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DOE OSTI2021

Theory of Trotter Error with Commutator Scaling

The Lie-Trotter formula, together with its higher-order generalizations, provides a simple approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, nearly matching or even outperforming the best previous results. Our applications include: (i) a simulation of second-quantized plane-wave electronic structure, nearly matching the interaction-picture algorithm of Low and Wiebe; (ii) a simulation of $k$-local Hamiltonians almost with induced one-norm scaling, faster than the qubitization algorithm of Low and Chuang; (iii) a simulation of rapidly decaying power-law interactions, outperforming the Lieb-Robinson-based approach of Tran et al.; (iv) a hybrid simulation of clustered Hamiltonians, dramatically improving the result of Peng, Harrow, Ozols, and Wu; and (v) quantum Monte Carlo simulations of the transverse field Ising model and quantum ferromagnets, tightening previous analyses of Bravyi and Gosset. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound nearly matching a recent result of Tran et al. Our analysis reproduces known tight bounds for first- and second-order formulas. We further investigate the tightness of our bounds for higher-order formulas. For quantum simulation of a one-dimensional Heisenberg model with an even-odd ordering of terms, our result overestimates the complexity by only a factor of $5$. Our bound is also close to tight for power-law interactions and other orderings of terms. This suggests that our theory can accurately characterize Trotter error in terms of both the asymptotic scaling and the constant prefactor.

quantum computing, numerical analysis↗

DOE OSTI2018

Measurements and correction of the 1/1 error field in Wendelstein 7-X

In this paper, vacuum flux surface mapping is used to measure the error field in Wendelstein 7-X. Two methods for discriminating the perturbation from other co-resonant modes are applied: measurements of the helical axis shift in a magnetic configuration with the rotational transform barely above one on the axis; and measurements of the edge island structure with cancellation of intrinsic islands by divertor control coils. The normalized radial amplitude in Boozer coordinates is found to be about in the first case and about in the second one, with the discrepancy being attributable to different currents in the planar coils. The error field can be reliably compensated by using error field trim coils with currents about 100 A. Here, this compensation also helps to identify the error field of about . During plasma operation in divertor configurations, it is confirmed that the present field leads to asymmetries in the power distribution and that the compensation improves this symmetry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2017

Evidence for Reduced, Carbon-rich Regions in the Solar Nebula from an Unusual Cometary Dust Particle

Geochemical indicators in meteorites imply that most formed under relatively oxidizing conditions. However, some planetary materials, such as the enstatite chondrites, aubrite achondrites, and Mercury, were produced in reduced nebular environments. Because of large-scale radial nebular mixing, comets and other Kuiper Belt objects likely contain some primitive material related to these reduced planetary bodies. Here, we describe an unusual assemblage in a dust particle from comet 81P/Wild 2 captured in silica aerogel by the NASA Stardust spacecraft. The bulk of this ∼20 μ m particle is comprised of an aggregate of nanoparticulate Cr-rich magnetite, containing opaque sub-domains composed of poorly graphitized carbon (PGC). The PGC forms conformal shells around tiny 5–15 nm core grains of Fe carbide. The C, N, and O isotopic compositions of these components are identical within errors to terrestrial standards, indicating a formation inside the solar system. Magnetite compositions are consistent with oxidation of reduced metal, similar to that seen in enstatite chondrites. Similarly, the core–shell structure of the carbide + PGC inclusions suggests a formation via FTT reactions on the surface of metal or carbide grains in warm, reduced regions of the solar nebula. Together, the nanoscale assemblage in the cometary particle is most consistent with the alteration of primary solids condensed from a C-rich, reduced nebular gas. The nanoparticulate components in the cometary particle provide the first direct evidence from comets of reduced, carbon-rich regions that were present in the solar nebula.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids—A case study in diamond

While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for ab initio electronic structure calculations, in practice, the fermionic sign problem necessitates the use of the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros). This approximation introduces a variational error in the energy that potentially can be tested and systematically improved. Here, we present a computational method that produces trial wavefunctions with systematically improvable nodes for DMC calculations of periodic solids. These trial wavefunctions are efficiently generated with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. A simple protocol in which both exact and approximate results for finite supercells are used to extrapolate to the thermodynamic limit is introduced. This approach is illustrated in the case of the carbon diamond using Slater–Jastrow trial wavefunctions including up to one million Slater determinants. Fixed-node DMC energies obtained with such large expansions are much improved, and the fixed-node error is found to decrease monotonically and smoothly as a function of the number of determinants in the trial wavefunction, a property opening the way to a better control of this error. The cohesive energy extrapolated to the thermodynamic limit is in close agreement with the estimated experimental value. Interestingly, this is also the case at the single-determinant level, thus, indicating a very good error cancellation in carbon diamond between the bulk and atomic total fixed-node energies when using single-determinant nodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1995

Test load verification through strain data analysis

A traditional binding acceptance criterion on polycrystalline structures is the experimental verification of the ultimate factor of safety. At fracture, the induced strain is inelastic and about an order-of-magnitude greater than designed for maximum expected operational limit. At this extreme strained condition, the structure may rotate and displace at the applied verification load such as to unknowingly distort the load transfer into the static test article. Test may result in erroneously accepting a submarginal design or rejecting a reliable one. A technique was developed to identify, monitor, and assess the load transmission error through two back-to-back surface-measured strain data. The technique is programmed for expediency and convenience. Though the method was developed to support affordable aerostructures, the method is also applicable for most high-performance air and surface transportation structural systems.

Verderaime, V.↗

NASA NTRS2018

Quantifying Boreal Forest Structure and Composition Using UAV Structure from Motion

The vast extent and inaccessibility of boreal forest ecosystems are barriers to routine monitoring of forest structure and composition. In this research, we bridge the scale gap between intensive but sparse plot measurements and extensive remote sensing studies by collecting forest inventory variables at the plot scale using an unmanned aerial vehicle (UAV) and a structure from motion (SfM) approach. At 20 Forest Inventory and Analysis (FIA) subplots in interior Alaska, we acquired overlapping imagery and generated dense, 3D, RGB (red, green, blue) point clouds. We used these data to model forest type at the individual crown scale as well as subplot-scale tree density (TD), basal area (BA), and aboveground biomass (AGB). We achieved 85% cross-validation accuracy for five species at the crown level. Classification accuracy was maximized using three variables representing crown height, form, and color. Consistent with previous UAV-based studies, SfM point cloud data generated robust models of TD (r(sup 2) = 0.91), BA (r(sup 2) = 0.79), and AGB (r(sup 2) = 0.92), using a mix of plot- and crown-scale information. Precise estimation of TD required either segment counts or species information to differentiate black spruce from mixed white spruce plots. The accuracy of species-specific estimates of TD, BA, and AGB at the plot scale was somewhat variable, ranging from accurate estimates of black spruce TD (+/−1%) and aspen BA (−2%) to misallocation of aspen AGB (+118%) and white spruce AGB (−50%). These results convey the potential utility of SfM data for forest type discrimination in FIA plots and the remaining challenges to develop classification approaches for species-specific estimates at the plot scale that are more robust to segmentation error.

aboveground biomass↗

DOE OSTI2022

Generalized Brønsted‐Evans‐Polanyi Relationships for Reactions on Metal Surfaces from Machine Learning

Abstract Brønsted‐Evans‐Polanyi (BEP) relationships, i. e., a linear scaling between reaction and activation energies, lie at the core of computational design of heterogeneous catalysts. However, BEPs are not general and often require reparameterization for each class of reactions. Here we construct generalized BEPs (gBEPs), which can predict activation energies for a diverse dataset of reactions of C, O, N and H containing molecules on metal surfaces. In a first step we develop a set of descriptors based on scaling relationships that can capture the change in chemical identity of reactants during the reaction. Subsequently, we use the reaction energy, these descriptors and a single descriptor for the surface structure to parameterize machine learning based regression approaches for the prediction of activation energies. The best approach we developed shows a Mean Absolute Error (MAE) of 0.11 eV for the training set (80 % of the data set) and 0.23 eV for the test set (20 % of the data set). The methodology presented here allows to calculate activation energies within fractions of seconds on a typical personal computer and due to its generality, accuracy and simplicity in application it might prove to be useful in transition metal catalyst design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

RDPM: An Extensible Tool for Resilience Design Patterns Modelling

Resilience to faults, errors, and failures in extreme-scale high-performance computing (HPC) systems is a critical challenge. Resilience design patterns offer a new, structured hardware and software design approach for improving resilience. While prior work focused on developing performance, reliability, and availability models for resilience design patterns, this paper extends it by providing a Resilience Design Patterns Modeling (RDPM) tool which allows (1) exploring performance, reliability, and availability of each resilience design pattern, (2) offering customization of parameters to optimize performance, reliability, and availability, and (3) allowing investigation of trade-off models for combining multiple patterns for practical resilience solutions.

Kumar, Mohit↗

DOE OSTI2018

A digital twin for rapid qualification of 3D printed metallic components

The customized production of complex components by 3D printing has been hailed as a potentially transformative tool in manufacturing with important applications in health care, automotive and aerospace industries. However, after about a quarter of a century of research and development, only a handful of commercial alloys can be printed and the market value of all 3D printed products now amounts to a negligible portion of the manufacturing economy. This difficulty is attributable to a remarkable diversity in structure and properties of the printed components and susceptibility to defects. In addition, the current practice of qualifying components by prolonged trial and error with expensive printing equipment and feed stock material confine the printed products to a niche market where the high product cost and the delay in the qualification are not critical factors. In this report we explain how a digital twin or a digital replica of the printing machine will reduce the number of trial and error tests to obtain desired product attributes and reduce the time required for part qualification to make the printed components cost effective. It is shown that a comprehensive digital twin of 3D printing machine consisting of mechanistic, control and statistical models of 3D printing, machine learning and big data can reduce the volume of trial and error testing, reduce defects and shorten time between the design and production.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Respecting causality for training physics-informed neural networks

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this work we attribute this shortcoming to the inability of existing PINNs formulations to respect the spatio-temporal causal structure that is inherent to the evolution of physical systems. We argue that this is a fundamental limitation and a key source of error that can ultimately steer PINN models to converge towards erroneous solutions. We address this pathology by proposing a simple re-formulation of PINNs loss functions that can explicitly account for physical causality during model training. We demonstrate that this simple modification alone is enough to introduce significant accuracy improvements, as well as a practical quantitative mechanism for assessing the convergence of a PINNs model. Here we provide state-of-the-art numerical results across a series of benchmarks for which existing PINNs formulations fail, including the chaotic Lorenz system, the Kuramoto–Sivashinsky equation in the chaotic regime, and the Navier–Stokes equations. To the best of our knowledge, this is the first time that PINNs have been successful in simulating such systems, introducing new opportunities for their applicability to problems of industrial complexity.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

PGM-Free Oxygen-Reduction Catalyst Development for Proton-Exchange Membrane Fuel Cells: Challenges, Solutions, and Promises

Proton-exchange membrane fuel cells (PEMFCs) are efficient and clean hydrogen energy technologies for transportation and stationary applications. Highly active and durable low-cost cathode catalysts for the oxygen-reduction reaction (ORR) under challenging acidic environments are desperately needed to address the cost and durability issues of PEMFCs. The most promising platinum group metal (PGM)-free catalysts for the ORR in acidic media are atomically dispersed and nitrogen-coordinated metal site catalysts denoted as M–N–C, M = Fe, Co, or Mn. Due to significant efforts in the past few decades, these catalysts have demonstrated much-improved ORR activity and promising initial fuel cell performance approaching traditional Pt/C catalysts. However, the insufficient long-term stability (up to 5000 h) under PEMFC operation represents a primary technical barrier to making current PGM-free catalysts less viable yet in PEMFCs. In this Account, we highlight recent advances in synthesizing efficient PGM-free catalysts for the ORR in PEMFCs, emphasizing effective strategies to improve mass and intrinsic activity and the possible degradation mechanisms. In particular, a chemical doping method based on the zeolitic imidazolate framework (ZIF)-8 represents the key to developing efficient M–N–C catalysts containing atomically dispersed and nitrogen-coordinated single metal active sites (i.e., MN 4 ). The newly acquired understanding of the formation mechanism of MN 4 active sites during the thermal activation and its correlation to catalytic properties guide the rational catalyst design rather than relying on current trial-and-error approaches. Considerable efforts have further been invested in increasing the active site density and enhancing intrinsic activity by regulating carbon-phase structures and the local coordination environment. Furthermore, these highly active catalysts usually suffer from significant activity loss during the ORR. Therefore, breaking the activity–stability trade-off is the key to simultaneously achieving activity and stability in one catalyst, which is discussed on the basis of our recent successes in regulating local carbon structures surrounding active single metal sites. Significant research efforts toward understanding the degradation mechanisms and improving the lifetime of PGM-free catalysts are still crucial for viable applications in the future. Novel electrode designing strategies are needed to translate the PGM-free catalysts’ ORR activity to solid-state electrolyte-based membrane electrode assemblies (MEAs) with robust three-phase (i.e., gas–liquid–solid) interfaces for efficient charge and mass transports for performance improvement. On the basis of our effort at the University at Buffalo supported by ElectroCat Consortium associated with U.S. DOE’s Hydrogen and Fuel Cell Technologies Office, we provide a perspective on PGM-free cathode catalysts concerning remaining bottlenecks and future opportunities, aiming to inspire the community in both mechanistic understanding and technological development.

08 HYDROGEN↗

DOE OSTI2021

Methods to determine the radiated power in SPI-mitigated disruptions in JET

Here we present techniques for evaluating the radiated power in JET disruptions. Disrupting plasmas are shown to have non-axisymmetric radiation profiles, motivating the re-evaluation of the standard techniques for calculating the total radiated power at JET using bolometry. Four single-channel bolometers at different toroidal locations are exploited to quantify the radiation asymmetry. Toroidal radiation peaking factors integrated over the entire disruption of up to 1.5 have been observed when varying the quantity of neon in pellets used in disruptions mitigated by shattered pellet injection. Using synthetic bolometer diagnostics developed with the Cherab spectroscopy modeling framework, we can estimate the systematic error on total power calculations for relevant radiation profiles and improve estimates of the total radiated power. We show that the component of the systematic error on the total power due to the poloidal radiation profile can be reduced from 70% to 10% with suitable assumptions about the structure of the poloidal profile.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Relativistic resolution-of-the-identity with Cholesky integral decomposition

In this study, we present an efficient integral decomposition approach called the restricted-kinetic-balance resolution-of-the-identity (RKB-RI) algorithm, which utilizes a tunable RI method based on the Cholesky integral decomposition for in-core relativistic quantum chemistry calculations. The RKB-RI algorithm incorporates the restricted-kinetic-balance condition and offers a versatile framework for accurate computations. Notably, the Cholesky integral decomposition is employed not only to approximate symmetric large-component electron repulsion integrals but also those involving small-component basis functions. In addition to comprehensive error analysis, we investigate crucial conditions, such as the kinetic balance condition and variational stability, which underlie the applicability of Dirac relativistic electronic structure theory. Here we compare the computational cost of the RKB-RI approach with the full in-core method to assess its efficiency. To evaluate the accuracy and reliability of the RKB-RI method proposed in this work, we employ actinyl oxides as benchmark systems, leveraging their properties for validation purposes. This investigation provides valuable insights into the capabilities and performance of the RKB-RI algorithm and establishes its potential as a powerful tool in the field of relativistic quantum chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Quantum chemically calculated Abraham parameters for quantifying and predicting polymer hydrophobicity

The leakage and accumulation of plastic in the environment is a significant and growing problem with numerous detrimental impacts and has led to a push toward the design and development of more environmentally benign materials. To this end, we have developed a quantum chemistry-based model for predicting the mobility of polymer materials from molecular structure. Hydrophobicity is used as a surrogate for mobility given that hydrophobic interactions drive much of the partitioning of contaminants in and out of various environmentally relevant compartments. To model polymer hydrophobicity, we adjusted a previously developed Quantum Chemically Calculated Abraham Parameter model to calculate Abraham parameters of small molecules from molecular structure information. The resulting model predicted the octanol-water partition coefficient (K OW ) of polymer repeating units with a root mean square error (RMSE) of 0.48 (log scale). Additionally, the hydrophobicity of high molecular weight polymer materials was captured through solubility parameters and Nile red staining experiments from the literature and predicted with RMSEs of 1.21 (J/cc) 0.5 and 3.42 nm, respectively. Finally, to test the environmental applicability of the model, the relative adsorption capacity of three polymers was predicted and used to unify sorption isotherms across multiple sorbates and polymer sorbents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

MO-FG-204-01: Improved Noise Suppression for Dual-Energy CT Through Entropy Minimization

Purpose: In dual energy CT (DECT), noise amplification during signal decomposition significantly limits the utility of basis material images. Since clinically relevant objects contain a limited number of materials, we propose to suppress noise for DECT based on image entropy minimization. An adaptive weighting scheme is employed during noise suppression to improve decomposition accuracy with limited effect on spatial resolution and image texture preservation. Methods: From decomposed images, we first generate a 2D plot of scattered data points, using basis material densities as coordinates. Data points representing the same material generate a highly asymmetric cluster. We orient an axis by minimizing the entropy in a 1D histogram of these points projected onto the axis. To suppress noise, we replace pixel values of decomposed images with center-of-mass values in the direction perpendicular to the optimal axis. To limit errors due to cluster overlap, we weight each data point’s contribution based on its high and low energy CT values and location within the image. The proposed method’s performance is assessed on physical phantom studies. Electron density is used as the quality metric for decomposition accuracy. Our results are compared to those without noise suppression and with a recently developed iterative method. Results: The proposed method reduces noise standard deviations of the decomposed images by at least one order of magnitude. On the Catphan phantom, this method greatly preserves the spatial resolution and texture of the CT images and limits induced error in measured electron density to below 1.2%. In the head phantom study, the proposed method performs the best in retaining fine, intricate structures. Conclusion: The entropy minimization based algorithm with adaptive weighting substantially reduces DECT noise while preserving image spatial resolution and texture. Future investigations will include extensive investigations on material decomposition accuracy that go beyond the current electron density calculations. This work was supported in part by the National Institutes of Health (NIH) under Grant Number R21 EB012700.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2024

Machine Learning-Based Identification of the Interface Regions for Coupling Local and Nonlocal Models

Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. However, the coupling process can be challenging, requiring expertise to identify the interface between local and nonlocal regions. Here, this study introduces a machine learning-based approach to automatically detect the regions in which the local and nonlocal models should be used. The method uses loading functions evaluated at grid points to decide the model selection at those points. Training of the networks is based on datasets provided by classes of loading functions for which reference coupling configurations are computed using accurate coupled solutions, where accuracy is measured in terms of the relative error between the solution to the coupling approach and the solution to the nonlocal model. We study two approaches that vary in data structure. The first, the full-domain input data approach, uses the entire load vector and outputs a complete label vector, performing a global classification. The second, a window-based approach, processes loads into windows and addresses the problem as a node-wise classification where each window's central point is classified individually. The classification problems are solved via deep learning algorithms based on convolutional neural networks. The performance of these approaches is studied on one-dimensional numerical examples using F1-scores and accuracy metrics. Notably, the windowing approach achieves an accuracy of 0.96 and an F1-score of 0.97, highlighting its potential to automate coupling processes effectively and enhance computational efficiency in material science applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Homoclinic tangles in the DIII-D divertor tokamak

A new approach was developed for the calculation of homoclinic tangles of the primary unperturbed separatrix in divertor tokamaks. This new approach is different than calculating tangles by following single trajectories in phase space [M. V. Berry, Topics in Nonlinear Dynamics (Ed. S. Jorna), Am. Inst. Phys. Conf. Proc. 46, 16-120 (1978)] or calculating the trajectories asymptotically in canonical time [R. K. W. Roeder, B. I. Rapoport, and T. E. Evans, Phys. Plasmas 10, 3796 (2003)]. The approach is to consider an equilibrium manifold as a whole and to calculate how the entire manifold evolves in phase space in time under the influence of perturbations. When the forward moving and the backward moving manifolds meet in a poloidal plane and intersect, they form tangles to preserve the topological invariance of the Hamiltonian system. This approach was applied to the DIII-D tokamak. The low mn, the high mn, the peeling-ballooning modes, and topological noise and field error perturbations were considered. The results of the peeling-ballooning modes were analyzed. It was found that the perturbations create very complicated structures in phase space [A. Punjabi and A. Boozer, Phys. Lett A 378, 2410-2416 (2014); A. Punjabi, Phys. Plasmas 21, 122516 (2014)]. The structure of tangles gives a possible cause for generation of radial electric fields in divertor tokamaks, and the possible consequent drifts, currents, shears, and curvature effects from the resulting complicated electric fields can possibly indicate a path to L to H mode transition [F. Wagner F et al, Phys. Rev. Lett. 49, 1408 (1982)] in divertor tokamaks. During the present period, four (4) refereed paper were published; six (6) contributed papers were presented at the EPS Conference on Plasma Physics and published in the EPS conference proceedings; six (6) contributed poster papers, co-authored with HU undergraduate students, were presented at APS/DPP Annual Meetings; three contributed papers were presented at HU School of Science Annual Research Symposia; four (4) invited talks were given; one talk, co-authored by Dr. Allen Boozer and the PI, was given by Dr. Boozer at the 20th International Stellarator-Heliotron Workshop 2015, in Greifswald, Germany; and four (4) graduate students and nine (9) undergraduate students were mentored and provided research experience in fusion science. For the renewal period, it is planned to work on four (4) new problems. These are: Homoclinic tangles of the separatrices of the DIII-D and the simple map, magnetic topology and homoclinic tangles of separatrices in divertor tokamaks, resonant stellarator divertors, and nonresonant stellarator divertors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1972

Solar sensor with autocollimator

Monolithic structure, consisting of fused quartz fabricated solar sensor and autocollimator, measures angle between reference surface on spacecraft and solar vector. Device compensates for errors caused by changes in the alignment of its mountings or component parts. Integrated concept is advantageous whenever sensor mounting errors constitute problems.

Fain, D. L.↗