Heavy-Flavor Event Selection

  • On simulated charm events at √s = 200 GeV, the sPHENIX trigger achieved 0.945 track-reconstruction efficiency and about 0.79 precision and recall for heavy-flavor identification.It uses spatial hit information from fast silicon detectors to meet online latency constraints; the GNN encodes track topology, the BGNN captures track correlations, and an MLP identifies heavy-flavor events.Source: §1 · p. 15, Figure 8 · p. 16

B. Real-Time Online Triggering and Data Processing with AI

  • For online triggering, a GNN-based system classifies signal versus background and retains signal data, learning correlations in high-multiplicity events rather than relying on hand-crafted thresholds and cuts.Experimental ML must also contend with acceptance, pileup, occupancy, resolution, calibration drift, and latency.Source: §IV · p. 14, §1 · pp. 15–16

2. CNN-Based Online Trigger for QGP Event Selection

The section surveys AI-based QGP event selection and detector reconstruction alongside contrastive shower clustering, then introduces data-constrained inference in holographic QCD. Across these applications, validation and physical constraints remain important.

2. CNN-Based Online Trigger for QGP Event Selection

  • For Au+Au collisions at 30 AGeV, QGP-trigger accuracy fell from 95.1% on generator-level PHSD events to 83.7% after full reconstruction, while retaining practical separation power.SHAP analysis identified particle-species contributions to the decision.Source: §2 · p. 16

3. Neural Networks for Real-Time Cluster Finding and Track Reconstruction

  • A real-time TPC neural network reconstructs clusters and assigns probabilities that signals arise from noise or charged particles, separating overlapping features under LHC processing constraints.An attention-based GNN with two-stage aggregation was also developed for MPD TPC track reconstruction.Source: §3 · p. 16

4. Contrastive Metric Learning for Stable Shower Reconstruction

  • Compared with object condensation, contrastive metric learning yields narrower, more stable shower-separation margins and higher efficiency, purity, multiplicity-ratio stability, and energy resolution, with the largest gains at high multiplicity.CML also maintains performance across particle types in mixed-particle training, while OC degrades particularly for electromagnetic showers.Source: §4 · p. 17, Figure 10 · p. 17

V. HOLOGRAPHIC QCD WITH MACHINE LEARNING

  • ML-assisted holographic inference uses boundary observables to constrain model parameters or reconstruct bulk functions before calculating further observables, rather than beginning only with a specified bulk model [147].This data-driven shift does not eliminate model dependence, so physical constraints and uncertainty quantification remain important.Source: §V · pp. 17–18, Figure 11 · p. 18

A. From Renormalization Group to Deep Generative Models

The section links holography’s radial direction to renormalization and generative learning, then describes ML as a means of reconstructing bulk geometry and dynamics from boundary data. The inverse problem is generally non-unique, motivating physical priors and uncertainty estimates.

A. From Renormalization Group to Deep Generative Models

  • A flow-type generative model learned a mapping between uncorrelated bulk variables and an interacting boundary ensemble; in critical 2D complex ϕ4 theory, its latent geometry was consistent with three-dimensional hyperbolic space [152].This provides numerical evidence for an AdS-like structure emerging from data-driven learning.Source: A. From Renormalization Group to Deep… · p. 18

B. Methodological Core: Geometric Reconstruction and Holographic Inverse Problems

  • Holographic reconstruction is generally non-unique because different bulk potentials, coordinate choices, or matter couplings can reproduce the same limited boundary observables.ML approaches therefore need physical priors, constraints, and uncertainty estimates to better pose the inverse problem.Source: B. Methodological Core: Geometric… · p. 18

1. Foundational frameworks and early works

  • Early AdS/deep-learning models represented radial bulk evolution with network layers and learned weights, allowing structures such as a black-hole horizon to emerge from boundary-data training [153] [154].The construction shifted the workflow from forward modeling toward inverse reconstruction.Source: §1 · pp. 18–19

2. Algorithmic refinements and physically informed architectures

  • Neural ODEs model the continuous radial direction with trainable differential equations, reducing discretization artifacts and enabling smoother, more efficient background reconstruction [155] [156].They have been used to improve extraction of thermodynamic quantities.Source: §2 · p. 19
  • PINNs add bulk-equation residuals to data-matching losses, while a complementary flavor-brane approach minimizes the regularized DBI action directly [158] [159] [160] [161] [162].The former enforces dynamical consistency; the latter imposes the extremization principle at the action level.Source: §2 · p. 19
  • Transformers target geometric information in nonlocal quantum data, while KAN-based parametrizations may yield more interpretable functional relations and approximate analytic bulk functions [163] [164] [165].The transformer application is motivated by its ability to learn long-range correlations.Source: §2 · p. 19

3. Boundary observables used as training data

Holographic reconstruction now draws on diverse boundary observables to infer bulk models, from hadron spectra to thermodynamics and phase structure. The review highlights joint constraints and uncertainty-aware inference as steps toward broader data-driven phenomenology.

3. Boundary observables used as training data

  • Boundary inputs span thermodynamic quantities, real-time response, nonlocal probes, and hadronic structure functions, each constraining different aspects of the holographic model.Thermodynamics constrains equilibrium backgrounds; response data probe near-horizon dynamics and couplings; nonlocal observables probe extended geometry and infrared confinement.Source: §3 · pp. 19–20
  • A physics-guided network for proton F2 embeds the AdS5 Dirac equation and holographic string-diffusion kernel, extending applications toward deep-inelastic scattering [174].The application addresses the transition between resonance-dominated and diffractive regimes.Source: §3 · p. 20

C. Vacuum Structure and Hadron Spectroscopy

  • Meson spectra have been used to reconstruct effective holographic backgrounds and dilaton potentials, reducing reliance on hand-tuned soft-wall profiles [175–179].Inputs include meson trajectories, broader unflavoured spectra, chiral condensates, and heavy-quarkonium spectra.Source: C. Vacuum Structure and Hadron… · p. 20
  • An ML-assisted Einstein-dilaton model was constrained simultaneously by lattice thermodynamics and the pure Yang-Mills scalar glueball spectrum, suggesting one background can describe finite-temperature and zero-temperature observables [180].The reconstruction workflow uses glueball data and equation-of-state constraints before comparing predicted entropy density with lattice results.Source: C. Vacuum Structure and Hadron… · p. 20

D. QCD Thermodynamics and the Phase Diagram

  • At zero baryon chemical potential, flavor and EMD holographic models use lattice thermodynamic data to calibrate equations of state and reconstruct metric or coupling functions [181] [182] [183] [184] [185] [186].Some constructions also address chiral observables and quark-mass dependence.Source: D. QCD Thermodynamics and the Phase… · p. 21
  • After calibration at µB = 0, ML-assisted models explore possible critical-endpoint locations at finite baryon chemical potential, though numerical results vary with model assumptions [147, 184–186].Neural ODE reconstruction with magnetic-field boundary conditions has also produced lattice-agreeing results and indications of richer critical behavior, including possible multiple endpoints in some regimes [187].Source: D. QCD Thermodynamics and the Phase… · p. 21, Figure 14 · p. 21
  • Bayesian holographic approaches infer posterior distributions for parameters and observables, enabling credible intervals for the equation of state, phase boundary, or critical-endpoint location [188] [189].The review identifies uncertainty-controlled prediction as an increasingly supported outcome of ML calibration to lattice data.Source: D. QCD Thermodynamics and the Phase… · p. 21

E. Heavy Quarkonium in the Quark-Gluon Plasma

Holographic studies use calibrated models to examine quarkonium dissociation and to predict plasma transport properties from reconstructed backgrounds. Together, these applications extend data-driven holography from equilibrium thermodynamics toward hard-probe dynamics, with uncertainty and predictive validation still central challenges.

E. Heavy Quarkonium in the Quark-Gluon Plasma

  • Bayesian holographic calibration to lattice-QCD thermodynamics supports uncertainty-aware predictions of heavy-quarkonium observables at finite temperature and baryon chemical potential.The studied quantities include interquark distance, potential energy, entropy, binding energy, and internal energy.Source: E. Heavy Quarkonium in the Quark-Gluon… · p. 22
  • Across potential and spectral-function studies, excited quarkonium states are more fragile than ground states, peaks weaken as the medium heats or densifies, and anisotropy can enhance dissociation.The sequential melting pattern is qualitatively consistent with sequential suppression.Source: E. Heavy Quarkonium in the Quark-Gluon… · p. 22

F. Transport Properties of the Quark-Gluon Plasma

  • After a holographic background is calibrated to thermodynamic data, probe-string configurations and bulk fluctuation equations yield transport and hard-probe observables.KAN-based and Bayesian studies compute drag force, jet-quenching parameter, heavy-quark diffusion, and viscosities; some coefficients depend centrally on near-horizon data, while hard-probe observables can depend on the full radial background.Source: F. Transport Properties of the… · p. 22
  • Bayesian transport calculations report 68% and 95% credible intervals, enabling more meaningful comparison with lattice estimates and phenomenological constraints, including ALICE data.The analysis propagates model uncertainty, although uncertainties can remain substantial.Source: F. Transport Properties of the… · p. 22
  • Transport studies use backgrounds trained on equilibrium observables as holographic simulators for real-time properties that are difficult to measure directly or calculate conventionally.This proposed predictive role remains subject to the broader challenge of establishing out-of-training-regime predictivity.Source: F. Transport Properties of the… · p. 22, G. Short Summary and Outlook · p. 22

G. Short Summary and Outlook

  • ML-assisted holographic QCD now spans vacuum spectroscopy, finite-temperature and finite-density thermodynamics, proton structure, heavy-quarkonium dynamics, and plasma transport.The program formulates model building as an inverse problem, but reconstructed bulk structures still need to be unique, interpretable, and predictive beyond training; richer data, stronger priors, transparent architectures, and systematic uncertainty quantification are identified as future needs.Source: G. Short Summary and Outlook · pp. 22–23

VI. NEUTRON STAR

Neutron-star EoS inference is an inverse problem because observations constrain the EoS only indirectly through stellar structure and related models. ML offers flexible representations and inference methods, but present data leave high-density EoS degeneracies that must be reported alongside physical constraints and modeling assumptions.

VI. NEUTRON STAR

  • Neutron-star observations constrain the dense-matter EoS indirectly through stellar observables and models, so inference must respect stability, causality, and high-density behavior.The relevant observables include masses, radii, tidal deformabilities, moments of inertia, cooling behavior, and gravitational-wave signals; the forward map includes TOV equations and, for mergers, dynamical simulations.Source: §VI · p. 23

A. Neural EoS Reconstruction

  • Structured variational autoencoders separate supervised stellar quantities such as Mmax and R1.4 from latent variables that encode residual EoS freedom, then generate candidates for physical and astrophysical checks.Conditional variational autoencoders also reconstruct pressure curves from mass-radius observations after training on physically filtered EoS samples.Source: A. Neural EoS Reconstruction · p. 23, Figure 15 · p. 23
  • Neural EoS representations coupled to differentiable TOV solvers back-propagate observational residuals to the EoS; studies applied this approach to mock data and accumulated mass-radius observations.Automatic differentiation also provides a route to investigating possible first-order phase transitions.Source: A. Neural EoS Reconstruction · p. 23, Figure 16 · p. 24
  • Neural simulation-based inference and normalizing flows support posterior inference that can accommodate non-Gaussian, correlated constraints on masses, radii, and tidal deformabilities.Other studies include realistic observational uncertainties or combine simulation-based inference with universal relations to improve accuracy and reduce dimensional burden.Source: A. Neural EoS Reconstruction · p. 23

B. Physical constraints

  • Present observations do not determine a unique high-density EoS, so ML can expose and quantify degeneracy but cannot remove it; inference must respect density-dependent physical constraints.Low-density behavior should agree with nuclear theory, high-density behavior should respect causality, stability, and perturbative QCD, and intermediate-density changes may indicate new degrees of freedom or phase transitions.Source: B. Physical constraints · p. 24, A. Neural EoS Reconstruction · p. 24

C. Connections to HICs

  • Heavy-ion and neutron-star data probe different temperature and isospin regimes, so their constraints can be complementary but cannot be merged by directly identifying collision matter with the cold stellar EoS.Joint inference with heavy-ion, multimessenger, microscopic-theory, and other constraints is a longer-term direction for representing functional uncertainty across forward maps.Source: C. Connections to HICs · p. 24

D. Gravitational-wave inference and multimessenger workflows

  • Dingo-BNS combines physics-informed compression, neural inference, and importance weighting for rapid binary-neutron-star parameter estimation, supporting merger localization and timely electromagnetic follow-up.Importance weighting corrects an approximate neural posterior only subject to proposal support and adequate effective sample size; a cold beta-equilibrated EoS alone also lacks the additional inputs required for merger dynamics.Source: D. Gravitational-wave inference and… · pp. 24–25

VII. AI FOR LATTICE QFT: FROM RECONSTRUCTION TO DISCOVERY

ML in lattice QFT addresses reconstruction, field learning, and sampling problems while increasingly seeking to infer theories from data. Its usefulness in precision applications depends on preserving physical structures and demonstrating controlled systematics, exactness, and reliable uncertainty estimates.

VII. AI FOR LATTICE QFT: FROM RECONSTRUCTION TO DISCOVERY

  • Lattice-QFT ML spans reconstruction of physical information, phase and correlation learning, generative sampling, sign-problem strategies, and emerging attempts to infer operators and effective theories from data.The review organizes this progression as reconstruction and learning, then generation, then theory discovery.Source: §VII · p. 25

A. Inverse reconstruction from Euclidean data

  • Neural parameterizations optimized through the Euclidean-correlator integral relation offer flexible spectral reconstruction, but they do not remove analytic continuation’s ill-posedness.Positivity, smoothness, asymptotic behavior, sum rules, and correlator uncertainty still require explicit treatment.Source: A. Inverse reconstruction from… · p. 25

B. Learning phases, fields, and correlations

  • Gauge-equivariant networks and flows build gauge symmetry into their architectures, while controlled scalar-field studies test whether models learn genuine correlations rather than small-dataset artifacts.Gauge covariance or invariance is not automatic in generic neural networks, and data augmentation alone is less reliable than incorporating symmetry.Source: B. Learning phases, fields, and… · p. 25

C. Generative models for lattice QFT, and sign-problems

  • Flow-based samplers, including stochastic normalizing flows, target reduced sampling cost and autocorrelation while preserving the target distribution or enabling controlled reweighting.Applications include four-dimensional SU(3) ensembles, topology sampling with open boundaries, and flows between lattice resolutions.Source: C. Generative models for lattice QFT,… · p. 25
  • Diffusion models learn stochastic evolution from a simple prior toward interacting field distributions, and coupling-conditioned generators aim to span lattice-gauge ensembles.Parameter-scan use depends on generalization across couplings while preserving observables, autocorrelations, and topology; the cited gauge-theory work had not fully succeeded on topological sectors in the two-dimensional U(1) case.Source: C. Generative models for lattice QFT,… · pp. 25–26, Figure 18 · p. 26
  • The Stochastic Path Sampler learns nonlocal configuration-space paths through trainable forward and backward stochastic kernels, but remains a proposal mechanism without exact correction or controlled estimation.Gauge-theory extensions still need to demonstrate compatibility, topology sampling, acceptance behavior, autocorrelation reduction, and continuum scaling.Source: C. Generative models for lattice QFT,… · p. 26
  • Physics-informed kernels define field transport through prescribed intermediate actions, while complex extensions of these transformations deform integration contours while preserving the integration weight.Sign-problem methods also include changing the integration manifold, learning phase-quenched corrections, and improving proposals; demonstrations cited include zero-dimensional complex-weight theories and the real-time quantum harmonic oscillator.Source: C. Generative models for lattice QFT,… · p. 26
  • Sampler validation must use physical observables and lattice benchmarks, including topological tunneling, continuum scaling, finite-volume behavior, and chiral properties.Precision use also requires exactness or controlled residual bias, systematic uncertainty, symmetry preservation, and reproducible error estimates.Source: C. Generative models for lattice QFT,… · pp. 26–27

D. Learning Quantum Field Theories Across Scales

The review describes a shift toward physics-integrated ML, including learning effective QFTs across scales and agentic scientific workflows. It surveys examples from foundation-style models, LQCD, and heavy-ion hydrodynamics.

D. Learning Quantum Field Theories Across Scales

  • Using tunnel-coupled quantum gases, Hamiltonian learning distinguished an interacting sine-Gordon description from a free quadratic theory and extracted effective parameters.Measurements at finite spatial resolution are converted to field correlations, which inform the effective Hamiltonian's operator content and couplings.Source: D. Learning Quantum Field Theories… · p. 27, Figure 19 · p. 27
  • Learning effective Hamiltonians at different resolutions connects data-driven operator and coupling estimates to renormalization-group flows.The resulting flow can reveal operators that are relevant, irrelevant, or approximately scale invariant over a given range.Source: D. Learning Quantum Field Theories… · p. 27
  • For lattice QFT, the proposed research program learns effective operators and their scale dependence from lattice configurations or combined lattice and experimental data.The implementation would need gauge invariance, locality, global symmetries, conservation laws, and the appropriate continuum limit; it could complement conventional calculations with a route to coarse-grained descriptions.Source: D. Learning Quantum Field Theories… · p. 27

A. Foundation models for HENP

  • HENP foundation models are envisioned as domain-specific pretrained models adapted to downstream tasks, with physics constraints and data provenance treated as essential [248] [249] [41] [250].Examples span particle clouds and events, lattice configurations, hydrodynamic fields, correlators, and equation-of-state ensembles; without physics constraints and provenance, models may interpolate simulation artifacts.Source: A. Foundation models for HENP · p. 28

B. LLM-based agents and autonomous scientific workflows

  • Agentic systems span detector design, end-to-end data analysis, collider phenomenology, and nuclear-science simulations, while BESIII's Dr. Sai system reports over 90% workflow success [251] [252] [253] [254] [255] [256] [257] [258].The review frames trust as established through audit and notes that safety-critical hardware interaction requires uncertainty quantification, hallucination mitigation, and human approval.Source: B. LLM-based agents and autonomous… · p. 28
  • A proposed agentic Bayesian campaign logs its actions while researchers retain the final scientific decision.The workflow covers simulation design, checks of conservation and stability, emulator training, calibration diagnostics, posterior prediction, and reporting failures and suggested simulations.Source: B. LLM-based agents and autonomous… · p. 28
  • CLVisc Agent uses a scan–compose–validate workflow to support hydrodynamic studies from source-code parsing and parameter handling through simulations and physical interpretation [260].Its reported applications include identifying the high-temperature branch of η/s as dominant for viscous suppression in Pb+Pb simulations and grouping four 16O structure models using darea and β2 diagnostics.Source: B. LLM-based agents and autonomous… · pp. 28–29
  • LQCDMaster reproduced expert implementations to machine precision in 63 of 70 tasks and reduced implementation time from hours to minutes [261].It also enabled computations such as light-cone distribution amplitudes and multibaryon spectra.Source: B. LLM-based agents and autonomous… · p. 29

C. AI for High-Energy Nuclear Physics: From Symbolic Effective Laws to Scalable Many-Body Sampling

This section surveys AI for symbolic law discovery and high-dimensional nuclear sampling, then discusses exploratory quantum ML and physics-oriented benchmarks. The approaches range from recovering known laws to proposing standards for validation and comparison.

C. AI for High-Energy Nuclear Physics: From Symbolic Effective Laws to Scalable Many-Body Sampling

  • AI-Newton rediscovered Newton's second law, energy conservation, and universal gravitation across 46 noisy Newtonian-mechanics experiments, averaging approximately 90 physical concepts and 50 general laws [262].Its symbolic-regression system uses a symbols–concepts–laws knowledge base and plausible reasoning to revise laws when they fail in new scenarios.Source: C. AI for High-Energy Nuclear Physics:… · p. 29
  • The Schrödinger Generator demonstrated stable, scalable integration and sampling for nuclear many-body states in dimensions exceeding 600, reproducing short-range nucleon correlations in finite nuclei [263].It combines an adaptive map that learns marginal structure with a normalizing flow for non-factorizable correlations, followed by resampling that guarantees unbiased samples even when the learned transformation is imperfect.Source: C. AI for High-Energy Nuclear Physics:… · p. 30, Figure 21 · p. 31

D. Quantum machine learning

  • The 1P1Q scheme maps each particle's kinematics to a qubit; its QAE outperformed classical autoencoders for signal–QCD-background discrimination, while its VQC achieved competitive performance with greatly reduced complexity.Tests using 2016 CMS collision data are reported as robust; the method's general limitations include hardware noise, data-loading costs, circuit depth, and difficulty demonstrating quantum advantage.Source: D. Quantum machine learning · p. 30, Figure 22 · p. 31

E. Benchmarking and community infrastructure

  • The review proposes physics-oriented benchmarks across lattice QFT, heavy-ion, neutron-star, and functional, EFT, and holographic tasks, with metrics tailored to each domain.Metrics include observable bias and autocorrelation for lattice tasks, calibration and generator-shift performance for heavy-ion tasks, and posterior coverage and physical-constraint satisfaction for neutron-star inference.Source: E. Benchmarking and community… · p. 30
  • Proposed negative controls test whether models generalize beyond training signals, withheld observables, or familiar equation-of-state families.Examples include criticality classifiers tested without a critical signal and neutron-star inference tested on equation-of-state families absent from training.Source: E. Benchmarking and community… · p. 30
  • Open benchmark data should record domain-specific provenance and assumptions, because missing metadata makes comparisons difficult to interpret.Specified records include generator settings and observable definitions for heavy-ion data, lattice action and algorithm history, and distinctions among neutron-star prior samples, posterior samples, likelihood summaries, and physical filters.Source: E. Benchmarking and community… · p. 31

IX. CONCLUSIONS AND OUTLOOK

ML in HENP is moving from pattern recognition toward integrated scientific workflows that combine learned representations, uncertainty-aware inference, and physics-constrained simulation. The outlook is to connect faster forward models with inference across QCD regimes while maintaining independent validation and human oversight.

IX. CONCLUSIONS AND OUTLOOK

  • ML workflows combine learned representations, probabilistic uncertainty propagation, and physics-respecting generative models to address high-dimensional data and expensive calculations.Generative models should be validated against observables and inference, not visual plausibility alone.Source: §IX · p. 31
  • A closed QCD inference loop would pair faster, bias-quantified generation with Bayesian extraction of posteriors and cross-regime consistency tests.The proposed loop connects lattice, hydrodynamic, particle-level, and equation-of-state outputs with collider and astrophysical data.Source: §IX · pp. 31–32
  • Reusing one simulator family for training and validation can amplify shared biases, so independent holdouts, discrepancy tests, provenance, and human review remain necessary.Benchmarks alone are insufficient; the text also calls for negative controls and periodic checks against first-principles constraints and new data.Source: §IX · p. 32
  • Physics constraints, built-in uncertainty quantification, reproducibility, and community benchmarks are recommended to support trustworthy comparisons across common tasks.The recommendations include gauge equivariance, conservation laws, thermodynamic stability, causality, open datasets, and recording negative results.Source: §IX · p. 32
  • Future work is framed by whether AI can lower high-fidelity calculation costs, extract more information from data, and connect historically separate QCD sectors.These questions span lattice samplers, hydrodynamic emulators, differentiable solvers, heavy-ion learning, neutron-star inference, and unified QCD inference.Source: §IX · p. 32
  • AI cannot by itself solve the full-QCD sign problem, determine the critical point, or infer neutron-star core composition without assumptions; forthcoming data should be handled under unchanged inference standards.The review also anticipates expanded collider, gravitational-wave, X-ray, and multimessenger data streams.Source: §IX · p. 32

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