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DOE OSTI2023

Topological terms with qubit regularization and relativistic quantum circuits

Qubit regularization provides a rich framework to explore quantum field theories. The freedom to choose how the important symmetries of the theory are embedded in the qubit regularization scheme allows us to construct new lattice models with rich phase diagrams. Some of the phases can contain topological terms which lead to critical phases. In this work we introduce and study the SU(3)-F qubit regularization scheme to embed the SO(3) spin-symmetry. We argue that qubit models in this regularization scheme contain several phases including a critical phase which describes the k = 1 Wess-Zumino-Witten (WZW) conformal field theory (CFT) at long distances, and two massive phases one of which is trvially gapped and the other which breaks the lattice translation symmetry. We construct a simple space-time Euclidean lattice model with a single coupling U and study it using the Monte Carlo method. We show the model has a critical phase at small U and a trivially massive phase at large U with a first order transition separating the two. Another feature of our model is that it is symmetric under space-time rotations, which means the temporal and spatial lattice spacing are connected to each other. The unitary time evolution operator obtained by a Wick rotation of the transfer matrix of our model can help us compute the physics of the k = 1 WZW CFT in real time without the need for tuning the temporal lattice spacing to zero. We use this idea to introduce the concept of a relativistic quantum circuit on a discrete space-time lattice.

Bhattacharya, Tanmoy↗

DOE OSTI2024

Efficient six-dimensional phase space reconstructions from experimental measurements using generative machine learning

Next-generation accelerator concepts, which hinge on the precise shaping of beam distributions, demand equally precise diagnostic methods capable of reconstructing beam distributions within six-dimensional position-momentum spaces. However, the characterization of intricate features within six-dimensional beam distributions using current diagnostic techniques necessitates a substantial number of measurements, using many hours of valuable beam time. Novel phase space reconstruction techniques are needed to reduce the number of measurements required to reconstruct detailed, high-dimensional beam features in order to resolve complex beam phenomena and as a feedback in precision beam shaping applications. In this study, we present a novel approach to reconstructing detailed six-dimensional phase space distributions from experimental measurements using generative machine learning and differentiable beam dynamics simulations. We demonstrate that this approach can be used to resolve six-dimensional phase space distributions from scratch, using basic beam manipulations and as few as 20 two-dimensional measurements of the beam profile. We also demonstrate an application of the reconstruction method in an experimental setting at the Argonne Wakefield Accelerator, where it is able to reconstruct the beam distribution and accurately predict previously unseen measurements 75× faster than previous methods.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

Machine Learning for First Principles Calculations of Material Properties for Ferromagnetic Materials

The investigation of finite temperature properties using Monte-Carlo (MC) methods requires a large number of evaluations of the system’s Hamiltonian to sample the phase space needed to obtain physical observables as function of temperature. DFT calculations can provide accurate evaluations of the energies, but they are too computationally expensive for routine simulations. To circumvent this problem, machine-learning (ML) based surrogate models have been developed and implemented on high-performance computing (HPC) architectures. In this paper, we describe two ML methods (linear mixing model and HydraGNN) as surrogates for first principles density functional theory (DFT) calculations with classical MC simulations. These two surrogate models are used to learn the dependence of target physical properties from complex compositions and interactions of their constituents. We present the predictive performance of these two surrogate models with respect to their complexity while avoiding the danger of overfitting the model. An important aspect of our approach is the periodic retraining with newly generated first principles data based on the progressive exploration of the system’s phase space by the MC simulation. The numerical results show that HydraGNN model attains superior predictive performance compared to the linear mixing model for magnetic alloy materials.

Eisenbach, Markus↗

DOE OSTI2023

Adaptive autoencoder latent space tuning for more robust machine learning beyond the training set for six-dimensional phase space diagnostics of a time-varying ultrafast electron-diffraction compact accelerator

In this work, we present a general adaptive latent space tuning approach for improving the robustness of machine learning tools with respect to time variation and distribution shift. We demonstrate our approach by developing an encoder-decoder convolutional neural network-based virtual 6D phase space diagnostic of charged particle beams in the HiRES ultrafast electron diffraction (UED) compact particle accelerator with uncertainty quantification. Our method utilizes model-independent adaptive feedback to tune a low dimensional 2D latent space representation of ~1 million dimensional objects which are the 15 unique 2D projections (x, y),...,(z, p z ) of the 6D phase space (x, y, z, p x , p y , p z ) of the charged particle beams. We demonstrate our method with numerical studies of short electron bunches utilizing experimentally measured UED input beam distributions.

43 PARTICLE ACCELERATORS↗

DOE OSTI2020

A machine learning study on spinodal clumping in heavy ion collisions

Possible observables of baryon number clustering due to the instabilities occurring at a first order QCD phase transition are discussed. The dynamical formation of baryon clusters at a QCD phase transition can be described by numerical fluid dynamics, augmented with a gradient term and an equation of state with a mechanically unstable region. It is shown that the dynamical description of this phase transition, in nuclear collisions, will lead to the formation of dense baryon clusters at the phase boundary. State-of-the-art machine learning methods find that the coordinate space clumping leaves characteristic imprints on the spatial net density distribution in almost every event. On the other hand the momentum distributions do not show any clear event-by-event features. Lastly, it is shown that the 'third order' cumulant, the skewness, shows a peak at the beam energy where the system, created in the heavy ion collision, reaches the deconfinement phase transition.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Synthesis of bulk reactive Ni–Al composites using high pressure torsion

Self-propagating exothermic reactions, for instance in the nickel-aluminum (Ni-Al) system, have been widely studied to create high performance intermetallic compounds or for in-situ welding. Their easy ignition once the phase spacing is reduced below the micron scale, makes top-down methods like high-energy ball milling, ideal to fabricate such reactive nanostructures. A major drawback of ball milling is the need of a sintering step to form bulk pieces of the reactive material. However, this is not possible, as the targeted reactions would already proceed. Therefore, we investigate the ability of high pressure torsion as an alternative process, capable to produce bulk nanocomposites from powder mixtures. Severe straining of powder mixtures with a composition of 50 wt% Ni and 50 wt% Al enables fabrication of self-reactive bulk samples with microstructures similar to those obtained from ball milling or magnetron sputtering. Additionally, samples deformed at ambient temperature are highly reactive and can be ignited significantly below the Al melting point, finally predominantly consisting of Al 3 Ni 2 and Al 3 Ni, independent of the applied strain. Although the reaction proceeds first at the edge of the disk, the strain gradient present in the disks does not prevent reaction of the whole sample.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Unveiling the Electrocatalytic Hydrogen Evolution Reaction Pathway on RuP 2 through Ab Initio Grand Canonical Monte Carlo

In this study, the high catalytic reactivity of ruthenium phosphide (RuP 2 ) has been identified by first-principles density functional theory (DFT) calculations for the electrocatalytic hydrogen evolution reaction (HER). Complex surface reconstructions are considered by applying the ab initio grand canonical Monte Carlo (ai-GCMC) algorithm, efficiently providing a sufficient phase-space exploration of possible surfaces. Combined with surface-phase Pourbaix diagrams, we are able to identify the actual surfaces that obtained under specific experimental environments, thus leading to a more accurate understanding of the nature of the active sites and the binding strength of adsorbates. Specifically, through hundreds of surface reconstructions and hydrogenation states generated with ai-GCMC, we identify the most favorable surface phases of RuP 2 under aqueous acidic conditions. We discover that the HER activity is determined by multiple surfaces with different stoichiometries within a narrow electrode potential window. Low HER overpotential (η) has been found for each of the identified surfaces, as low as 0.04 V. High H-coverage reconstructed surfaces have been discovered under acidic conditions, and the surface Ru sites introduced by additional Ru adatoms or exposed by P-vacancies serve as the active sites for HER based on their nearly reversible H binding. Furthermore, this work provides atomistic insights into the origin of high HER activity on RuP 2 by exploring the dynamic surface phases of electrocatalysts and features a generalizable method to explore the reconstructed/hydrogenated surface space as a function of experimental conditions.

25 ENERGY STORAGE↗

DOE OSTI2023

Towards inverse microstructure-centered materials design using generative phase-field modeling and deep variational autoencoders

The field of Integrated Computational Materials Engineering (ICME) combines a broad range of methods to study materials’ responses over a spectrum of length scales. A relatively unexplored aspect of microstructure-sensitive materials design is uncertainty propagation and quantification (UP/UQ) of materials’ microstructure, as well as establishing process-structure–property (PSP) relationships for inverse material design. In this study, an efficient UP technique built on the idea of changing probability measures and a deep generative unsupervised representative machine learning method for microstructure-based design of thermal conductivity of materials is proposed. Probability measures are used to represent microstructure space, and Wasserstein metrics are used to test the efficiency of the UP method. By using deep Variational AutoEncoder (VAE), we identify the correlations between the material/process parameters and the thermal conductivity of heterogeneous dual-phase microstructures. Through high-throughput screening, UP, and the deep-generative VAE method, PSP relationships that are too complex can be revealed by exploiting the materials’ design space with an emphasis on microstructures. As a last point, we demonstrate generative machine learning serves as a useful tool for inverse microstructure-centered materials design, and we demonstrate this by examining the inverse design of thermal conductivity in nano-structured materials. Here, the results reveal the effects of morphology, volume fraction, characteristic length scale, and the individual thermal diffusivity of phases on the thermal conductivity of dual-phase alloys. Our findings emphasize the advantages of high-throughput phase-field modeling and generative deep learning for linking PSP and inverse microstructure-centered materials design.

36 MATERIALS SCIENCE↗

DOE OSTI2021

A snapshot review—Fluctuations in quantum materials: from skyrmions to superconductivity

Abstract By measuring a linear response function directly, such as the dynamic susceptibility, one can understand fundamental material properties. However, a fresh perspective can be offered by studying fluctuations. This can be related back to the dynamic susceptibility through the fluctuation–dissipation theorem, which relates the fluctuations in a system to its response, an alternate route to access the physics of a material. Here, we describe a new X-ray tool for material characterization that will offer an opportunity to uncover new physics in quantum materials using this theorem. We provide details of the method and discuss the requisite analysis techniques in order to capitalize on the potential to explore an uncharted region of phase space. This is followed by recent results on a topological chiral magnet, together with a discussion of current work in progress. We provide a perspective on future measurements planned for work in unconventional superconductivity. Graphical abstract We describe a new X-ray tool for material characterization that will offer an opportunity to uncover new physics in quantum materials using coherent, short-pulsed X-rays. We provide details of the method and discuss the requisite analysis techniques in order to capitalize on the potential to explore an uncharted region of phase space. This is followed by recent results on a topological chiral magnet, together with a discussion of current work in progress. We provide a perspective on future measurements planned for work in unconventional superconductivity.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Macromolecular phasing using diffraction from multiple crystal forms

A phasing algorithm for macromolecular crystallography is proposed that utilizes diffraction data from multiple crystal forms – crystals of the same molecule with different unit-cell packings (different unit-cell parameters or space-group symmetries). The approach is based on the method of iterated projections, starting with no initial phase information. The practicality of the method is demonstrated by simulation using known structures that exist in multiple crystal forms, assuming some information on the molecular envelope and positional relationships between the molecules in the different unit cells. With incorporation of new or existing methods for determination of these parameters, the approach has potential as a method for ab initio phasing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

LDRD Abbreviated report: High-Order General-Discrete-Ordinates Method Enabling Efficient Deterministic Transport in Hydrodynamic Simulations

Deterministic transport simulations for national-security and energy applications often operate in high-dimensional phase-space, where accuracy and cost both become major challenges. A common numerical artifact in such problems is the “ray-effect,” which appears as unphysical streaks. Beyond misinterpretation, these artifacts can contaminate tightly coupled physics, such as fluid dynamics, radiation-hydrodynamics, and laser-plasma interactions, eroding the predictive capability of entire multiphysics workflows. Our objective was to make high-dimension studies practical on modern hardware while mitigating the ray-effect without relying on prohibitively expensive sampling approaches such as Monte Carlo methods. We developed the Generic Discretization Library (GenDiL), a Graphics Processing Unit (GPU)-first framework that uses high-order Discontinuous Galerkin (DG) methods and matrix-free algorithms to reduce memory usage and improve computational efficiency, critical for phase-space simulations. GenDiL supports phase-space adaptivity in both mesh size and polynomial order (hp-adaptivity) to place resolution only where it is needed. A central capability is Local Dimensional Refinement (LDR), which couples lower-dimension continuum models to higher-dimension kinetic models through stable and conservative interfaces, so that high-fidelity physics is applied only in regions where it is essential. Building on the GenDiL framework, we developed the General SN (GSN) family of algorithms as a true generalization of the polar SN approach (discrete ordinates, often denoted SN). Rather than tying discrete ordinates to a specific polar change of coordinates, GSN formulates transport on an arbitrary change of coordinates chosen to reduce ray-effect. We studied two complementary variants: an analytic variant, where the coordinate map is prescribed in advance by a closed-form function; and a data-driven variant, where a quantity of interest, such as the net flux, guides the coordinate system. GenDiL provides the library infrastructure for efficient GPU execution, but the GSN concept is algorithmic and independent of any one library. Across representative high-dimension tests, including non-symmetric solutions, both variants delivered strong ray-effect mitigation at practical cost, moving four- to six-dimensional analysis toward repeatable, routine studies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Rapid 3D nanoscale coherent imaging via physics-aware deep learning

Phase retrieval, the problem of recovering lost phase information from measured intensity alone, is an inverse problem that is widely faced in various imaging modalities ranging from astronomy to nanoscale imaging. The current process of phase recovery is iterative in nature. As a result, the image formation is time consuming and computationally expensive, precluding real-time imaging. Here, we use 3D nanoscale X-ray imaging as a representative example to develop a deep learning model to address this phase retrieval problem. We introduce 3D-CDI-NN, a deep convolutional neural network and differential programing framework trained to predict 3D structure and strain, solely from input 3D X-ray coherent scattering data. Our networks are designed to be “physics-aware” in multiple aspects; in that the physics of the X-ray scattering process is explicitly enforced in the training of the network, and the training data are drawn from atomistic simulations that are representative of the physics of the material. We further refine the neural network prediction through a physics-based optimization procedure to enable maximum accuracy at lowest computational cost. 3D-CDI-NN can invert a 3D coherent diffraction pattern to real-space structure and strain hundreds of times faster than traditional iterative phase retrieval methods. Our integrated machine learning and differential programing solution to the phase retrieval problem is broadly applicable across inverse problems in other application areas.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2020

Landau level of fragile topology

Here, we study the Hofstadter butterfly and Landau levels of the twisted bilayer graphene (TBG). We show that the nontrivial fragile topology of the lowest two bands near the charge neutral point makes their Hofstadter butterfly generically connected with higher bands, closing the gap between the first and second conduction (valence) bands at a certain magnetic flux per unit cell. We also develop a momentum space method for calculating the TBG Hofstadter butterfly, from which we identify three phases where the Hofstadter butterflies of the lowest two bands and the higher bands are connected in different ways. We show this leads to a crossing between the $\textit{ν}$ = 4 Landau fan from the charge neutral point and the zero-field band gap at one flux per moiré unit cell, which corresponds to a magnetic field 25$θ^2$ T (twist angle $\textit{θ}$ in degrees). This provides an experimentally testable feature of the fragile topology. In general, we expect it to be a generic feature that the Hofstadter butterfly of the topological bands are connected with the Hofstadter spectra of other bands. We further show the TBG band theory with Zeeman splitting being the most sizable splitting could result in Landau fans at the charge neutral point and half fillings near the magic angle, and we predict their variations under an in-plane magnetic field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Crystal Structure of an Anisotropic Pyrope Garnet That Contains Two Cubic Phases

The crystal structure of two different samples of pyrope garnet, ideally Mg 3 Al 2 Si 3 O 12 , from South Africa was refined using the Rietveld method, space group Ia3¯d, and monochromatic synchrotron high-resolution powder X-ray diffraction (HRPXRD) data. Sample 1 from Wesselton Mine is a single cubic phase and is optically isotropic. Electron-probe microanalysis (EPMA) provided an average composition {Mg 2.30 Fe 2+ 0.26 Ca 0.42 Mn 2+ 0.02 } Σ3 [Al 1.53 Fe 3+ 0.06 Cr 3+ 0.40 Ti 4+ 0.01 Fe 2+ 0.01 ] Σ2 Si 3 O 12 , which contains a significant amount of Cr cations. The unit-cell parameter (Å) and bond distances (Å) are a = 11.56197(1) Å, average = 2.2985, Al-O = 1.9101(4), and Si-O = 1.6343(3) Å. Sample 2 from De Beers Diamond Mine has an average composition {Mg 2.33 Fe 2+ 0.33 Ca 0.33 Mn 2+ 0.01 } Σ3 [Al 1.73 Fe 3+ 0.12 Cr 3+ 0.06 Ti 4+ 0.05 Fe 2+ 0.05 ] Σ2 Si 3 O 12 and is a fine-scale intergrowth of two cubic phases. The weight percentage, unit-cell parameter (Å), and bond distances (Å) for phase 2a are 62.2(1)%, a = 11.56185(1) Å, average = 2.3006, Al-O = 1.9080(4), Si-O = 1.6334(4) Å. The corresponding values for phase 2b are 37.8(1)%, a = 11.53896(1) Å, average = 2.2954, Al-O = 1.9020(6), Si-O = 1.6334(6) Å. The two cubic phases in sample 2 cause the crystal to be optically anisotropic because of strain induce birefringence. The unit-cell parameter and bond distances for sample 1 are similar to those in phase 2a.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Elastic depths for detecting shape anomalies in functional data

This this paper, we propose a new family of depth measures called the elastic depths that can be used to greatly improve shape anomaly detection in functional data. Shape anomalies are functions that have considerably different geometric forms or features from the rest of the data. Identifying them is generally more difficult than identifying magnitude anomalies because shape anomalies are often not distinguishable from the bulk of the data with visualization methods. The proposed elastic depths use the recently developed elastic distances to directly measure the centrality of functions in the amplitude and phase spaces. Measuring shape outlyingness in these spaces provides a rigorous quantification of shape which, in turn, gives the elastic depths a strong theoretical and practical advantage over other methods in detecting shape anomalies. A simple boxplot and thresholding method are introduced to identify shape anomalies using the elastic depths. We assess the elastic depth's detection skill on simulated shape outlier scenarios and compare them against popular shape anomaly detectors. Finally, bond yields, image outlines, and hurricane trajectories are used to demonstrate our method's applicability to functional data observed on three different manifolds.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Machine-assisted discovery of integrable symplectic mappings

Integrable systems possess a hidden symmetry associated with the existence of conserved quantities known as integrals of motion. These systems play an important role in understanding general dynamics in accelerators and have potential for future designs. This work will cover two automated methods for finding integrable symplectic maps of the plane. The first algorithm is based on the observation that the evolution of an integrable system in phase space is confined to a lower-dimensional submanifold of a specific type. The second algorithm relies on an analysis of dynamical variables. Both methods rediscover some of the famous McMillan-Suris integrable mappings and ultra-discrete Painlev\'e equations. Over 100 new integrable families are presented and analyzed, some of which are isolated in the space of parameters, while others are families with one parameter (or the ratio of parameters) being either continuous or discrete. In addition, the newly discovered maps are related to a general 2D symplectic map through the use of discrete perturbation theory. A method is proposed for constructing smooth near-integrable dynamical systems based on mappings with polygon invariants.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Machine-Assisted Discovery of Integrable Symplectic Mappings

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

A single-atom library for guided monometallic and concentration-complex multimetallic designs

Atomically dispersed single-atom catalysts have the potential to bridge heterogeneous and homogeneous catalysis. Dozens of single-atom catalysts have been developed, and they exhibit notable catalytic activity and selectivity that are not achievable on metal surfaces. Although promising, there is limited knowledge about the boundaries for the monometallic single-atom phase space, not to mention multimetallic phase spaces. Here, single-atom catalysts based on 37 monometallic elements are synthesized using a dissolution-and-carbonization method, characterized and analyzed to build the largest reported library of single-atom catalysts. In conjunction with in situ studies, we uncover unified principles on the oxidation state, coordination number, bond length, coordination element and metal loading of single atoms to guide the design of single-atom catalysts with atomically dispersed atoms anchored on N-doped carbon. We utilize the library to open up complex multimetallic phase spaces for single-atom catalysts and demonstrate that there is no fundamental limit on using single-atom anchor sites as structural units to assemble concentration-complex single-atom catalyst materials with up to 12 different elements. Furthermore, our work offers a single-atom library spanning from monometallic to concentration-complex multimetallic materials for the rational design of single-atom catalysts.

36 MATERIALS SCIENCE↗