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At least 73 records · Page 4

Supercharging simulation-based inference for Bayesian optimal experimental design

Abstract Bayesian optimal experimental design (BOED) seeks to maximize the expected information gain (EIG) of experiments. This requires a likelihood estimate, which in many settings is intractable. Simulation-based inference (SBI) provides powerful tools for this regime. However, existing work explicitly connecting SBI and BOED is restricted to a single contrastive EIG bound. We show that the EIG admits multiple formulations which can directly leverage modern SBI density estimators, encompassing neural posterior, likelihood, and ratio estimation. Building on this perspective, we define a novel EIG estimator using neural likelihood estimation. Further, we identify optimization as a key bottleneck of gradient based EIG maximization and show that a simple multi-start parallel gradient ascent procedure can substantially improve reliability and performance. With these innovations, our SBI-based BOED methods are able to match or outperform by up to 22% existing state-of-the-art approaches across standard BOED benchmarks.

97 MATHEMATICS AND COMPUTING↗

Computational Imaging for Intelligence in Highly Scattering Aerosols (Final Report)

Natural and man-made degraded visual environments pose major threats to national security. The random scattering and absorption of light by tiny particles suspended in the air reduces situational awareness and causes unacceptable down-time for critical systems and operations. To improve the situation, we have developed several approaches to interpret the information contained within scattered light to enhance sensing and imaging in scattering media. These approaches were tested at the Sandia National Laboratory Fog Chamber facility and with tabletop fog chambers. Computationally efficient light transport models were developed and leveraged for computational sensing. The models are based on a weak angular dependence approximation to the Boltzmann or radiative transfer equation that appears to be applicable in both the moderate and highly scattering regimes. After the new model was experimentally validated, statistical approaches for detection, localization, and imaging of objects hidden in fog were developed and demonstrated. A binary hypothesis test and the Neyman-Pearson lemma provided the highest theoretically possible probability of detection for a specified false alarm rate and signal-to-noise ratio. Maximum likelihood estimation allowed estimation of the fog optical properties as well as the position, size, and reflection coefficient of an object in fog. A computational dehazing approach was implemented to reduce the effects of scatter on images, making object features more readily discernible. We have developed, characterized, and deployed a new Tabletop Fog Chamber capable of repeatably generating multiple unique fog-analogues for optical testing in degraded visual environments. We characterized this chamber using both optical and microphysical techniques. In doing so we have explored the ability of droplet nucleation theory to describe the aerosols generated within the chamber, as well as Mie scattering theory to describe the attenuation of light by said aerosols, and correlated the aerosol microphysics to optical properties such as transmission and meteorological optical range (MOR). This chamber has proved highly valuable and has supported multiple efforts inclusive to and exclusive of this LDRD project to test optics in degraded visual environments. Circularly polarized light has been found to maintain its polarization state better than linearly polarized light when propagating through fog. This was demonstrated experimentally in both the visible and short-wave infrared (SWIR) by imaging targets made of different commercially available retroreflective films. It was found that active circularly polarized imaging can increase contrast and range compared to linearly polarized imaging. We have completed an initial investigation of the capability for machine learning methods to reduce the effects of light scattering when imaging through fog. Previously acquired experimental long-wave images were used to train an autoencoder denoising architecture. Overfitting was found to be a problem because of lack of variability in the object type in this data set. The lessons learned were used to collect a well labeled dataset with much more variability using the Tabletop Fog Chamber that will be available for future studies. We have developed several new sensing methods using speckle intensity correlations. First, the ability to image moving objects in fog was shown, establishing that our unique speckle imaging method can be implemented in dynamic scattering media. Second, the speckle decorrelation over time was found to be sensitive to fog composition, implying extensions to fog characterization. Third, the ability to distinguish macroscopically identical objects on a far-subwavelength scale was demonstrated, suggesting numerous applications ranging from nanoscale defect detection to security. Fourth, we have shown the capability to simultaneously image and localize hidden objects, allowing the speckle imaging method to be effective without prior object positional information. Finally, an interferometric effect was presented that illustrates a new approach for analyzing speckle intensity correlations that may lead to more effective ways to localize and image moving objects. All of these results represent significant developments that challenge the limits of the application of speckle imaging and open important application spaces. A theory was developed and simulations were performed to assess the potential transverse resolution benefit of relative motion in structured illumination for radar systems. Results for a simplified radar system model indicate that significant resolution benefits are possible using data from scanning a structured beam over the target, with the use of appropriate signal processing.

58 GEOSCIENCES↗

Estimating Large Global Significances with a New Monte Carlo Extrapolation Method

In particle physics, it is needed to evaluate the possibility that excesses of events in mass spectra are due to statistical fluctuations as quantified by the standards of local and global significances. Without prior knowledge of a particle’s mass, it is especially critical to estimate its global significance. The usual approach is to count the number of times a significance limit is exceeded in a collection of simulated Monte Carlo (MC) “toy experiments”. To demonstrate this conventional method for global significance, we performed simulation studies according to a recent Compact Muon Solenoid (CMS) result to show its effectiveness. However, this counting method is not practical for computing large global significances. To address this problem, we developed a new “extrapolation” method to evaluate the global significance. We compared the global significance estimated by our new method with that of the conventional approach, and verified its feasibility and effectiveness. This method is also applicable for cases where only small toy MC samples are available. In this approach, the significance is calculated based on p-values, assuming symmetrical Gaussian distributions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Pronghorn Porous Media Model Validation with Pressure Drop Measurements

The verification and validation (V&V) of Pronghorn is imperative to assert its accuracy when predicting the fluid velocity, temperature, and pressure in high temperature gas-cooled reactors. Pronghorn is a coarse-mesh, intermediate-fidelity, and multidimensional thermal-hydraulics (TH) code developed by the Idaho National Laboratory (INL). New pebble bed experiments are used to observe the details of the fluid motion and pressure drop in the porous bed under the reactor normal operation. This paper focuses on the validation of the Pronghorn compressible and incompressible Navier-Stokes equations using the pressure drop measurements performed at the engineering-scale pebble bed facility at the Texas A&M university (TAMU). Various pressure drop correlations and porosity functions are implemented in both Pronghorn and STAR-CCM+ to compare the pressure drop due to the combined viscous and inertial resistances in the porous bed. The correlations accounting for the near-wall effect are also utilized to observe if the pressure drop estimates can be improved. Pronghorn porous media models predict the pressure drop well relative to the STAR-CCM+ simulation results and 1D correlations, and both the finite element method (FEM) and finite volume method (FVM) perform accurately. Pronghorn models are also validated with the experimental measurements given the different Reynolds number ranges and specific aspect ratios. The likelihood of the statistical significance between the pressure drop measurements and specific correlations or simulations is low provided that the overlap of their confidence intervals is more than the half of a single arm. Several validation metrics are reasonable in regard to the similar studies from other literature. The precise average pebble bed porosity estimation has much impact on the pressure drop, and the Foumeny and Montillet (dense packing) models carry out the accurate pressure drop prediction by considering the near-wall effect.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Strong Lensing Cosmology with Population-level Calibrated Neural Ratio Estimation

Strong gravitational lensing contains key information about cosmic acceleration. Modern and next-generation galaxy imaging surveys are expected to provide high-quality data on $\mathcal{O}(10^5)$ galaxy-galaxy lensing systems. The plethora and complexity of the data are likely to present computational challenges for parameter inference methods for fitting high-dimensional likelihoods, which are often analytically intractable. Neural Ratio Estimation (NRE) efficiently computes individual likelihood ratios that can be combined into population-level posteriors. We use simulations to study the capacity of NRE to jointly predict the dark energy equation-of-state parameter $w$ and the total matter density $Ω_{m}$ from lensing images and companion spectroscopic information. We also introduce a post hoc posterior coverage calibration procedure that mitigates the model overconfidence that is typically found in neural density estimation applications. Our experiments show that the errors on both parameters decrease with increasing inference population sizes. In particular, for 100 lenses in a standard $Λ$CDM Universe, our calibrated NRE model achieves median fractional uncertainty of $22.8\%$ in $w$ and $2.9\%$ in $Ω_{m}$. This proof of concept demonstrates a potentially scalable approach for efficient cosmological parameter inference with large populations of galaxy-scale lenses observed in future surveys.

Jarugula, Sreevani [Fermilab] (ORCID:0000000253867↗

Population-level Dark Energy Constraints from Strong Gravitational Lensing using Simulation-Based Inference

In this work, we present a scalable approach for inferring the dark energy equation-of-state parameter ($w$) from a population of strong gravitational lens images using Simulation-Based Inference (SBI). Strong gravitational lensing offers crucial insights into cosmology, but traditional Monte Carlo methods for cosmological inference are computationally prohibitive and inadequate for processing the thousands of lenses anticipated from future cosmic surveys. New tools for inference, such as SBI using Neural Ratio Estimation (NRE), address this challenge effectively. By training a machine learning model on simulated data of strong lenses, we can learn the likelihood-to-evidence ratio for robust inference. Our scalable approach enables more constrained population-level inference of $w$ compared to individual lens analysis, constraining $w$ to within $1\sigma$.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Population-level Dark Energy Constraints from Strong Gravitational Lensing using Simulation-Based Inference

In this work, we present a scalable approach for inferring the dark energy equation-of-state parameter ($w$) from a population of strong gravitational lens images using Simulation-Based Inference (SBI). Strong gravitational lensing offers crucial insights into cosmology, but traditional Monte Carlo methods for cosmological inference are computationally prohibitive and inadequate for processing the thousands of lenses anticipated from future cosmic surveys. New tools for inference, such as SBI using Neural Ratio Estimation (NRE), address this challenge effectively. By training a machine learning model on simulated data of strong lenses, we can learn the likelihood-to-evidence ratio for robust inference. Our scalable approach enables more constrained population-level inference of $w$ compared to individual lens analysis, constraining $w$ to within $1\sigma$. Our model can be used to provide cosmological constraints from forthcoming strong lens surveys, such as the 4MOST Strong Lensing Spectroscopic Legacy Survey (4SLSLS), which is expected to observe 10,000 strong lenses.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Population-level Dark Energy Constraints from Strong Gravitational Lensing using Simulation-Based Inference

In this work, we present a scalable approach for inferring the dark energy equation-of-state parameter ($w$) from a population of strong gravitational lens images using Simulation-Based Inference (SBI). Strong gravitational lensing offers crucial insights into cosmology, but traditional Monte Carlo methods for cosmological inference are computationally prohibitive and inadequate for processing the thousands of lenses anticipated from future cosmic surveys. New tools for inference, such as SBI using Neural Ratio Estimation (NRE), address this challenge effectively. By training a machine learning model on simulated data of strong lenses, we can learn the likelihood-to-evidence ratio for robust inference. Our scalable approach enables more constrained population-level inference of $w$ compared to individual lens analysis, constraining $w$ to within 1$\sigma$. Our model can be used to provide cosmological constraints from forthcoming strong lens surveys, such as the 4MOST Strong Lensing Spectroscopic Legacy Survey (4SLSLS), which is expected to observe 10,000 strong lenses.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Exploring the transition from continuous turbulence fluctuations to bursting ELMs in high SOL density regimes

BOUT++ turbulence simulations of the DIII-D reveal that the density profile between the separatrix and pedestal plays a crucial role in the dynamics of edge localized modes (ELMs) and edge plasma turbulent transport. Nonlinear simulations demonstrate that small ELMs in the DIII-D hybrid scenario under high SOL density conditions are predominantly driven by local ballooning modes near the separatrix, stabilizing global instabilities while enhancing localized pressure fluctuations. A key control parameters for ELM dynamics is the separatrix-to-pedestal density ratio, n e,sep /n e,ped . A high ratio indicates a shallow gradient, favoring small ELMs, while a lower ratio signals a steep gradient, which increases the likelihood of large ELMs. Comprehensive parameter scans, including n e,sep /n e,ped , density gradient profiles near the separatrix, and resistivity, reveal the critical role of these parameters in shaping transitions between turbulence-driven transport and ELM bursting. The scans demonstrate that in high SOL density regimes, small ELMs can result from either global resistive MHD instabilities or local ballooning modes near the separatrix, depending on the steepness of the separatrix density gradient. These findings also highlight the transition from continuous turbulence to small ELMs. The post-crash peak in pressure fluctuations, δP rms serves as a critical metric for identifying transition from continuous turbulence fluctuations to ELM bursting. Larger δP rms values correlate with ELM bursts driven by local or global instabilities, whereas smaller values indicate turbulence-dominated transport. Drift-Alfvén and resistive ballooning turbulence enhance the entrainment of fluctuations from the pedestal to the SOL, contributing to the complex interplay of dynamics in this regime. These findings emphasize the importance of separatrix density shaping and pedestal gradient control for optimizing ELM behavior in ITER and future fusion devices.

Li, Nami [Lawrence Livermore National Laboratory (↗

Simons Observatory: Constraining inflationary gravitational waves with multitracer B-mode delensing

We introduce and validate a delensing framework for the Simons Observatory (SO), which will be used to improve constraints on inflationary gravitational waves by reducing the lensing noise in measurements of the B modes in CMB polarization. SO will initially observe CMB by using three small aperture telescopes and one large-aperture telescope. While polarization maps from small-aperture telescopes will be used to constrain inflationary gravitational waves, the internal CMB lensing maps used to delens will be reconstructed from data from the large-aperture telescope. Since lensing maps obtained from the SO data will be noise dominated on subdegree scales, the SO lensing framework constructs a template for lensing-induced B modes by combining internal CMB lensing maps with maps of the cosmic infrared background from Planck as well as galaxy density maps from the LSST survey. We construct a likelihood for constraining the tensor-to-scalar ratio r that contains auto and cross spectra between observed B modes and the lensing B-mode template. We test our delensing analysis pipeline on map-based simulations containing survey nonidealities, but that, for this initial exploration, does not include contamination from Galactic and extragalactic foregrounds. We find that the SO survey masking and inhomogeneous and atmospheric noise have very little impact on the delensing performance, and the r constraint becomes σ(r)≈0.0015 which is close to that obtained from the idealized forecasts in the absence of the Galactic foreground and is nearly a factor of 2 tighter than without delensing. We also find that uncertainties in the external large-scale structure tracers used in our multitracer delensing pipeline lead to bias much smaller than the 1σ statistical uncertainties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Evidence against the Efimov effect in 12 C from spectroscopy and astrophysics

Background: The Efimov effect is a universal phenomenon in physics whereby three-body systems are stabilized via the interaction of an unbound two-body subsystems. A hypothetical state in 12 C at 7.458-MeV excitation energy, comprising a loose structure of three α particles in mutual two-body resonance, has been suggested in the literature to correspond to an Efimov state in nuclear physics. The existence of such a state has not been demonstrated experimentally. Purpose: Using a combination of γ spectroscopy, charged-particle spectroscopy, and astrophysical rate calculations allowing for strict limits on the existence of such a state to been established here. Method: Using the combined data sets from two recent experiments, one with the TexAT (Texas Active Target) TPC (Time Projection Chamber) to measure α decay and the other with Gammasphere to measure γ decay of states in 12 C populated by 12 N and 12 B β decay, respectively, we achieve high sensitivity to states in close proximity to the α threshold in 12 C. Results: No evidence of a state at 7.458 MeV is seen in either data set. Using a likelihood method, the 95% confidence limit γ -decay branching ratio is determined as a function of the β-decay feeding strength relative to the Hoyle state. In parallel, calculations of the 3α reaction rate show the inclusion of the Efimov corresponds to a large increase in the reaction rate around 5 × 10 7 K. Conclusion: From decay spectroscopy—at the 95% confidence limit, the Efimov state cannot exist at 7.458 MeV with any γ-decay branching ratio unless the β strength is less than 0.7% of the Hoyle state. This limit is evaluated for a range of different excitation energies and the results are not favorable for existence of the hypothetical Efimov state in 12 C . Furthermore, the 3α reaction rate with the inclusion of a state between 7.43 and 7.53 MeV exceeds the rate required for stars to undergo the red giant phase.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Photoproduction of two charged pions off protons in the resonance region

Photoproduction of charged pions pairs off protons is studied within the invariant masses of the final state hadrons from 1.6 to 2.4 GeV at the Thomas Jefferson National Accelerator Facility with the CLAS detector. The total and differential cross sections and spin-density matrix elements are presented for the isobars pρ 0 (770), Δ(1232) ++ π − , and Δ(1232) 0 π + . The data are included in the Bonn-Gatchina coupled-channel analysis and provide the information necessary to determine the branching fractions of Nρ(770) decays for most known N* and Δ* resonances. For the first time, the Nρ branching ratios are obtained here from an event-based likelihood to γp → π + π − p.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Effect of likelihood misspecification in Gaussian process-driven autonomous experimentation

In recent years, several groups have designed Autonomous Experiment (AE) models with the aim of using them as an alternative method for neutron scattering scanning. In an AE, Gaussian processes (GPs) are most frequently used due to their interpretability, their non-parametric nature, their universal approximation, and their closed-form predictive distribution. GPs have two key components, namely, the model for the likelihood of a neutron count knowing the underlying dynamic structure factor and the acquisition function. In this paper, we investigate the impact, on the quality of an AE, of the likelihood and acquisition function choices, in energy scans and (Q, ω) ones, with respect to the signal-over-noise ratio. While we hypothesized that the quality of GP predictions would decrease when the normal to Poisson likelihood approximation breaks down at low count rates, we found that the use of the correct Poisson likelihood does not improve the quality of the data collected, as well as yields very poor results in (Q, ω) scans at low count rates. In fact, the best results are obtained with a combination of normal likelihood, including the observation noise, and the change in variance acquisition function. In addition, we find that the performance, or quality of the predictive distribution, is a misleading measure of efficiency, that is, of the quality of the data collected.

Perryman, David Elliott [Inst. Laue-Langevin (ILL)↗

Dark Energy Survey Year 3 results: Exploiting small-scale information with lensing shear ratios

Using the first three years of data from the Dark Energy Survey (DES), we use ratios of small-scale galaxy-galaxy lensing measurements around the same lens sample to constrain source redshift uncertainties, intrinsic alignments and other systematics or nuisance parameters of our model. Instead of using a simple geometric approach for the ratios as has been done in the past, we use the full modeling of the galaxy-galaxy lensing measurements, including the corresponding integration over the power spectrum and the contributions from intrinsic alignments and lens magnification. We perform extensive testing of the small-scale shear-ratio (SR) modeling by studying the impact of different effects such as the inclusion of baryonic physics, nonlinear biasing, halo occupation distribution descriptions and lens magnification, among others, and using realistic N -body simulations of the DES data. We validate the robustness of our constraints in the data by using two independent lens samples with different galaxy properties, and by deriving constraints using the corresponding large-scale ratios for which the modeling is simpler. The results applied to the DES Y3 data demonstrate how the ratios provide significant improvements in constraining power for several nuisance parameters in our model, especially on source redshift calibration and intrinsic alignments. For source redshifts, SR improves the constraints from the prior by up to 38% in some redshift bins. Such improvements, and especially the constraints it provides on intrinsic alignments, translate to tighter cosmological constraints when shear ratios are combined with cosmic shear and other 2pt functions. In particular, for the DES Y3 data, SR improves S 8 constraints from cosmic shear by up to 31%, and for the full combination of probes ( 3 × 2 pt ) by up to 10%. The shear ratios presented in this work are used as an additional likelihood for cosmic shear, 2 × 2 pt and the full 3 × 2 pt in the fiducial DES Y3 cosmological analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

Dark Energy Survey Year 3 results: A 2.7% measurement of baryon acoustic oscillation distance scale at redshift 0.835

We present angular diameter measurements obtained by measuring the position of baryon acoustic oscillations (BAO) in an optimized sample of galaxies from the first three years of Dark Energy Survey data (DES Y3). The sample consists of 7 million galaxies distributed over a footprint of 4100 deg 2 with 0.6 < z photo < 1.1 and a typical redshift uncertainty of 0.03 ( 1 + z ) . The sample selection is the same as in the BAO measurement with the first year of DES data, but the analysis presented here uses three times the area, extends to higher redshift, and makes a number of improvements, including a fully analytical BAO template, the use of covariances from both theory and simulations, and an extensive preunblinding protocol. We used two different statistics; angular correlation function and power spectrum, and validate our pipeline with an ensemble of over 1500 realistic simulations. Both statistics yield compatible results. We combine the likelihoods derived from angular correlations and spherical harmonics to constrain the ratio of comoving angular diameter distance D M at the effective redshift of our sample to the sound horizon scale at the drag epoch. We obtain D M ( z eff = 0.835 ) / r d = 18.92 ± 0.51 , which is consistent with, but smaller than, the Planck prediction assuming flat Λ CDM , at the level of 2.3 σ . The analysis was performed blind and is robust to changes in a number of analysis choices. It represents the most precise BAO distance measurement from imaging data to date, and is competitive with the latest transverse ones from spectroscopic samples at z > 0.75 . When combined with DES 3 x 2 pt + SNIa , they lead to improvements in H 0 and Ω m constraints by ∼ 20 % .

79 ASTRONOMY AND ASTROPHYSICS↗

Simulating Continuum-based Redshift Measurement in the Roman’s High Latitude Spectroscopic Survey

We investigate the capability of the Nancy Grace Roman Space Telescope’s (Roman) Wide-Field Instrument G150 slitless grism to detect red, quiescent galaxies based on the current reference survey. We simulate dispersed images for Roman reference High-Latitude Spectroscopic Survey (HLSS) and analyze two-dimensional spectroscopic data using the grism Redshift and Line Analysis (Grizli) software. This study focus on assessing Roman grism’s capability for continuum-level redshift measurement for a redshift range of 0.5 ≤ z ≤ 2.5. The redshift recovery is assessed by setting three requirements of: σ z = $\frac{|z–z_{true}|}{1+z}$ ≤ 0.01, signal-to-noise ratio≥ 5 and the presence of a single dominant peak in redshift likelihood function. We find that, for quiescent galaxies, the reference HLSS can reach a redshift recovery completeness of ≥50% for F158 magnitude brighter than 20.2 mag. We also explore how different survey parameters, such as exposure time and the number of exposures, influence the accuracy and completeness of redshift recovery, providing insights that could optimize future survey strategies and enhance the scientific yield of the Roman in cosmological research.

Astronomical simulations↗

A Machine Learning Method for the Forensics Attribution of Separated Plutonium

Plutonium (Pu) source attribution would be a powerful tool to support nuclear nonproliferation efforts. This capability to find the source of a Pu sample would act as a deterrent to smuggling efforts, and also help regulatory agencies verify declared nuclear activities. Work at Texas A&M University yielded a nuclear forensics methodology, which is capable of determining separated Pu’s reactor of origin, fuel burnup, and the time since irradiation (TSI)—three parameters of interest. The methodology used a set of ten intra-element isotopic ratios found in separated Pu, which was compared to a library of isotopic ratio values produced using neutronics simulations for reactors of interest. By calculating the probability that unknown Pu sample’s isotopic ratio set matched a set in the library, the methodology could predict the three parameters of interest of the sample. One shortcoming of this methodology was an inability to correctly attribute spoofed Pu, where Pu sourced from two different reactors or two different fuel burnup levels are mixed. A new methodology to rectify this vulnerability using machine learning (ML) technique is developed, instead of the maximum likelihood calculation previously used and the results are satisfactory. The ML approach leverages the existing simulated data for training the algorithm, but use them efficiently by only using intra-element isotope ratios that contribute to the attribution one of the three parameters at a time. Previously, all isotope ratios were used to attribute all three parameters together. The new methodology attributes the Pu parameters in three steps, one for each parameter, rather than resolving all of the three parameters simultaneously like the previous maximum likelihood approach. First, a support vector machine classifier with a set of seven isotopic ratios finds the reactor of origin and a set of regression models trained using gaussian process predicts the burnup with a different set of seven isotopes. Finally, TSI is calculated analytically using decay equations. Thus far, the new methodology is capable of attributing pure Pu samples and has been validated using experimental data. The next step will to be augment the classifier training data set with spoofed Pu data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

High-dimensional and permutation invariant anomaly detection

Methods for anomaly detection of new physics processes are often limited to low-dimensional spaces due to the difficulty of learning high-dimensional probability densities. Particularly at the constituent level, incorporating desirable properties such as permutation invariance and variable-length inputs becomes difficult within popular density estimation methods. In this work, we introduce a permutation-invariant density estimator for particle physics data based on diffusion models, specifically designed to handle variable-length inputs. We demonstrate the efficacy of our methodology by utilizing the learned density as a permutation-invariant anomaly detection score, effectively identifying jets with low likelihood under the background-only hypothesis. To validate our density estimation method, we investigate the ratio of learned densities and compare to those obtained by a supervised classification algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗