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At least 559 records · Page 31

Improved machine learning algorithm for predicting ground state properties

Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding geometric locality. The proposed ML model can efficiently predict ground state properties of an n-qubit gapped local Hamiltonian after learning from only $\mathcal{O}$(log(n)) data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require $\mathcal{O}$(n c ) data for a large constant c. Furthermore, the training and prediction time of the proposed ML model scale as $\mathcal{O}$(n log n) in the number of qubits n. Numerical experiments on physical systems with up to 45 qubits confirm the favorable scaling in predicting ground state properties using a small training dataset.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Efficient and universal characterization of atomic structures through a topological graph order parameter

Abstract A graph-based order parameter, based on the topology of the graph itself, is introduced for the characterization of atomistic structures. The order parameter is universal to any material/chemical system and is transferable to all structural geometries. Four sets of data are used to validate both the generalizability and accuracy of the algorithm: (1) liquid lithium configurations spanning up to 300 GPa, (2) condensed phases of carbon along with nanotubes and buckyballs at ambient and high temperature, (3) a diverse set of aluminum configurations including surfaces, compressed and expanded lattices, point defects, grain boundaries, liquids, nanoparticles, all at nonzero temperatures, and (4) eleven niobium oxide crystal phases generated with ab initio molecular dynamics. We compare our proposed method to existing, state-of-the-art methods for the cases of aluminum and niobium oxide. Our order parameter uniquely classifies every configuration and outperforms all studied existing methods, opening the door for its use in a multitude of complex application spaces that can require fine structure-level characterization of atomistic graphs.

36 MATERIALS SCIENCE↗

Sampling frequency thresholds for the quantum advantage of the quantum approximate optimization algorithm

We compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers Gurobi and MQLib to solve the MaxCut problem on 3-regular graphs. We identify the minimum noiseless sampling frequency and depth p required for a quantum device to outperform classical algorithms. There is potential for quantum advantage on hundreds of qubits and moderate depth with a sampling frequency of 10 kHz. We observe, however, that classical heuristic solvers are capable of producing high-quality approximate solutions in linear time complexity. In order to match this quality for large graph sizes N, a quantum device must support depth p > 11. Additionally, multi-shot QAOA is not efficient on large graphs, indicating that QAOA p ≤ 11 does not scale with N. These results limit achieving quantum advantage for QAOA MaxCut on 3-regular graphs. Other problems, such as different graphs, weighted MaxCut, and 3-SAT, may be better suited for achieving quantum advantage on near-term quantum devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Three-State Majority-vote Model on Scale-Free Networks and the Unitary Relation for Critical Exponents

Abstract We investigate the three-state majority-vote model for opinion dynamics on scale-free and regular networks. In this model, an individual selects an opinion equal to the opinion of the majority of its neighbors with probability 1 − q , and different to it with probability q . The parameter q is called the noise parameter of the model. We build a network of interactions where z neighbors are selected by each added site in the system, a preferential attachment network with degree distribution k − λ , where λ = 3 for a large number of nodes N . In this work, z is called the growth parameter. Using finite-size scaling analysis, we obtain that the critical exponents $$\beta /\bar{\nu }$$ β / ν ¯ and $$\gamma /\bar{\nu }$$ γ / ν ¯ associated with the magnetization and the susceptibility, respectively. Using Monte Carlo simulations, we calculate the critical noise parameter q c as a function of z for the scale-free networks and obtain the phase diagram of the model. We find that the critical exponents add up to unity when using a special volumetric scaling, regardless of the dimension of the network of interactions. We verify this result by obtaining the critical noise and the critical exponents for the two and three-state majority-vote model on cubic lattice networks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Re-evaluation of the TSL for Yttrium Hydride

Yttrium hydride (YH x ) is of interest as a high-temperature moderator material in advanced nuclear reactor systems because of its superior ability to retain hydrogen at elevated temperatures. Thermal neutron scattering laws (TSL) for hydrogen bound in yttrium hydride (H-YH 2 ) and yttrium bound in yttrium hydride (Y-YH 2 ) were previously evaluated by Naval Nuclear Laboratory using the ab initio approach and released in ENDF/B-VIII.0. In that work, density functional theory, incorporating the generalized gradient approximation (GGA) for the exchange-correlation energy, was used to simulate the face-centered cubic structure of YH 2 and calculate the interatomic Hellmann-Feynman forces for a 2×2×2 supercell containing 96 atoms. Lattice dynamics calculations using PHONON were used to determine the phonon density of states. The calculated phonon density of states for H and Y in YH 2 were then used to prepare H-YH 2 and Y-YH 2 TSL evaluations, in the incoherent approximation, using the LEAPR module of NJOY. In addition, elastic scattering was assumed to be incoherent for both H and Y. While the incoherent elastic scattering approximation is appropriate for H-YH 2 , it introduces an undesirable approximation for Y-YH 2 . In this work, we re-evaluate the TSL for Y-YH 2 using FLASSH (Full Law Analysis Scattering System Hub). Y-YH 2 is evaluated using the FLASSH generalized coherent elastic scattering capability in order to capture the Bragg peaks associated with the YH 2 crystal structure which were neglected in the prior NJOY-based evaluation due to limitations in LEAPR. An experimental approach to validate the Y-YH 2 TSL using neutron transmission measurements is discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Using Prompt Neutron Decay Constant Measurements to Obtain Additional Kinetics Information

Prompt neutron decay constant measurements are typically used to infer the prompt neutron lifetime in a chain-reacting system, but these measurements include much more information about the kinetics of the system. This work focuses specifically on the Rossi-α method of measuring the prompt neutron decay constant. The Rossi-α system of equations consists of five unknown parameters. With five unknowns and three equations, the system of equations solved by the Rossi-α measurement is under-determined. It has been postulated that a well posed problem can be formulated using independent measurement configurations on a single system. The external source strength, the effective delayed neutron fractions, and Diven’s parameter do not typically change for different configurations of a single experiment. If good detector geometry is chosen, the detector efficiency does not change for multiple measurements of a single experiment using Rossi-α measurements. By making these assumptions, there are only two unique variables. This knowledge can be used to solve for most of the unique parameters using two independent, unique Rossi-α measurements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Bayesian Monte Carlo Evaluation of Imperfect (n, 233 U) Data and Model

Conventional nuclear data evaluation methods using generalized linear least squares make the following assumptions: prior and posterior probability distribution functions (PDFs) of all model parameters and data are normal (Gaussian); the linear approximation is sufficiently accurate to minimize the cost function (even for nonlinear models); the model (e.g., of neutron cross section) and experimental data (including covariance data) are without defect and prior PDFs of parameters and measured data are known perfectly. Neglect of covariance between model parameters and measured data in conventional evaluations contributes to imperfections. These assumptions are inherent to the generalized linear least squares minimization method commonly used for resolved resonance region neutron cross section evaluations but are often not justified due to the presence of non-normal PDFs, nonlinear models (e.g., R-matrix formalism), and inherent imperfections in data and models (e.g., imperfect covariance data). Here, these assumptions are removed in a mathematical framework of Bayes’ theorem, which is implemented using the Metropolis-Hastings Monte Carlo method. Most importantly, new parameters are introduced to parameterize discrepancies between the theoretical model and measured data to quantify judgement about discrepancies or imperfections in a reproducible manner. An evaluation of 233U in the eV region using the ENDF-B/VIII.0 library and transmission data (Guber et al.) is presented, and posterior parameters are compared to those obtained by conventional evaluation methods. This example illustrates the effects of removing the most harmful assumption: that of model-data perfection.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Resolved Resonance Region Analysis of 206 Pb, 207 Pb, and 208 Pb for Next Generation Lead-Cooled Fast Systems

Recently, great interest has been generated in using lead as a coolant for fast neutron systems and as a result it is important to investigate the ENDF/B-VIII.0 isotopic evaluations that comprise stable le ad. To this end, resonance parameters for 206 Pb, 207 Pb, and 208 Pb were re-evaluated because their resolved reso­nance regions extend beyond 0.5 MeV meaning resonance parameters used in reconstructing cross sections and elastic scattering angular distributions impact fast systems. The impact of resonance parameters is demon­strated by the differences between the evaluations in predicting experimental results from the fully modeled RPI Quasi-Differential Scattering Experiment via MCNPv6.2. In addition, MCNP KCODE calculations of lead-sensitive fast spectra critical benchmarks showed variations of keff on average of 400 pcm, caused solely from differences in elastic scattering angular distributions in 208 Pb. Re-evaluation entailed fitting data with the program SAMMY.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Extended Lagrangian Born–Oppenheimer molecular dynamics using a Krylov subspace approximation

It is shown how the electronic equations of motion in extended Lagrangian Born–Oppenheimer molecular dynamics simulations can be integrated using low-rank approximations of the inverse Jacobian kernel. This kernel determines the metric tensor in the harmonic oscillator extension of the Lagrangian that drives the evolution of the electronic degrees of freedom. The proposed kernel approximation is derived from a pseudoinverse of a low-rank estimate of the Jacobian, which is expressed in terms of a generalized set of directional derivatives with directions that are given from a Krylov subspace approximation. The approach allows a tunable and adaptive approximation that can take advantage of efficient preconditioning techniques. The proposed kernel approximation for the integration of the electronic equations of motion makes it possible to apply extended Lagrangian first-principles molecular dynamics simulations to a broader range of problems, including reactive chemical systems with numerically sensitive and unsteady charge solutions. This can be achieved without requiring exact full calculations of the inverse Jacobian kernel in each time step or relying on iterative non-linear self-consistent field optimization of the electronic ground state prior to the force evaluations as in regular direct Born–Oppenheimer molecular dynamics. We note the low-rank approximation of the Jacobian is directly related to Broyden’s class of quasi-Newton algorithms and Jacobian-free Newton–Krylov methods and provides a complementary formulation for the solution of nonlinear systems of equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Lowest-dimensional portals to SU( N ) exotics

New matter fields charged under the strong nuclear force would have dramatic phenomenological implications. In this work, we systematically explore how these new states, which we postulate belong to some representation of SU(3) of quantum chromo-dynamics, could interact with standard model fields: We analyze all lowest-dimensional “portal” operators for any SU(3) representation, and motivated by grand unification, we extend our results to SU( N ) for N > 3. We provide a publicly available python code, “tessellation,” that automatically constructs said lowest-dimensional portal operators for any new exotic matter field charged under SU( N ) for any N .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Impact of Numerical Hydrodynamics in Turbulent Mixing Transition Simulations

Underresolved simulations are unavoidable in high Reynolds (Re) and Mach (Ma) number turbulent flow applications at scale. Implicit large-Eddy simulation (ILES) often becomes the effective strategy to capture the dominating effects of convectively driven flow instabilities. We evaluate the impact of three distinct numerical strategies in simulations of transition and turbulence decay with ILES: the Harten–Lax–van Leer (HLL) Riemann solver applying Strang splitting and a Lagrange-plus-Remap formalism to solve the directional sweep—denoted split; the Harten–Lax–Van Leer-Contact (HLLC) Riemann solver using a directionally unsplit strategy and parabolic reconstruction—denoted unsplit; and the HLLC Riemann solver using unsplit and a low-Ma correction (LMC)—denoted unsplit*. Three case studies are considered: (1) a shock tube problem prototyping shock-driven turbulent mixing, (2) the Taylor–Green Vortex (TGV) prototyping transition to turbulence, and, (3) an homogeneous isotropic turbulence (HIT) case, focusing on the impact of discretization on transition and decay from fixed well-characterized initial conditions. Significantly more accurate predictions are provided by the unsplit schemes, in particular, when augmented with the LMC. For given resolution, only the unsplit schemes predict the turbulent mixing transition after reshock observed in the shock tube experiments. Relevant comparisons of ILES based on Euler and Navier–Stokes equations addressing potential occurrence of low-Re regimes in the applications are presented. Unsplit schemes are instrumental in allowing to capture the spatial development of the TGV flow and its validation at prescribed Re with significantly less resolution. HIT analysis confirms higher simulated turbulence Re and increased small-scale content associated with the unsplit discretizations.

74 ATOMIC AND MOLECULAR PHYSICS↗

Investigating boosted decision trees as a guide for inertial confinement fusion design

Inertial confined fusion experiments at the National Ignition Facility have recently entered a new regime approaching ignition. Improved modeling and exploration of the experimental parameter space were essential to deepening our understanding of the mechanisms that degrade and amplify the neutron yield. The growing prevalence of machine learning in fusion studies opens a new avenue for investigation. Here in this paper, we have applied the Gradient-Boosted Decision Tree machine-learning architecture to further explore the parameter space and find correlations with the neutron yield, a key performance indicator. We find reasonable agreement between the measured and predicted yield, with a mean absolute percentage error on a randomly assigned test set of 35.5%. This model finds the characteristics of the laser pulse to be the most influential in prediction, as well as the hohlraum laser entrance hole diameter and an enhanced capsule fabrication technique. We used the trained model to scan over the design space of experiments from three different campaigns to evaluate the potential of this technique to provide design changes that could improve the resulting neutron yield. While these data-driven model cannot predict ignition without examples of ignited shots in the training set, it can be used to indicate that an unseen shot design will at least be in the upper range of previously observed neutron yields.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Optimization techniques in self-similar compressible flow

We investigate the one-dimensional (1D) inviscid compressible flow equations for an ideal gas through the lens of optimization techniques. It is the case that, to our knowledge, optimization analysis applied to the so-called “linear velocity” solutions of the Euler compressible flow equations has not been previously conducted. Through both gradient-based and variational techniques, new variants of well-studied flow scenarios, i.e., self-similar, 1D, linear velocity solution class to idealized inviscid compressible flow equations, are determined, as encoded in both the kinematic and thermodynamic properties of this self-similar solution class. With the kinematics of the said solutions being driven by a self-similar “scale radius” and the thermodynamics being driven separately through the appearance of an arbitrary function, a myriad of new solution classes is possible. Acting as a guide to more realistic physical circumstances as well as discovery, it is the hope that the presented cases serve as the framework for future investigations into the intersection of self-similarity and optimization techniques. Fields of study that may find this work to be of interest include aerodynamic design, flow control, inertial confinement fusion, physics-informed neural networks, and other related areas of interest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Correlation of plastic events with local structure in jammed packings across spatial dimensions

Significance Mean-field theories, exact in the limit of infinite spatial dimensions, succeed in describing many features of glasses and amorphous solids in low dimensions, leading to considerable effort to understand how behavior evolves with dimension. Until now, all evidence has supported a picture in which “localized physics,” responsible for deviations from mean-field behavior in low dimensions, fades away with rising dimension. Our work shows that rearrangements, in which particles change relative positions leading to fluid-like response, reveal a different picture of dimensional cross-over. We find that rearrangements, which are localized in two- and three-dimensional systems and correlated with local structure, remain just as correlated with local structure up to five dimensions, suggesting that local structure is important even in high dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SAM: A Modern System Code for Advanced Non-LWR Safety Analysis

The System Analysis Module (SAM), developed at Argonne National Laboratory and by collaborators at other organizations, is for advanced non–light water reactor safety analysis. SAM aims to provide fast-running, modest-fidelity, whole-plant transient analysis capabilities that are essential for fast-turnaround design scoping and engineering analyses of advanced reactor concepts. To facilitate code development, SAM utilizes the MOOSE object-oriented application framework, its underlying finite element library, and linear and nonlinear solvers to leverage modern advanced software environments and numerical methods. SAM aims to solve tightly coupled physical phenomena, including fission reaction, heat transfer, fluid dynamics, and thermal-mechanical responses in advanced reactor structures, systems, and components with high accuracy and efficiency. Finally, this paper gives an overview of the SAM code development, including goals and functional requirements, physical models, current capabilities, verification and validation, software quality assurance, and examples of simulations for advanced nuclear reactor applications.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Simulated Performance of the Micro-Pocket Fission Detector in the Advanced Test Reactor Critical Facility

The Micro-Pocket Fission Detector (MPFD) is a small-form–factor real-time fission chamber. MPFD performance has been simulated in the Advanced Test Reactor Critical Facility (ATRC), located at Idaho National Laboratory (INL). Here, the neutron and gamma-ray flux profiles and magnitudes were simulated using Monte Carlo N-Particle (MCNP) in the near-core B-8 irradiation position. These simulations were performed at 69 discrete axial locations inside the B-8 position for three separate orientations of the nearby hafnium outer shim control cylinders and at a power level of 700 Wth. The resulting neutron and gamma-ray flux values were used to determine the MPFD response for various fissile masses and detector gas pressures. The optimal gas-operating pressure was determined to be between 30 and 60 psig. The required fissile-layer mass was determined to be between 1–2 µg of 235 U. Additionally, the gamma-ray to fission-fragment interaction rate was determined to be 4.42 × 10 -3 with average energy deposition for gamma rays and fission fragments in 30 psig argon gas to be 1 keV and 9.5 MeV, respectively.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗