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Energy Intensity Baselining and Tracking Guidance

Each company joining the U.S. Department of Energy’s (DOE’s) Better Buildings, Better Plants Program (Better Plants) commits to establishing an energy consumption and energy intensity (EI) baseline and to tracking its energy performance over a 10-year period against that baseline. The baseline must reflect a company’s energy consumption over a 12-month period, covering all its U.S.-based operations. Energy consumption is calculated by fuel type in terms of primary energy (also known as source energy). EI is broadly defined as the amount of energy consumed per unit of output produced. For this guidance document and for the program, the term energy performance represents an evaluation of a facility’s capacity to use energy efficiently. Metrics used to assess a facility’s energy performance can include EI, energy consumption, improvements in EI, etc. Establishing an energy baseline and tracking system is a critical first step in effectively managing energy use. Developing a baseline can help a company understand energy use within the corporation and give it a point of comparison to evaluate future efforts to improve energy performance. It can also support efforts to validate a company’s energy management activities, improve comparative analyses when using benchmarks, and help in predicting future energy needs. In addition, a company that normalizes its performance data can determine highly defensible measures of energy savings generated through implemented energy efficiency projects. Establishing a baseline and tracking energy performance is also a requirement for ISO 50001 certification. Although basic energy data can be collected through utility bills, most manufacturers will have to perform additional analyses to develop accurate and robust energy baselines and tracking systems. Energy is consumed in many ways within the manufacturing sector and can come from multiple sources. Energy is sometimes generated and sold to other parties or captured and reused on-site. External events can exert a significant impact on a facility or company’s energy use independent of any purposeful efforts to improve energy efficiency. Operational changes, such as production shifts—which may be inevitable for some companies over the 10-year period covered by the program—can also make a big difference in energy use. Since Better Plants asks companies to account for all their U.S.-based operations, mergers, acquisitions, and divestitures can also have significant implications for a company’s energy metrics. This document aims to demystify the sometimes complex baselining process. It devotes special attention to the task of normalizing and adjusting energy consumption to account for external factors, such as weather and production changes. A key recommendation is that companies use regression analysis to normalize their energy consumption data whenever possible. Regression analysis is a statistical technique that estimates the dependence of a variable (i.e., energy use in the context of Better Plants) on one or more independent variables such as ambient temperature, while controlling for the influence of other variables at the same time. A properly developed regression analysis can provide a reliable estimate of energy savings resulting from energy improvement strategies and projects by accounting for the effects of variables such as annual production levels and weather. DOE has developed a companion Energy Performance Indicator software tool (EnPI) to simplify the baselining process. This tool can run regression models, calculate changes in EI at the facility level, and automatically compile facility-level data into a corporate-wide metric. Note that although the relevant equations used to calculate EI are provided in this document, the EnPI tool will automatically perform most calculations for the user. Additionally, Better Plants Partners (Partners) can call on their Technical Account Manager (TAM) to help them establish a baseline and assist with the necessary calculations to track progress.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Generalization Across Experimental Parameters in Neural Network Analysis of High-Resolution Transmission Electron Microscopy Datasets

Neural networks are promising tools for high-throughput and accurate transmission electron microscopy (TEM) analysis of nanomaterials, but are known to generalize poorly on data that is “out-of-distribution” from their training data. Given the limited set of image features typically seen in high-resolution TEM imaging, it is unclear which images are considered out-of-distribution from others. Here, we investigate how the choice of metadata features in the training dataset influences neural network performance, focusing on the example task of nanoparticle segmentation. We train and validate neural networks across curated, experimentally collected high-resolution TEM image datasets of nanoparticles under various imaging and material parameters, including magnification, dosage, nanoparticle diameter, and nanoparticle material. Overall, we find that our neural networks are not robust across microscope parameters, but do generalize across certain sample parameters. Additionally, data preprocessing can have unintended consequences on neural network generalization. Our results highlight the need to understand how dataset features affect deployment of data-driven algorithms.

42 ENGINEERING↗

Characterization and identification of HPC applications at leadership computing facility

High Performance Computing (HPC) is an important method for scientific discovery via large-scale simulation, data analysis, or artificial intelligence. Leadership-class supercomputers are expensive, but essential to run large HPC applications. The Petascale era of supercomputers began in 2008, with the first machines achieving performance in excess of one petaflops, and with the advent of new supercomputers in 2021 (e.g., Aurora, Frontier), the Exascale era will soon begin. However, the high theoretical computing capability (i.e., peak FLOPS) of a machine is not the only meaningful target when designing a supercomputer, as the resources demand of applications varies. A deep understanding of the characterization of applications that run on a leadership supercomputer is one of the most important ways for planning its design, development and operation. In order to improve our understanding of HPC applications, user demands and resource usage characteristics, we perform correlative analysis of various logs for different subsystems of a leadership supercomputer. This analysis reveals surprising, sometimes counter-intuitive patterns, which, in some cases, conflicts with existing assumptions, and have important implications for future system designs as well as supercomputer operations. For example, our analysis shows that while the applications spend significant time on MPI, most applications spend very little time on file I/O. Combined analysis of hardware event logs and task failure logs show that the probability of a hardware FATAL event causing task failure is low. Combined analysis of control system logs and file I/O logs reveals that pure POSIX I/O is used more widely than higher level parallel I/O. Based on holistic insights of the application gained through combined and co-analysis of multiple logs from different perspectives and general intuition, we engineer features to "fingerprint" HPC applications. We use t-SNE (a machine learning technique for dimensionality reduction) to validate the explainability of our features and finally train machine learning models to identify HPC applications or group those with similar characteristic. To the best of our knowledge, this is the first work that combines logs on file I/O, computing, and inter-node communication for insightful analysis of HPC applications in production.

Liu, Zhengchun↗

Preliminary Results of Ancillary Safety Analyses Supporting TREAT LEU Conversion Activities

The Transient Reactor Test Facility (TREAT), located at Idaho National Laboratory (INL), is a test facility designed to evaluate the performance of reactor fuels and materials under transient accident conditions. The facility, an air-cooled, graphite-moderated reactor designed to utilize fuel containing high-enriched uranium (HEU), has been in non-operational standby status since 1994. Currently, in support of the missions of the Department of Energy (DOE) National Nuclear Security Administration (NNSA) Material Management and Minimization (M3) Reactor Conversion Program, a new core design is being developed for TREAT that will utilize low-enriched uranium (LEU). The primary objective of this conversion effort is to design an LEU core that is capable of meeting the performance characteristics of the existing HEU core. Minimal, if any, changes are anticipated for the supporting systems (e.g. reactor trip system, filtration/cooling system, etc.); therefore, the LEU core must also be able to function with the existing supporting systems, and must also satisfy acceptable safety limits. In support of the LEU conversion effort, a range of ancillary safety analyses are required to evaluate the LEU core operation relative to that of the existing facility. These analyses cover neutronics, shielding, and thermal hydraulic topics that have been identified as having the potential to have reduced safety margins due to conversion to LEU fuel, or are required to support the required safety analyses documentation. The majority of these ancillary tasks have been identified in [1] and [2]. The purpose of this report is to document the ancillary safety analyses that have been performed at Argonne National Laboratory during the early stages of the LEU design effort, and to describe ongoing and anticipated analyses. For all analyses presented in this report, methodologies are utilized that are consistent with, or improved from, those used in analyses for the HEU Final Safety Analysis Report (FSAR) [3]. Depending on the availability of historical data derived from HEU TREAT operation, results calculated for the LEU core are compared to measurements obtained from HEU TREAT operation. While all analyses in this report are largely considered complete and have been reviewed for technical content, it is important to note that all topics will be revisited once the LEU design approaches its final stages of maturity. For most safety significant issues, it is expected that the analyses presented here will be bounding, but additional calculations will be performed as necessary to support safety analyses and safety documentation. It should also be noted that these analyses were completed as the LEU design evolved, and therefore utilized different LEU reference designs. Preliminary shielding, neutronic, and thermal hydraulic analyses have been completed and have generally demonstrated that the various LEU core designs will satisfy existing safety limits and standards also satisfied by the existing HEU core. These analyses include the assessment of the dose rate in the hodoscope room, near a loaded fuel transfer cask, above the fuel storage area, and near the HEPA filters. The potential change in the concentration of tramp uranium and change in neutron flux reaching instrumentation has also been assessed. Safety-significant thermal hydraulic items addressed in this report include thermally-induced mechanical distortion of the grid plate, and heating in the radial reflector.

Brunett, A. J.↗

AP-105 Melter Offgas Condensate and EMF Evaporator Concentrate Raman and LIBS Qualitative Evaluation for the use of In-Line Monitoring (Rev. 0)

The Pacific Northwest National Laboratory (PNNL) was tasked to perform Raman spectroscopy and laser induced breakdown spectroscopy (LIBS) testing on the melter off-gas condensate generated during low-activity waste process testing of a sample from Hanford Site tank AP-105 and/or evaporate from evaporation of the condensate. This was a proof-of-principle demonstration that Raman spectroscopy and LIBS have the potential to be used as analytical tools for in-line process analysis of key aqueous phase analytes in radioactive process streams associated with the Hanford Waste Treatment and Immobilization Plant. The work completed under this project complements work completed for WRPS with the development of in-line monitoring systems to characterize and quantify constituents of tank waste following Cs removal and filtration. The WRPS work is currently limited to Raman sensors and utilizes chemometric models for quantification of several anionic species in the sample system. It should be noted that while this approach can be applied to off-gas condensate streams, new chemometric models are needed to accurately quantify analytes under off-gas condensate conditions. The work completed under this project makes timely use of available samples and equipment at PNNL. The project utilized the opportunity to collect off-gas samples from planned AP-105 processing work and included the direct condensate and the evaporate from the DFLAW Radioactive Waste Test Platform. Samples were characterized by instruments already in place at PNNL including a Raman spectrometer optimized for in-line monitoring of flowing and stationary samples as well as a LIBS instrument, which was optimized for static liquid droplet analysis. The ultimate objective was to determine if these techniques could be used to qualitatively characterize analytes present within the off-gas samples. The testing confirmed the use of the Raman as an in-line monitoring system was able to qualitatively observe NO 3 - , NO 2 - , aluminum (as aluminate, Al(OH) 4 - ), SO 4 2- , CrO 4 2- , CO 3 2- , and PO 4 3- in the AP-105 melter feed evaporator condensate samples. The testing also confirmed LIBS as a potential useful technique for in-line monitoring, able to qualitatively detect Na, N, Al, and tentatively Cr and Cl in a simulant stock evaporate solution.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Merged Aerosol Value-Added Product Report

The Merged Aerosol Value-Added Product (VAP) simplifies scientists’ use of Atmospheric Radiation Measurement (ARM) User Facility aerosol data by performing several tedious, time-consuming tasks for the users. First, the VAP identifies the best data available when multiple datastreams exist for a single geophysical quantity so that ARM users do not have to research this for themselves. Second, the VAP consolidates multiple ARM aerosol datastreams into a single file for ARM data users so that they do not have to download, open, and read multiple files for their analysis. Next, the VAP transforms all measurements onto a common one-hour timestamp. The one-hour resolution matches the time resolution of the slowest instrument. Instruments with faster sampling rates than one measurement per hour are averaged over the time interval. Finally, the VAP reads the QA/QC variables and marks data with known issues as missing, so that users do not have to spend excessive time cleaning data. This includes incorporating Data Quality Reports (DQRs) that exist at the time when the VAP data is generated. DQRs are reports filed by instrument mentors or data users that indicate a problem with the output data of individual instruments.

54 ENVIRONMENTAL SCIENCES↗

Welding Defect Classification from Simulated Ultrasonic Signals

Nondestructive testing is widely used to detect and to size up discontinuities embedded in a material. Among the several ultrasonic techniques, time of flight diffraction (TOFD) combines high speed inspection, high sizing reliability and low rate of incorrect results. However, the classification of defects through ultrasound signals acquired by the TOFD technique depends heavily on the knowledge and experience of the operator and thus, this classification is still frequently questioned. Besides, this task requires long processing time due to the large amount of data to be analyzed. Nevertheless, computational tools for pattern recognition can be employed to analyze a high amount of data with large efficiency. In the present work, simulation of ultrasound propagation in two-dimensional media containing, each one, different kinds of modeled discontinuities which mimic defects in welded joints were performed. Clustering (k-means) and classification (principal component analysis and k-nearest neighbors) algorithms were employed to associate each simulated ultrasound signal with its corresponding modeled defects. The results for each method were analyzed, discussed and compared. The results are very promising.

42 ENGINEERING↗

Autoencoder node saliency: Selecting relevant latent representations

The autoencoder is an artificial neural network that performs nonlinear dimension reduction and learns hidden representations of unlabeled data. With a linear transfer function it is similar to the principal component analysis (PCA). While both methods use weight vectors for linear transformations, the autoencoder does not come with any indication similar to the eigenvalues in PCA that are paired with eigenvectors. In this work, we propose a novel autoencoder node saliency method that examines whether the features constructed by autoencoders exhibit properties related to known class labels. The supervised node saliency ranks the nodes based on their capability of performing a learning task. It is coupled with the normalized entropy difference (NED). We establish a property for NED values to verify classifying behaviors among the top ranked nodes. Lastly, by applying our methods to real datasets, we demonstrate their ability to provide indications on the performing nodes and explain the learned tasks in autoencoders.

97 MATHEMATICS AND COMPUTING↗

The agile alert system for gamma-ray transients

In recent years, a new generation of space missions has offered great opportunities for discovery in high-energy astrophysics. In this article we focus on the scientific operations of the Gamma-Ray Imaging Detector (GRID) on board the AGILE space mission. AGILE-GRID, sensitive in the energy range of 30 MeV-30 GeV, has detected many γ-ray transients of both galactic and extragalactic origin. This work presents the AGILE innovative approach to fast γ-ray transient detection, which is a challenging task and a crucial part of the AGILE scientific program. The goals are to describe (1) the AGILE Gamma-Ray Alert System, (2) a new algorithm for blind search identification of transients within a short processing time, (3) the AGILE procedure for γ-ray transient alert management, and (4) the likelihood of ratio tests that are necessary to evaluate the post-trial statistical significance of the results. Special algorithms and an optimized sequence of tasks are necessary to reach our goal. Data are automatically analyzed at every orbital downlink by an alert pipeline operating on different timescales. As proper flux thresholds are exceeded, alerts are automatically generated and sent as SMS messages to cellular telephones, via e-mail, and via push notifications from an application for smartphones and tablets. These alerts are crosschecked with the results of two pipelines, and a manual analysis is performed. Being a small scientific-class mission, AGILE is characterized by optimization of both scientific analysis and ground-segment resources. The system is capable of generating alerts within two to three hours of a data downlink, an unprecedented reaction time in γ-ray astrophysics.

79 ASTRONOMY AND ASTROPHYSICS↗

Statistical and systematic errors in the measurement of weak-lensing Minkowski functionals: Application to the Canada-France-Hawaii Lensing Survey

The measurement of cosmic shear using weak gravitational lensing is a challenging task that involves a number of complicated procedures. We study in detail the systematic errors in the measurement of weak-lensing Minkowski Functionals (MFs). Specifically, we focus on systematics associated with galaxy shape measurements, photometric redshift errors, and shear calibration correction. We first generate mock weak-lensing catalogs that directly incorporate the actual observational characteristics of the Canada-France-Hawaii Lensing Survey (CFHTLenS). We then perform a Fisher analysis using the large set of mock catalogs for various cosmological models. We find that the statistical error associated with the observational effects degrades the cosmological parameter constraints by a factor of a few. The Subaru Hyper Suprime-Cam (HSC) survey with a sky coverage of ∼1400 deg{sup 2} will constrain the dark energy equation of the state parameter with an error of Δw {sub 0} ∼ 0.25 by the lensing MFs alone, but biases induced by the systematics can be comparable to the 1σ error. We conclude that the lensing MFs are powerful statistics beyond the two-point statistics only if well-calibrated measurement of both the redshifts and the shapes of source galaxies is performed. Finally, we analyze the CFHTLenS data to explore the ability of the MFs to break degeneracies between a few cosmological parameters. Using a combined analysis of the MFs and the shear correlation function, we derive the matter density Ω{sub m0}=0.256±{sub 0.046}{sup 0.054}.

79 ASTRONOMY AND ASTROPHYSICS↗

FY23 Year End Report of Delivery Environments Predictive Capabilities Use in Analysis of SRP Programs

As was established in a previous milestone report for FY20, W-13 continues to be tasked with analyses that require knowledge of in-flight environments and require an in-house capability to generate such environments. To this end, FY21 work included obtaining and benchmarking the use of such tools for an in-house capability. With these tools available for analysis tasks, ongoing work has been to continue the development of analysis capabilities and understanding while specifically using the tools for Responsive Development Experiment (ReDX) flights in the Stockpile Responsiveness Program (SRP). In FY23, design and analysis of ReDX flight 3A continued while targeting an FY24 launch date. This report shows that a variety of vehicle characterization and flight analysis tools were used in W-13, under the Delivery Environments Program. This work was performed in order to aid in vehicle design by predicting flight stability, trajectory, and induced environments while adapting to a series of changing internal payload configurations that resulted in significant changes to mass properties and associated flight stability.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Laboratory Validation of Integrated Lighting Systems Retrofit Performance and Energy Savings

Light-emitting diodes (LED) fixtures and lamps have emerged as leading technologies for general illumination and are a well-established energy efficiency retrofit measure in commercial buildings (from around 2% of installed fixtures and lamps in 2013 to 28% by 2020). Retrofit approaches that integrate elements, such as networked controls, daylight dimming, and advanced shade technologies lag in comparison. Integrated retrofits have been shown to increase savings over single end-use retrofits, but are perceived as higher complexity and risk. More validation of integrated lighting system performance is needed. This study presents results from laboratory testing of three packages combining fixtures, networked controls, task tuning, and daylight dimming, advanced shades, and lighting layout changes. We characterize performance in perimeter open-office zones, finding energy savings from 20% for daylight dimming and automated shades (no LED retrofit) to over 70% for LED retrofits with advanced controls and shades or lighting layout changes. We present some implementation details, including lessons learned from installation and commissioning in the laboratory setting. We also discuss cost-benefit analysis approaches for the types of packages presented, including the need to quantify and incorporate energy and non-energy benefits for advanced shades packages, which enhance occupant comfort but add significant cost.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

BOTTLE 1 - Introduction and BOTTLE Overview

The Bio-Optimized Technologies to keep Thermoplastics out of Landfills and the Environment (BOTTLE) Consortium aims to develop robust processes to upcycle existing waste plastics and to develop new plastics that are recyclable-by-design, both in direct alignment with DOE's Strategy for Plastics Innovation. We accomplish our work in the BOTTLE Consortium through an organizational framework that includes three primary research tasks, Deconstruction, Upcycling, and Redesign, which are supported by three cross-cutting tasks, Analysis, Characterization, and Modeling, BOTTLE also has tasks focused on Industry Engagement and Diversity, Equity, and Inclusion (DEI). This presentation will review the approach and management structure of BOTTLE, the importance of analysis-guided research, and the key metrics for carbon, economic, energy, and greenhouse gas emissions. In the FY21-FY23 period, BOTTLE has drafted and enacted a comprehensive DEI plan, assembled a world-class Technical Advisory Board (TAB) to provide constructive feedback on our performance, had our first in-person all-hands meeting in summer 2022, and on-boarded and off-boarded research activities based on active project management and analysis. From an impact perspective, BOTTLE researchers have published over 40 peer-reviewed manuscripts (many in leading journals), submitted >30 patent applications, and initiated 6 funds-in industry partnerships.

BIOMASS FUELS↗

Griffin-m

Griffin-m is a MOOSE-based reactor multiphysics application that streamlines the analysis of a variety of nuclear multiphysics simulations, including steady-state and transient radiation transport, core performance, fuel depletion, criticality and decay heat calculations, reprocessing and post-irradiation examination. This streamlining is accomplished via enhanced flexibility of the tools, uniform syntax in the MOOSE framework, dynamic linking of all relevant physics and a single point of execution. The design for flexible multi-physics, multi-radiation, multi-scheme tasks demands and ultimately makes Griffin-m a highly extendable code system. A software quality assurance (SQA) procedure is enforced during Griffin-m development. The Griffin-m version will be the main production version and it includes the MCC3 code, which was originally developed at Argonne National Laboratory to prepare cross sections for fast reactors.

Ortensi, Javier [Idaho National Laboratory (INL), ↗

Griffin: A Moose-based Reactor Multiphysics Application For Radiation Transport And Depletion Simulations

Griffin is a MOOSE-based reactor multiphysics application that streamlines the analysis of a variety of nuclear multiphysics applications, including steady-state and transient radiation transport, core performance, fuel depletion, criticality and decay heat calculations, reprocessing and post-irradiation examination. This streamlining is accomplished via enhanced flexibility of the tools, uniform syntax in the MOOSE framework, dynamic linking of all relevant physics and a single point of execution. The design for flexible multi-physics, multi-radiation, multi-scheme tasks demands and ultimately makes Griffin a highly extendable code system. A software quality assurance (SQA) procedure is enforced during Griffin development.

DeHart, MarkD.↗

UNESE Data Analysis - Disko Elm Gas Transport Characteristics (NA-22 Quarterly Report)

Two research papers describing gas transport studies in subsurface containment environments appropriate for underground nuclear explosions were revised and accepted for publication in the peer-reviewed journals, Nature – Scientific Reports and Journal of Geophysical Research. The Nature – Scientific Reports paper is a primary deliverable and describes the gas-transport experiment performed in P Tunnel (NNSS) and 1) subsequent analysis of field data as part of the UNESE program. The Journal of Geophysical Research paper describes an experiment, supported mainly by DARPA and led by researchers at Weston Geophysical and New Mexico Tech., with 2) analyses supported by this project to evaluate the ability of SF6 gas tracer to track xenon gas migration under conditions related to a previous UNESE experiment. Two new tasks consider 3) evaluation of detonation heating and multiphase flow on arrival of xenon at the surface and 4) the impact of surface or Langmuir adsorption of gases being transported through pores and along fractures.

58 GEOSCIENCES↗

Enhancing segmentation fairness through curriculum learning and progressive loss: a centralized and federated perspective on radiograph analysis

Bias in medical image segmentation can lead to unequal performance across demographic subgroups, raising concerns about fairness and reliability in clinical AI systems. While deep learning models have achieved high segmentation accuracy, ensuring equitable performance across race and gender remains a significant challenge, particularly in privacy-sensitive healthcare environments. This study investigates fairness-aware medical image segmentation for hip and knee radiographs using deep learning models evaluated in both centralized and Federated Learning (FL) settings. We introduce Curriculum Learning (CL) strategies and Progressive Loss (PL) functions to regulate sample difficulty during training. In addition, we propose two novel fairness-oriented federated learning algorithms, Federated Intersection over Union (FedIoU) and Federated Intersection over Union with Outlier Analysis (FedIoUoutlier). Experiments are conducted using multiple segmentation backbones and simulated multi-site data partitions derived from the Osteoarthritis Initiative dataset. Model performance is evaluated using Intersection over Union (IoU), IoU standard deviation, Skewed Error Ratio (SER), and Min-Max Disparity across race and gender subgroups. Statistical significance was verified using paired t-tests to compare per-sample IoU performance against baseline configurations. Across both hip and knee segmentation tasks, curriculum learning and progressive loss strategies consistently improved segmentation accuracy and reduced demographic performance disparities in centralized training. In federated settings, fairness-aware aggregation further enhanced performance. Notably, FedIoUoutlier combined with balanced curriculum learning and tiered progressive loss achieved the highest mean IoU while yielding the lowest SER and Min-Max Disparity, indicating improved fairness without sacrificing accuracy. In several configurations, federated models matched or exceeded the performance of optimized centralized models, with statistically significant improvements in per-sample IoU over baseline configurations. The results demonstrate that structured training strategies and fairness-aware federated aggregation can jointly improve accuracy, stability, and demographic fairness in medical image segmentation. By integrating curriculum learning, progressive loss, and novel FL algorithms, this work provides a practical pathway toward equitable and privacy-preserving AI systems for medical imaging.

97 MATHEMATICS AND COMPUTING↗

Representation Learning via Quantum Neural Tangent Kernels

Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear. Here we discuss these problems, analyzing variational quantum circuits using the theory of neural tangent kernels. We define quantum neural tangent kernels, and derive dynamical equations for their associated loss function in optimization and learning tasks. We analytically solve the dynamics in the frozen limit, or lazy training regime, where variational angles change slowly and a linear perturbation is good enough. We extend the analysis to a dynamical setting, including quadratic corrections in the variational angles. We then consider a hybrid quantum classical architecture and define a large-width limit for hybrid kernels, showing that a hybrid quantum classical neural network can be approximately Gaussian. The results presented here show limits for which analytical understandings of the training dynamics for variational quantum circuits, used for quantum machine learning and optimization problems, are possible. These analytical results are supported by numerical simulations of quantum machine-learning experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗