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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Revealing the Structure and Dynamics of Self-Generated Electric and Magnetic Fields Near Plasma Stagnation in Laser-Driven Hohlraums

By coupling newly developed triparticle charged particle radiography with radiography reconstruction algorithms and novel reconstruction postprocessing techniques, the spatial structure and time evolution of self-generated electric and magnetic fields in laser-driven vacuum hohlraums have been quantitatively revealed. Through high-fidelity data from a series of experiments, it is shown that late in the hohlraum evolution (after the end of laser drive) these fields are strongly correlated in both space and time, providing evidence that their evolution is primarily dominated by advection with the plasma flow. At these late times, plasma flow velocities inferred from both gross radiography analysis and field reconstructions (and corroborated with Thomson scattering measurements) indicate that the plasma is approaching stagnation near the hohlraum axis. Finally, these experiments provide not only new physical insight into spontaneously generated hohlraum fields, but also provide important spatially and temporally resolved information for future benchmarking of numerical codes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Two-dimensional coherent spectrum of high-spin models via a quantum computing approach

Here in this work we present and benchmark a quantum computing approach to calculate the two-dimensional coherent spectrum (2DCS) of high-spin models. Our approach is based on simulating their real-time dynamics in the presence of several magnetic field pulses, which are spaced in time. We utilize the adaptive variational quantum dynamics simulation algorithm for the study due to its compact circuits, which enables simulations over sufficiently long times to achieve the required resolution in frequency space. Specifically, we consider an antiferromagnetic quantum spin model that incorporates Dzyaloshinskii-Moriya interactions and single-ion anisotropy. The obtained 2DCS spectra exhibit distinct peaks at multiples of the magnon frequency, arising from transitions between different eigenstates of the unperturbed Hamiltonian. By comparing the one-dimensional coherent spectrum with 2DCS, we demonstrate that 2DCS provides a higher resolution of the energy spectrum. We further investigate how the quantum resources scale with the magnitude of the spin using two different binary encodings of the high-spin operators: the standard binary encoding and the Gray code. At low magnetic fields both encodings require comparable quantum resources, but at larger field strengths the Gray code is advantageous. Numerical simulations for spin models with increasing number of sites indicate a polynomial system-size scaling for quantum resources. Lastly, we compare the numerical 2DCS with experimental results on a rare-earth orthoferrite system. The observed strength of the magnonic high-harmonic generation signals in the 2DCS of the quantum high-spin model aligns well with the experimental data, showing significant improvement over the corresponding mean-field results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A Performance Portable, Fully Implicit Landau Collision Operator with Batched Linear Solvers

Modern accelerators use hierarchical parallel programming models that enable massive multithreading within a processing element (PE), with multiple PEs per device driven by traditional processes. Batching is a technique for exposing PE-level parallelism in algorithms that have traditionally run on MPI processes or multiple threads within a single process. Opportunities for batching arise in, for example, kinetic discretizations of magnetized plasmas where collisions are advanced in velocity space at each spatial point independently. This paper builds on previous work on a high-performance, fully nonlinear, Landau collision operator by batching the linear solver, as well as batching the spatial point problems and adding new support for multiple grids for multiscale, multispecies problems. An anisotropic relaxation verification test that agrees well with previously published results and analytical models is presented. The performance results from NVIDIA A100 and AMD MI250X nodes are presented with hardware utilization analysis for each architecture. Finally, the entire implicit Landau operator time advance is implemented in Kokkos for performance portability, running entirely on the device and is available in the PETSc numerical library.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Hardware-Efficient Quantum Phase Estimation via Local Control

Quantum phase estimation plays a central role in quantum simulation as it enables the study of spectral properties of many-body quantum systems. Most variants of the phase estimation algorithm require the application of the global unitary evolution conditioned on the state of one or more auxiliary qubits, posing a significant challenge for current quantum devices. In this work, we present an approach to quantum phase estimation that uses only locally controlled operations, resulting in a significantly reduced circuit depth. At the heart of our approach are efficient routines to measure the complex phase of the expectation value of the time-evolution operator, the so-called Loschmidt echo, for both circuit dynamics and Hamiltonian dynamics. By tracking changes in the phase during the dynamics, the routines trade circuit depth for increased sampling cost and classical postprocessing. Our approach does not rely on reference states and is applicable to any efficiently preparable state, regardless of its correlations. We provide a comprehensive analysis of the sample complexity and illustrate the results with numerical simulations. Our methods offer a practical pathway for measuring spectral properties in large many-body quantum systems using current quantum devices.

Schiffer, Benjamin F. [Max Planck Institute of Qua↗
DOE OSTI2025

Automated nuclear cloud feature extraction from film

Chemical, biological, radiological, nuclear, and explosives incidents require rapid detection and characterization for appropriate response. For a nuclear detonation, visible-light cameras may be used to locate the cloud and characterize fallout deposition when coupled with numerical models. Films from the United States’ nuclear testing era compose the only sizeable collection of imagery depicting high-yield detonations. These films offer unique insights into characteristics of flows involving scales that are difficult to replicate experimentally, and they are a valuable source of data for the validation of models for nuclear fallout transport, either as part of emergency response or forensic activities. In this work, we implement modern computer vision and machine learning techniques to identify and track the cloud automatically and subsequently determine the time dependence of some of its features. We trained a ResNet-18 image classifier on hundreds of images to categorize nuclear cloud morphology. Each category or cloud regime is determined by early cloud evolution and is associated to constitutive properties of the flow, such as distribution of vorticity. Next, we identified keypoint features using the KAZE algorithm and tracked these keypoints in the images, allowing us to determine the dimensions and velocities of the cloud across film frames. These measurements converted to real-world units provide valuable experimental data that can be used in the development and validation of nuclear cloud models. We compared the results of this method against manual cloud rise measurements from two different films. In one, our automated method accelerated the feature extraction process without sacrificing measurement accuracy.

Khristy, Joel [ORNL] (ORCID:0000000209963060)↗
DOE OSTI2026

PyJMAK: An Open-Source Python Toolkit for Modeling Solid-State Metallurgical Phase Transformations

Accurate prediction of metallurgical phase transformations is an essential basis for autonomous optimization and rapid part qualification. Several methods can be used to estimate the evolution of phase fractions such as JMAK kinetics-based models, phase-field models, thermodynamic models, and data-driven machine learning models. Thermodynamic and phase-field-based methodologies solve multiphysics equations requiring numerous calibration parameters and significant computational resources. As a result, the computation domain is limited to a point or on order of micron-meters. The data-driven models rely on large datasets from experiments and simulations. While the JMAK model only provides information about phase fraction evolution, it can predict this evolution in near real-time using thermal history and thermodynamic data without restriction on the domain. JMAK models have been popularly used by researchers to model phase transformations occuring during additive manufacturing or over arbitrary temperature profiles. Commercial proprietary software such as Abaqus and Ansys or closed-source in-house implementations offer the ability to model JMAK based kinetics to predict phase transformation. However, these software packages are not open-source or freely available for use and development in conjunction with manufacturing machines, sensors, and machine learning algorithms. In addition, the use of the model is restricted by a license token. In contrast, given temperature profiles at multiple points in the domain, this Python-based PyJMAK model can compute phase evolution in parallel due to its stand-alone modular, voxel-based structure, and it can be executed on high-performance computing resources without any license restrictions.

Prabhune, Bhagya [Oak Ridge National Laboratory (O↗
DOE OSTI2024

Temperature-dependent mechanical properties and crystal plasticity parameters for additively manufactured Haynes-214 alloy: Experiments and numerical modeling

Our experimental mechanical testing data demonstrated that the additively manufactured (AM) laser powder bed fusion (L-PBF) Haynes-214 alloy exhibits non-linear mechanical properties as the temperature rises from ambient to 870 °C. Crystal plasticity (CP) simulations provide an effective approach to gaining deeper insights into microstructure-property linkages under thermomechanical loading. This method can reduce the need for costly high-temperature mechanical testing while accounting for the effects of crystallographic texture and grain morphology on the mechanical behavior of AM materials. However, calibrating a CP model is time-consuming because individual simulations are computationally expensive and hundreds (or more) of iterations over parameter sets may be required. To address this issue, we have designed a machine learning-differential evolution (ML-DE) CP framework that can accurately interpolate the tensile properties of AM L-PBF Haynes-214 alloy across a wide temperature range from ambient to 870 °C, with minimal reliance on experimental data. The framework uses electron backscatter diffraction (EBSD) measurements to generate statistically equivalent microstructural volume elements to serve as inputs to the CP modeling framework. Stress–strain curves were generated from 1000 CP simulations, which serve as the training data set for the three ML regression algorithms explored: linear, extra-trees, and multi-layer perceptron. These three regression models were independently evaluated to compare their efficiency and identify the most suitable algorithm for the given problem. Results revealed that the extra-trees ML regressor outperforms the other models in both qualitative and quantitative aspects with an R 2 of 0.98. Subsequently, the differential evolution optimization approach is employed to calibrate the ML-based CP material parameters with experimental results obtained at various temperatures. Finally, temperature-dependent CP material parameters are formulated. The effectiveness and efficiency of the designed framework are validated through comparison with experimental results, demonstrating a high degree of agreement. These calibrated parametric constitutive equations enable further use of the CP model to study the deformation behavior of this alloy under a wide range of thermo-mechanical loading conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Safety in Artificial Intelligence: Challenges and Opportunities for the U.S. National Labs and Beyond

This report discusses the importance of the critical and underexplored topic of artificial intelligence (AI) safety, as highlighted during the “Strategy Alignment on AI Safety” workshop convened at Lawrence Livermore National Laboratory (LLNL) in April 2024. Through a summary of keynote talks, panel discussions, and breakout sessions, world-leading AI safety experts from academic, industry, national labs, and government agencies clearly agree on the need for and importance of large-scale investments for research and capabilities in AI safety. With the field innovating at unprecedented rates, there is increasing urgency to develop novel evaluation methodologies that allow full considerations of risks/threats of AI technologies in different domains. Quantitative metrics and effective methodologies that can evaluate and audit the “safeness” of how a given AI technology is trained, deployed, or regulated are, at best, nascent for certain scenarios or, more commonly, nonexistent. This maturation gap presents the possibility of serious threats to national security, and further inaction may have serious consequences. Additionally, the gap between the public’s and research community’s perceptions of AI risks/rewards is significant. While numerous voices from the AI community have expressed concern that the risks could be so high that future AI systems could inflict extinction-level damage to humanity if deployed incorrectly, the public largely is aware only of risk in low-impact scenarios. This discrepancy highlights the crucial need for researchers to articulate to governmental bodies what, why, and when various AI risks matter as part of motivating funding requests. Thus, the call to action for this community is to pursue AI safety as a “Big Science” project on a scale comparable to the Manhattan Project. High risks and high payoffs are on the table, but safe AI is a fast-moving target, and large-scale investments are needed to guide development of this technology in a responsible way. We highlight the need for a multilayered solution combining the development of new methods and algorithmic approaches to mitigate threats with an active participation of the government(s) in setting high industry standards and regulations based on state-of-the-art technology. The U.S. Department of Energy (DOE) national laboratories have served as leading institutions for scientific innovation in the U.S. for more than 70 years. Drawing on their expertise in the AI community and their history of safeguarding critical and sensitive information, and as we look to the future, national labs are the best choice for evaluating and safeguarding AI technologies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Self Consistent 2D Simulation of Coherent Synchrotron Radiation Effects on Beam Dynamics

An increasing interest in high quality and high current electron beams necessitates a thorough understanding and prediction of coherent synchrotron radiation effects. The self-interaction of charged particles in a beam undergoing synchrotron motion is a physically significant process that is all too often computationally intensive with very little analytical results to rely on for the general case. The coherent spectrum of this interaction is of utmost importance to the design of free electron lasers (FELs) and an accurate assessment is imperative for their design. This work presents a novel implementation to the numerical simulation of charged particle beams. The simulation is a self-consistent approach including the self-fields generated by the beam of which coherent synchrotron radiation effects are of primary interest. A particle-in-cell model is used where a planar beam sampled by point particles is deposited on an encompassing grid at each timestep. The electromagnetic fields are calculated on the grid using the retarded potentials according to causality. The electromagnetic forces from the fields are interpolated on each particle which in turn advance in time. The simulation is benchmarked against well-established results for coherent synchrotron radiation effects. In addition, studies are provided that show the convergence of simulation results for increasing resolution. A study into the transverse beam size effects on beam dynamics is performed as well as a proof of concept where the simulation is used by a genetic algorithm to optimize the design parameters of a beam lattice. The results of these studies in tandem verify the efficacy of the simulation for its practical use in accelerator design or the study of synchrotron radiation effects

Duffin, Dallan [Old Dominion Univ., Norfolk, VA (U↗
DOE OSTI2024

Learning Functions Varying along a Central Subspace

Many functions of interest are in a high-dimensional space but exhibit low-dimensional structures. This paper studies regression of an s-Hölder function in $R^D$ which varies along a central subspace of dimension $d$ while $d \ll D$. A direct approximation of $f$ in $R^D$ with an accuracy $\varepsilon$ requires the number of samples in the order of $\varepsilon^{-(2s+D)/s}$. In this paper, we analyze the generalized contour regression (GCR) algorithm for the estimation of the central subspace and use piecewise polynomials for function approximation. GCR is among the best estimators for the central subspace, but its sample complexity is an open question. In this paper, we partially answer this questions by proving that if a variance quantity is exactly known, GCR leads to a mean squared estimation error of $O(n^{-1})$ for the central subspace. The estimation error of this variance quantity is also given in this paper. The mean squared regression error of $f$ is proved to be in the order of $(n/\log n)^{-\frac{2s}{2s+d}}$, where the exponent depends on the dimension of the central subspace instead of the ambient space . This result demonstrates that GCR is effective in learning the low-dimensional central subspace. We also propose a modified GCR with improved efficiency. Here, the convergence rate is validated through several numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Application of a Physics-Informed Convolutional Neural Network for Monitoring the Temperature Fields in High-Temperature Gas Reactors

Here, this work presents current advances in applying a physics-informed convolutional neural network (CNN) to evaluate temperature distributions in advanced reactors. Our goal is to demonstrate that the CNN can reconstruct temperature fields within the solid region of a prismatic fuel assembly in a high-temperature gas reactor (HTGR) with sensor data available in only a few cooling channels. Before that, we showcase the superior performance of the physics-informed CNN in comparison to a purely data-driven multilayer perceptron (MLP), considering a canonical heated channel setup. This analysis shows the advantages of our approach and justifies its choice. The datasets employed here are obtained upon numerical simulations performed with codes under the Nuclear Energy Advanced Modeling and Simulation program. This work is important, as industry experience indicates that the assembly material in HTGR concepts is prone to large thermal-mechanical loads nearing operational limits. This makes it crucial to characterize peak temperatures and their distributions near hot spots. Modern thermocouples are unreliable in these types of harsh environments because of the high neutron fluxes and elevated temperatures involved. The CNN-based field reconstruction represents an attractive solution, enabling sensor arrays in less aggressive locations and augmenting indirect predictions for less accessible regions. The results show that the CNN reduces prediction errors by orders of magnitude in comparison to the MLP, considering the simple yet well-representative heated channel case. In the case of the HTGR fuel assembly, the CNN can successfully reconstruct temperature fields over various cooling regimes. Furthermore, we also explore the algorithm’s ability to detect abnormalities. Interestingly, the CNN proves it has the capacity to detect blockage in one of the noninstrumented cooling channels.

Machine learning↗
DOE OSTI2024

Digital Analytics, Causal Knowledge Acquisition and Reasoning for Technical Language Processing

Complex engineering systems such as nuclear power plants (NPPs) generate and collect large amounts of equipment reliability (ER) data elements that contain information on the status of components, assets, and systems. Some of this information is textual in form and can be found in documents such as incident reports (IRs) and work orders (WOs). Analyses of textual data in current NPPs-using natural language processing (NLP) methods-have been expanded over the last decade, and it is only recently that the true potential of such analyses has emerged. So far, applications of NLP methods have mostly been limited to classification and prediction, the goal being to identify the nature of the textual element (e.g., safety or non-safety related). Here, we target a more complex problem: automatically extracting knowledge from a textual element in order to assist system engineers in conducting system health assessments. Knowledge extraction is a very broad concept, and its definition may vary depending on the application context. Our methods are a blend of both rule-based and machine learning (ML) algorithms. For our purposes, knowledge extraction means identifying the systems or assets mentioned in a given textual element, as well as the type of event described (e.g., component failure or maintenance activity). In addition, we want to capture details such as measured quantities and the temporal/cause-effect relations between events. In this tool, we also demonstrate how textual data elements are preprocessed in order to handle typos, acronyms, and abbreviations. One main feature of these methods is that they are not based solely on data, but are in fact model-based. In other words, they also rely on MBSE models that are designed to capture-from a functional point of view-the architecture of the systems/assets under consideration. The main purpose of such models is to digitally emulate system engineers' knowledge of system and asset architecture and to identify dependencies among systems, assets, and components. Provided these models, analyses of textual and numeric ER data can be performed by first identifying the OPM model elements to which the ER data elements are referring. The relationships between ER data elements are then identified by checking for any temporal or logical dependencies.

Mandelli, Diego [Idaho National Laboratory (INL), ↗
DOE OSTI2024

Robustness of neutron star merger simulations to changes in neutrino transport and neutrino-matter interactions

Binary neutron star mergers play an important role in nuclear astrophysics: Their gravitational wave and electromagnetic signals carry information about the equation of state of cold matter above nuclear saturation density, and they may be one of the main sources of r-process elements in the Universe. Neutrino-matter interactions during and after merger impact the properties of these electromagnetic signals and the relative abundances of the produced r-process elements. Existing merger simulations are, however, limited in their ability to realistically model neutrino transport and neutrino-matter interactions. Here, we perform a comparison of the impact of the use of state-of-the art two-moment or Monte Carlo transport schemes on the outcome of merger simulations, for a single binary neutron star system with a short-lived neutron star remnant [(5–10) ms]. We also investigate the use of different reaction rates in the simulations. While the best transport schemes generally agree well on the qualitative impact of neutrinos on the system, differences in the behavior of the high-density regions can significantly impact the collapse time and the properties of the hot tidal arms in this metastable merger remnant. The chosen interaction rates and transport algorithm as well as recent improvements by Radice et al. to the two-moment algorithms can all contribute to changes at the (10–30)% level in the global properties of the merger remnant and outflows. Furthermore, the limitations of previous moment schemes fixed by Radice et al. also appear sufficient to explain the large difference that we observed in the production of heavy-lepton neutrinos in a previous comparison of Monte Carlo and moment schemes in the context of a low-mass binary neutron star system.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Counterdiabatic Driving with Performance Guarantees

Counterdiabatic (CD) driving has the potential to speed up adiabatic quantum state preparation by suppressing unwanted excitations. However, existing approaches either require intractable classical computations or are based on approximations that do not have performance guarantees. We propose and analyze a nonvariational, system-agnostic CD expansion method and analytically show that it converges exponentially quickly in the expansion order. In finite systems, the required resources scale inversely with the spectral gap, which we argue is asymptotically optimal. To extend our method to the thermodynamic limit and suppress errors stemming from high-frequency transitions, we leverage finite-time adiabatic protocols. In particular, we show that a time determined by the quantum speed limit is sufficient to prepare the desired ground state, without the need to optimize the adiabatic trajectory. Numerical tests of our method on the quantum Ising chain show that our method can outperform state-of-the-art variational CD approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Peer-to-peer communication control for resilient operations of networked cyberphysical systems

This report includes two main accomplishments of the peer-to-peer communication control for resilient operation of networked microgrids project in FY24, which include a scheme for cyberattack-aware coordination of networked microgrids for supporting voltages of bulk power systems and a scheme for price signal-based operations of EV-rich networked microgrids with mixed ownership. First, the cyberattack-aware scheme enables networked microgrids to distributedly determine the amount of reactive power injection to support the voltage of bulk power system (BPS) in a fair manner. In this scheme, a risk-informed algorithm is presented to generate the peer-to- peer (P2P) communication graph with minimal risk of attack on communication links. To deal with cyberattacks on MG controllers, the resilient consensus algorithm (CA) is utilized for MG controllers to robustly estimate the total reactive power headroom, from which the MGs can accurately provide the needed amount of reactive power injection for supporting the voltage of BPS. The CA implementation and performance within the P2P communication framework are demonstrated on the IEEE 39-bus system with 6 microgrids contained in the distribution feeder under different cyberattack scenarios. Second, the price-based scheme enables the usage of the real-time price signal for the operations of electric vehicle (EV)-rich networked-microgrids with mixed ownership, in which not all the microgrids can communicate with the distribution system operator (DSO). In this scheme, a max consensus is introduced to enable the real-time price signal to be propagated from the DSO to all the microgrids, from which each microgrid controller will manage the DERs to balance the load demand and the power injection from the EV charging stations within its microgrid. Numerical results over one day with 288 slots of 5-minute intervals on the modified 123-node test feeder including 3 microgrids with high penetration of EV are presented to evaluate how the price signal affects the operations of networked microgrids under different charging strategies of the EV charging stations. The result indicates that our proposed EVCS (dis)charging strategy, which leverages the flexibility of EVs to support the grid through discharging during peak demand, proves to be a cost-effective solution that reduces operational costs while improving the social welfare of EV charging.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Quantum-Inspired Bayesian Sampling for Uncertainty Quantification and Machine Learning (Final Technical Report)

With increasing simulation and measurement data, machine learning and artificial intelligence have been widely used in computational decision-making of complex engineering systems. The resulting tools, such as uncertainty quantification solvers, reinforcement learning, and physics-informed machine learning, have achieved great success in critical DOE tasks such as material discovery and design, energy system modeling and control, and numerical weather and climate prediction. A core topic in scientific machine learning and artificial intelligence is Bayesian inference: given an observed data set, people want to estimate the posterior distribution of a (possibly large) number of hidden parameters. Due to the flexibility and weak assumptions, Bayesian sampling has been the mainstream Bayesian inference solvers despite the rapid progress of approximate Bayesian inference. Classical Bayesian sampling methods such as Markov-chain Monte Carlo suffer from a low-acceptance rate due to the random walk nature, therefore state-of-the-art techniques use Hamiltonian Monte Carlo and its variants to efficiently draw posterior samples in a high dimension. The key idea of Hamiltonian Monte Carlo and its variants is to simulate the Hamiltonian dynamics of a classical particle with a fixed mass, and their performance significantly degrades when the posterior distribution is highly spiky or has multiple modes. Leveraging the idea of quantum physics, this project has investigated new theory, algorithms and applications of Bayesian inference (especially Bayesian sampling). The main results include: (1) novel quantum-inspired Bayesian sampling methods that can lead to better accuracy for challenging multi-modal or spiky distributions, (2) more scalable machine learning framework leveraging tensor-compressed Bayesian inference, and (3) Bayesian and sampling approaches for verifying the robustness of continuous and binary neural networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Theory for Equivariant Quantum Neural Networks

Quantum neural network architectures that have little to no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by creating models encoding the symmetries of the learning task. This is materialized through the usage of equivariant neural networks the action of which commutes with that of the symmetry. In this work, we import these ideas to the quantum realm by presenting a comprehensive theoretical framework to design equivariant quantum neural networks (EQNNs) for essentially any relevant symmetry group. We develop multiple methods to construct equivariant layers for EQNNs and analyze their advantages and drawbacks. Our methods can find unitary or general equivariant quantum channels efficiently even when the symmetry group is exponentially large or continuous. As a special implementation, we show how standard quantum convolutional neural networks (QCNNs) can be generalized to group-equivariant QCNNs where both the convolution and pooling layers are equivariant to the symmetry group. We then numerically demonstrate the effectiveness of a S U ( 2 ) -equivariant QCNN over symmetry-agnostic QCNN on a classification task of phases of matter in the bond-alternating Heisenberg model. Our framework can be readily applied to virtually all areas of quantum machine learning. Lastly, we discuss about how symmetry-informed models such as EQNNs provide hopes to alleviate central challenges such as barren plateaus, poor local minima, and sample complexity. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Local conservation of energy in fully implicit PIC algorithms

We consider the issue of strict, fully discrete local energy conservation for a whole class of fully implicit local-charge- and global-energy-conserving particle-in-cell (PIC) algorithms. Earlier studies demonstrated these algorithms feature strict global energy conservation. However, whether a local energy conservation theorem exists (in which the local energy update is governed by a flux balance equation at every mesh cell) for these schemes is unclear. In this study, we show that a local energy conservation theorem indeed exists. We begin our analysis with the 1D electrostatic PIC model without orbit-averaging, and then generalize our conclusions to account for orbit averaging, multiple dimensions, and electromagnetic models (Darwin). In all cases, a temporally, spatially, and particle-discrete local energy conservation theorem is shown to exist, proving that these formulations (as originally proposed in the literature), in addition to being locally charge conserving and globally energy conserving, are strictly locally energy conserving as well. In contrast to earlier proofs of local conservation in the literature, which only considered continuum time, our result is valid for the fully implicit time-discrete version of all models considered, including important features such as orbit averaging. We demonstrate the local-energy-conservation property numerically with a paradigmatic numerical example.

97 MATHEMATICS AND COMPUTING↗