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High-accuracy emulators for observables in ΛCDM, N eff, Σ m ν, and w cosmologies

ABSTRACT We use the emulation framework CosmoPower to construct and publicly release neural network emulators of cosmological observables, including the cosmic microwave background (CMB) temperature and polarization power spectra, matter power spectrum, distance-redshift relation, baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) observables, and derived parameters. We train our emulators on Einstein–Boltzmann calculations obtained with high-precision numerical convergence settings, for a wide range of cosmological models including ΛCDM, wCDM, ΛCDM + Neff, and ΛCDM + Σmν. Our CMB emulators are accurate to better than 0.5 per cent out to ℓ = 104, which is sufficient for Stage-IV data analysis, and our P(k) emulators reach the same accuracy level out to $k=50 \, \, \mathrm{Mpc}^{-1}$, which is sufficient for Stage-III data analysis. We release the emulators via an online repository (CosmoPower Organisation), which will be continually updated with additional extended cosmological models. Our emulators accelerate cosmological data analysis by orders of magnitude, enabling cosmological parameter extraction analyses, using current survey data, to be performed on a laptop. We validate our emulators by comparing them to class and camb and by reproducing cosmological parameter constraints derived from Planck TT, TE, EE, and CMB lensing data, as well as from the Atacama Cosmology Telescope Data Release 4 CMB data, Dark Energy Survey Year-1 galaxy lensing and clustering data, and Baryon Oscillation Spectroscopic Survey Data Release 12 BAO and RSD data.

Astronomy & Astrophysics↗

Fusion Energy Sciences Network Requirements Review: Mild-cycle Update

The US Department of Energy (DOE) Office of Science (SC) world-class research infrastructure provides the research community with premier observational, experimental, computational, and network capabilities. Each user facility is designed to provide unique capabilities to advance core DOE mission science for its sponsor SC program and to stimulate a rich discovery and innovation ecosystem. Research communities gather and flourish around each user facility, bringing together diverse perspectives. The continual reinvention of the practice of science — as users and staff forge novel approaches expressed in research workflows — unlocks new discoveries and propels scientific progress.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Exploring Data Set Bias and Decision Support with Predictive Uncertainty Through Bayesian Approximations and Convolutional Neural Networks

Individual seismic catalogs can contain multiscale observations from fault level to global scales and associated waveforms from discrete events reflect crustal structure across many different scales and locations. Seismic network aperture, geographic location, and observation distance may not provide informative guidance or intuition on how different catalogs will behave across models trained under different conditions. We rely on uncertainty to provide guardrails for when to trust model decisions, but understanding when our uncertainty is trustworthy is an open challenge. Here, in this work, we explore Bayesian approximation methods for assigning predictive uncertainty in seismic event classification problems. We find that computationally expensive Bayesian approximations do not outperform simple ensemble methods. We also find that when exploiting multiple seismic event catalogs, joint training with data from all the catalogs combined with Bayesian approximations and supervised training for classification can obscure bias and result in less robust uncertainty while also not providing substantial performance benefits compared to training individual models for each catalog.

58 GEOSCIENCES↗

PSInet: a new global water potential network

Abstract Given the pressing challenges posed by climate change, it is crucial to develop a deeper understanding of the impacts of escalating drought and heat stress on terrestrial ecosystems and the vital services they offer. Soil and plant water potential play a pivotal role in governing the dynamics of water within ecosystems and exert direct control over plant function and mortality risk during periods of ecological stress. However, existing observations of water potential suffer from significant limitations, including their sporadic and discontinuous nature, inconsistent representation of relevant spatio-temporal scales and numerous methodological challenges. These limitations hinder the comprehensive and synthetic research needed to enhance our conceptual understanding and predictive models of plant function and survival under limited moisture availability. In this article, we present PSInet (PSI—for the Greek letter Ψ used to denote water potential), a novel collaborative network of researchers and data, designed to bridge the current critical information gap in water potential data. The primary objectives of PSInet are as follows. (i) Establishing the first openly accessible global database for time series of plant and soil water potential measurements, while providing important linkages with other relevant observation networks. (ii) Fostering an inclusive and diverse collaborative environment for all scientists studying water potential in various stages of their careers. (iii) Standardizing methodologies, processing and interpretation of water potential data through the engagement of a global community of scientists, facilitated by the dissemination of standardized protocols, best practices and early career training opportunities. (iv) Facilitating the use of the PSInet database for synthesizing knowledge and addressing prominent gaps in our understanding of plants’ physiological responses to various environmental stressors. The PSInet initiative is integral to meeting the fundamental research challenge of discerning which plant species will thrive and which will be vulnerable in a world undergoing rapid warming and increasing aridification.

Forestry↗

A Synoptic System for Capturing Ecosystem Control Points Across Terrestrial‐Aquatic Interfaces

Interconnected landscape features such as terrestrial‐aquatic interfaces play an outsized role in biogeochemical cycles as ecosystem control points, but it is notoriously challenging to characterize these. Here, we document a synoptic sensor network design that is (a) flexible to accommodate diverse ecosystem interfaces and gradients, (b) adaptable to monitoring and modeling needs of small and large projects alike, (c) standardized for intercomparability across sites and field experiments, and (d) adequately replicated to capture heterogeneity of each parameter monitored. This real‐time monitoring of surface water, groundwater, soil, and vegetation supports configuration and evaluation of models that span upland, wetland, open water strata, and transitions between them. We established the network at seven sites along the Chesapeake Bay and Lake Erie coastlines, including large‐scale flood manipulation experiments in both regions. A central design element is “one data logger program to rule them all”—a collection of sensor‐specific modules deployed on 40 loggers controlling ∼2,000 sensors, with the goal of streamlining maintenance, debugging, and reproducible data processing. The network generates ∼6 M observations per month, capturing system dynamics at the broad spatial and fine temporal scales needed to initialize and benchmark models; measurement frequency can be modified remotely to capture events. This network design has also revealed behaviors not represented in Earth system models, such as transient groundwater oxygen pulses. Completely documented and open source, this standardized, flexible, and efficient sensor network design can reduce barriers to understanding environmental changes and ecosystem responses across systems and scales.

Ward, Nicholas D. [Pacific Northwest National Labo↗

Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study

Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for understanding these scaling laws remains underdeveloped. In this paper, we explore the neural scaling laws for deep operator networks, which involve learning mappings between function spaces, with a focus on the Chen and Chen style architecture. These approaches, which include the popular Deep Operator Network (DeepONet), approximate the output functions using a linear combination of learnable basis functions and coefficients that depend on the input functions. We establish a theoretical framework to quantify the neural scaling laws by analyzing its approximation and generalization errors. We articulate the relationship between the approximation and generalization errors of deep operator networks and key factors such as network model size and training data size. Moreover, we address cases where input functions exhibit low-dimensional structures, allowing us to derive tighter error bounds. These results also hold for deep ReLU networks and other similar structures. Our results offer a partial explanation of the neural scaling laws in operator learning and provide a theoretical foundation for their applications.

97 MATHEMATICS AND COMPUTING↗

A 1 km soil moisture dataset over eastern CONUS generated by assimilating SMAP data into the Noah-MP land surface model

An improved fine-scale soil moisture (SM) dataset at 1 km grid spacing, covering much of the eastern continental US, was generated by assimilating 9 km Soil Moisture Active Passive (SMAP) SM data into the v4.0.1 Noah-MP land surface model. With 12 ensemble members, the assimilation was carried out using the ensemble Kalman filter algorithm within NASA's Land Information System. The SM analysis for 2016 was fully validated against in situ observations from four different networks and compared with four other existing datasets. Results indicate that this SM analysis surpasses other datasets in top-layer SM distribution, including a machine-learning-based product, despite all SM estimates being less heterogeneous than observed. The analysis of anomalous errors suggests that large similarity in intrinsic errors is likely due to overlapping data sources among the selected SM datasets. More detailed evaluations were performed over two geographic areas. The observations collected by the Atmospheric Radiation Measurement facility in Oklahoma suggest that soil temperature and surface heat fluxes are concurrently simulated with good accuracy. Investigation into the 2016 southeastern US drought response further indicates drier conditions and higher evapotranspiration estimates compared to GLEAMv4.1. Notably, large errors are associated with grids having clay soil textures, underscoring the need for refined model treatments for specific soil types to further improve SM estimates. The dataset is publicly available on Zenodo at https://doi.org/10.5281/zenodo.14370563 (Tai et al., 2024).

Tai, Sheng-Lun [Pacific Northwest National Laborat↗

Distributed and Secure Spectrum Sharing for 5G and 6G Networks

Secure spectrum sharing or spectrum co-existence of multiple 5G networks and future 6G networks is a powerful enabler technology. The National Spectrum Strategy (NSS) published by the White House in November, 2023, and the subsequent NSS implementation plan led by the National Telecommunication and Information Administration (NTIA) is the driver of a national effort to enable co-existence of government incumbents and commercial networks in selected spectrum bands. Cellular networks such as 5G & 6G and non-cellular Wi-Fi 6E & 7 are the prominent wireless technologies considered for co-existence with incumbent wireless links. Security of the spectrum sharing solutions is a must to make this transformation of spectrum use possible, specially for mission critical communications. However, current spectrum sharing solutions rely on centralized data bases with inherent vulnerabilities. This paper focuses on secure spectrum sharing among multiple 5G networks using unlicensed and shared frequency bands. It presents an innovative AI/ML based distributed spectrum sharing approach that can be autonomously used by multiple networks. Each sharing network uses its own observation of the Radio Frequency (RF) environment, which consists of RF measurements reported from the 5G User Equipment (UE), to adjust the transmission power levels for secure co-existence. Data is presented to illustrate the superior performance of this solution compared to other spectrum sharing solutions where each network can utilize usage data of the other networks. Finally it discusses how this efficient spectrum sharing solution can evolve in the future for the 6G networks.

5G↗

Data for Selective Oxidation of 3-Hydroxypropionic Acid to Malonic Acid over Pd/C: Mechanistic and Kinetic Study

Malonic acid (MA) is a high-value dicarboxylic acid with strong industrial demand, yet its current production heavily relies on petrochemical feedstocks. Here, we report the first systematic study for the sustainable production of MA via oxidation of 3-hydroxypropionic acid (3-HP) with a Pd/Carbon catalyst. The effects of oxidant type (O2 and H2O2), pH, and temperature on the reaction chemistry were comprehensively evaluated. Guided by experimental observation and DFT-calculated thermochemical energetics, reaction networks for 3-HP oxidation with both oxidants are proposed and validated through kinetic modeling. MA was identified as the primary oxidation product, while further oxidation yields acetic acid and oxalic acid. The kinetic model validated the network, displaying excellent agreement (R2 > 0.95). Kinetic observations also enabled a direct comparison between O2 and H2O2 and revealed their distinct behaviors. The model was further developed into a temperature-time map, providing insight into conditions that maximize MA production. Malonic acid selectivity of 56.9 % and yield of 50.5 % were achieved at 3 bar oxygen, equimolar NaOH:3-HP ratio, and 50 °C.

Bioproducts↗

Data and code from: Selective oxidation of 3-hydroxypropionic acid to malonic acid over Pd/C: Mechanistic and kinetic study

Malonic acid (MA) is a high-value dicarboxylic acid with strong industrial demand, yet its current production heavily relies on petrochemical feedstocks. Here, we report the first systematic study for the sustainable production of MA via oxidation of 3-hydroxypropionic acid (3-HP) with a Pd/Carbon catalyst. The effects of oxidant type (O2 and H2O2), pH, and temperature on the reaction chemistry were comprehensively evaluated. Guided by experimental observation and DFT-calculated thermochemical energetics, reaction networks for 3-HP oxidation with both oxidants are proposed and validated through kinetic modeling. MA was identified as the primary oxidation product, while further oxidation yields acetic acid and oxalic acid. The kinetic model validated the network, displaying excellent agreement (R2 > 0.95). Kinetic observations also enabled a direct comparison between O2 and H2O2 and revealed their distinct behaviors. The model was further developed into a temperature-time map, providing insight into conditions that maximize MA production. Malonic acid selectivity of 56.9 % and yield of 50.5 % were achieved at 3 bar oxygen, equimolar NaOH:3-HP ratio, and 50 °C.

3-Hydroxypropionic Acid↗

Tracking the reaction networks of acetaldehyde oxide and glyoxal oxide Criegee intermediates in the ozone-assisted oxidation reaction of crotonaldehyde

The reaction of unsaturated compounds with ozone (O 3 ) is recognized to lead to the formation of Criegee intermediates (CIs), which play a key role in controlling the atmospheric budget of hydroxyl radicals and secondary organic aerosols. The reaction network of two CIs with different functionality, i.e. acetaldehyde oxide (CH 3 CHOO) and glyoxal oxide (CHOCHOO) formed in the ozone-assisted oxidation reaction of crotanaldehyde (CA), is investigated over a temperature range between 390 K and 840 K in an atmospheric pressure jet-stirred reactor (JSR) at a residence time of 1.3 s, stoichiometry of 0.5 with a mixture of 1% crotonaldehyde, 10% O 2 , at an fixed ozone concentration of 1000 ppm and 89% Ar dilution. Molecular-beam mass spectrometry in conjunction with single photon tunable synchrotron vacuum-ultraviolet (VUV) radiation is used to identify elusive intermediates by means of experimental photoionization energy scans and ab initio threshold energy calculations for isomer identification. Addition of ozone (1000 ppm) is observed to trigger the oxidation of CA already at 390 K, which is below the temperature where the oxidation reaction of CA was observed in the absence of ozone. The observed CA + O 3 product, C 4 H 6 O 4 , is found to be linked to a ketohydroperoxide (2-hydroperoxy-3-oxobutanal) resulting from the isomerization of the primary ozonide. Products corresponding to the CIs uni- and bi-molecular reactions were observed and identified. A network of CI reactions is identified in the temperature region below 600 K, characterized by CIs bimolecular reactions with species like aldehydes, i.e., formaldehyde, acetaldehyde, and crotonaldehyde and alkenes, i.e., ethene and propene. The region below 600 K is also characterized by the formation of important amounts of typical low-temperature oxidation products, such as hydrogen peroxide (H 2 O 2 ), methyl hydroperoxide (CH 3 OOH), and ethyl hydroperoxide (C 2 H 5 OOH). Detection of additional oxygenated species such as alcohols, ketene, and aldehydes are indicative of multiple active oxidation routes. This study provides important information about the initial step involved in the CIs assisted oligomerization reactions in complex reactive environments where CIs with different functionalities are reacting simultaneously. It provides new mechanistic insights into ozone-assisted oxidation reactions of unsaturated aldehydes, which is critical for the development of improved atmospheric and combustion kinetics models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Observable optimization for precision theory: machine learning energy correlators

The practice of collider physics typically involves the marginalization of multi-dimensional collider data to uni-dimensional observables relevant for some physics task. In many cases, such as classification or anomaly detection, the observable can be arbitrarily complicated, such as the output of a neural network. However, for precision measurements, the observable must correspond to something computable systematically beyond the level of current simulation tools. In this work, we demonstrate that precision-theory-compatible observable space exploration can be systematized by using neural simulation-based inference techniques from machine learning. We illustrate this approach by exploring the space of marginalizations of the energy 3-point correlator to optimize sensitivity to the top quark mass. We first learn the energy-weighted probability density from simulation, then search in the space of marginalizations for an optimal triangle shape. Although simulations and machine learning are used in the process of observable optimization, the output is an observable definition which can be then computed to high precision and compared directly to data without any memory of the computations which produced it. We find that the optimal marginalization is isosceles triangles on the sphere with a side ratio approximately $1 : 1 : \sqrt{2}$ (i.e. right triangles) within the set of marginalizations we consider.

Jets and Jet Substructure↗

Selective oxidation of 3-hydroxypropionic acid to malonic acid over Pd/C: Mechanistic and kinetic study

Malonic acid (MA) is a high-value dicarboxylic acid with strong industrial demand, yet its current production heavily relies on petrochemical feedstocks. Here, we report the first systematic study for sustainable production of MA via oxidation of 3-hydroxypropionic acid (3-HP) with a Pd/Carbon catalyst. The effects of oxidant type (O 2 and H 2 O 2 ), pH, and temperature on the reaction chemistry were comprehensively evaluated. Guided by experimental observation and DFT-calculated thermochemical energetics, reaction networks for 3-HP oxidation with both oxidants are proposed and validated through kinetic modeling. MA was identified as the primary oxidation product, while further oxidation yields acetic acid and oxalic acid. The kinetic model validated the network, displaying excellent agreement (R 2 > 0.95). Kinetic observations also enabled a direct comparison between O 2 and H 2 O 2 and revealed their distinct behaviors. The model was further developed into a temperature-time map, providing insight into conditions that maximize MA production. Malonic acid selectivity of 56.9 % and yield of 50.5 % were achieved at 3 bar oxygen, equimolar NaOH:3-HP ratio, and 50 °C.

3-hydroxypropionic acid↗

Pressure-induced polyamorphic transition in CaA l 2 O 4 glass

In situ high-pressure ultrasonic velocity measurements of CaAl 2 O 4 glass reveal abrupt irreversible discontinuities in the elastic wave velocities at ~8–10 GPa. Total structure factor and pair distribution functions measured by synchrotron x-ray diffraction show a rapid change in the intermediate range structure attributed to a rearrangement of calcium ions over this narrow pressure region. Atomistic models obtained from molecular dynamics simulations reveal that this intermediate range structure is explained by a transition of Ca–O void radius distribution from a bimodal distribution with peaks at ~2.1 and ~2.4 Å to a single distribution centered at ~2.1 Å. Further, these abrupt structural changes involving the rapid increase in elastic wave velocity are markedly different to the continuous transformations observed in conventional network-forming glasses, such as SiO 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

COMPASS-FME Synoptic Sites Level 1 Sensor Data v2-1

This is the version 2-1 Level 1 (L1) data release for COMPASS-FME environmental sensors located at our synoptic field sites. COMPASS-FME is studying sites in two distinct regions, the Chesapeake Bay and the Western Lake Erie Basin. We established the network at seven "synoptic" (observational) sites along the Chesapeake Bay and Lake Erie coastlines, collectively generating over three million observations per month, to track and comprehend environmental changes where land and water intersect. Additionally, the two regions provide an interesting contrast of saltwater and freshwater coasts that allow us to differentiate the impacts of inundation and coastal water chemistries in two nationally important coastal systems. L1 data are close to raw, but are units-transformed and have out-of-instrument-bounds, out-of-service, and outlier flags added. Duplicates and missing data are removed but otherwise these data are not filtered, and have not been subject to any additional algorithmic or human QA/QC. Any scientific analyses of L1 data should be performed with care. **This dataset will be updated quarterly with new data for the duration of the project** This dataset includes: - An overall dataset README file that describes the current version, gives citation and contact information, etc. - Site- and year-specific folders, each holding up to 12 CSV (comma separated value) data files for each site and plot in that year. - Metadata files within each site-year folder provide full information on data units, expected ranges, contact information, as well as a general description of the site. - Environmental sensor types that appear in the data files include weather (ClimaVUE50, CS, RM Young, and LI instruments in the graphs below); soil conditions (TEROS12); soil redox state (Redox); groundwater variables (AquaTROLL200 and AquaTROLL600); open water sondes (Exo); tree sap velocity (Sapflow); and system voltage and state (Datalogger). Data are normally logged every 15 minutes. Please see v2-0 Synoptic L1 Sensor Package Quick Start.pdf for detailed information on data package structure, temporal coverage, and versioning. This dataset was updated 2026-03-12: (i) data now go through 2025-12-31 (previous end was 2025-06-30) and (ii) dataset and file names updated to “…v2-1” (previously was “v2-0”).

54 ENVIRONMENTAL SCIENCES↗

COMPASS-FME Synoptic Sites Level 2 Sensor Data v2-1

This is the version 2-1 Level 2 (L2) data release for COMPASS-FME environmental sensors located at our synoptic field sites. COMPASS-FME is studying sites in two distinct regions, the Chesapeake Bay and the Western Lake Erie Basin. We established the network at seven "synoptic" (observational) sites along the Chesapeake Bay and Lake Erie coastlines, collectively generating over three million observations per month, to track and comprehend environmental changes where land and water intersect. Additionally, the two regions provide an interesting contrast of saltwater and freshwater coasts that allow us to differentiate the impacts of inundation and coastal water chemistries in two nationally important coastal systems. Level 2 (L2) data consist of sensor observations from the COMPASS-FME synoptic sites, TEMPEST, and DELUGE. Compared to the L1 data, these are more consistent (always 15-minute timestamps for the entire year); better QA/QC’d (out of bounds, out of service, and extreme outlier values are removed); and more complete, with a gap-filled time series available alongside the main observations, and additional derived (calculated) variables. L2 data are intended to be rapidly and easily usable in analyses and simulations. However, algorithmic outlier identification always carries the risk of removing valid data, and Level 1 data may be more suitable for analyses that focus on variability or extreme events. This dataset includes: - An overall dataset README file that describes the current version, gives citation and contact information, etc. - Site- and year-specific folders, each holding variable-specific Parquet (a high performance, space efficient format; see https://parquet.apache.org) data files for each site and plot in that year. - Metadata files within each site-year folder provide full information on data units, expected ranges, contact information, detailed flood times, as well as a general description of the site. - Environmental sensor types that appear in the data files include weather (ClimaVUE50, CS, RM Young, and LI instruments in the graphs below); soil conditions (TEROS12); soil redox state (Redox); groundwater variables (AquaTROLL200 and AquaTROLL600); open water sondes (Exo); tree sap velocity (Sapflow); and system voltage and state (Datalogger). Data are reported every 15 minutes. Data files are in Apache Parquet, a high performance, space efficient format for tabular data. These files can be read using R's `arrow` package (https://arrow.apache.org/docs/r/), with similar tools available in other languages. Please see v2-1 L2 Sensor Package QStart.pdf for detailed information on data package structure, temporal coverage, and versioning.

EARTH SCIENCE > ATMOSPHERE > ATMOSPHERIC TEMPERATU↗

Gearbox bearing crack growth prognostics and uncertainty quantification with physics-informed machine learning

This paper introduces the extreme theory of functional connections (X-TFC), a physics-informed machine learning algorithm, and tailors it to estimate the remaining useful life (RUL) of wind turbine gearbox bearings experiencing fatigue crack growth. Unlike purely data-driven methods, X-TFC embeds a physics model, based on Head's theory in this work, into its training objective. The core of X-TFC is a random-projection single-layer neural network trained via an extreme learning machine, which requires only limited damage progression data and solves for output weights with a least-squares optimization algorithm. A composite loss function balances the network's fit to observed degradation data against the residuals of the governing crack growth differential equation, ensuring the learned damage trajectory remains physically plausible. When applied to a vibration-based health-index (HI) dataset measured during the growth of a crack on the inner ring of a high-speed bearing in a wind turbine gearbox (Bechhoefer and Dubé, 2020), X-TFC achieves near-zero prediction bias. Even when trained on only the first 10 %–20 % of the damage progression data, with sufficient physics weighting its predictions remain monotonic and smooth, delivering high prognosability and trendability. To quantify the epistemic uncertainty, we employ a Monte Carlo ensemble of independently initialized X-TFC models trained on noise-perturbed data, which yields confidence intervals around each RUL estimate and captures both model-parameter and epistemic uncertainty. In addition to a vibration-based HI, we demonstrate that the proposed framework can be directly applied to a supervisory control and data acquisition (SCADA) data-based HI (Eftekhari Milani et al., 2026) measured during similar wind turbine gearbox bearing crack faults, preserving its accuracy and interpretability. This extension shows the versatility of our approach, which is applicable to bearings of multiple gearbox manufacturers, models, and ratings using only SCADA data. By integrating domain knowledge with machine learning, X-TFC offers a rapid, reliable tool for crack prognostics. Its adaptability to other bearing failure modes, such as pitch bearing ring cracks, positions X-TFC as a powerful enabler of data-driven, physics-informed asset management in the wind energy sector and beyond.

17 WIND ENERGY↗

CaloTrilogy: Toward a Breakthrough in One-Step, End-to-End, Physics-Guided Shower Generation for Modern Calorimeters

High-precision calorimeter simulation at current and future colliders imposes rapidly growing computational demands, motivating the development of machine-learning surrogates for traditional Monte Carlo tools such as Geant4. Flow matching and diffusion-based generative models have become leading approaches for high-dimensional fast simulation because of their sample quality, but typically require ${\cal O}(100)$ function evaluations at inference and often rely on auxiliary networks to constrain global observables, compromising streamlined end-to-end generation. We introduce a unified framework that improves the balance between speed, shower quality, and physics fidelity. The method combines: (i) an average velocity field integrator that enables sampling in one or a few evaluations; (ii) a learned generative prior in shower space, constructed from data rather than random noise; and (iii) physics-guided loss terms that impose inductive biases on key observables during training. These elements are training time regularizers, preserving end-to-end inference with no additional cost. With only one or a few evaluation steps, the model achieves shower quality competitive with state-of-the-art flow and diffusion approaches, tested on several public high granularity calorimeter datasets. The results demonstrate inter-layer shower structure consistent with the underlying physics, providing a strong candidate for future fast simulation workflows.

Jiang, Cheng [Edinburgh U.]↗