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DOE OSTI2024

Self‐Consistent Convolutional Density Functional Approximations: Application to Adsorption at Metal Surfaces

The exchange-correlation (XC) functional in density functional theory is used to approximate multi-electron interactions. A plethora of different functionals are available, but nearly all are based on the hierarchy of inputs commonly referred to as “Jacob's ladder.” This paper introduces an approach to construct XC functionals with inputs from convolutions of arbitrary kernels with the electron density, providing a route to move beyond Jacob's ladder. We derive the variational derivative of these functionals, showing consistency with the generalized gradient approximation (GGA), and provide equations for variational derivatives based on multipole features from convolutional kernels. A proof-of-concept functional, PBEq, which generalizes the PBEα framework with mathematical equation being a spatially-resolved function of the monopole of the electron density, is presented and implemented. It allows a single functional to use different GGAs at different spatial points in a system, while obeying PBE constraints. Analysis of the results underlines the importance of error cancellation and the XC potential in data-driven functional design. After testing on small molecules, bulk metals, and surface catalysts, the results indicate that this approach is a promising route to simultaneously optimize multiple properties of interest.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Phase Selection Rules of Multi‐Principal Element Alloys

Abstract Computational prediction of phase stability of multi‐principal element alloys (MPEAs) holds a lot of promise for rapid exploration of the enormous design space and autonomous discovery of superior structural and functional properties. Regardless of many plausible works that rely on phenomenological theory and machine learning, precise prediction is still limited by insufficient data and the lack of interpretability of some machine learning algorithms, e.g., convolutional neural network. In this work, a comprehensive approach is presented, encompassing the development of a complete dataset that contains 72 387 density functional theory calculations, as well as a predictive global phenomenological descriptor. The phase selection descriptor, based on atomic electronegativity and valence electron concentration, significantly outperforms the widely used valence electron concentration, excelling in both accuracy (with an f1 score of 63% compared to 47%) and its ability to predict the HCP phase (0.48 recall compared to 0). The comprehensive data mining on the global design space of 61 425 quaternary MPEAs made from 28 possible metals, together with the phenomenological theory and physical interpretation, will set up a solid computational science foundation for data‐driven exploration of MPEAs.

Chemistry↗

DOE OSTI2024

Machine learning assisted search for Fe–Co–C ternary compounds with high magnetic anisotropy

We employ a machine learning (ML)-guided framework to explore rare earth free magnetic materials, specifically focusing on Fe–Co–C ternary compounds for potential use in permanent magnets. Utilizing a specifically trained crystal graph convolutional neural network model, we efficiently screen a vast space of nearly a million substitutional structures to select 620 promising structures for further investigation by first-principles calculation. We predict five low-energy metastable Fe–Co–C compounds with formation energy less than 150 meV/atom above the convex hull. These compounds exhibit high magnetization (Js > 1.0 T) and significant magnetic anisotropy (K1 > 1.0 MJ/m3), making them promising candidates for permanent magnet applications. The phonon calculations indicate these compounds are dynamically stable. Our ML-guided framework demonstrates the utility of rapidly identifying novel materials with tailored magnetic properties.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Machine learning enabled discovery of application dependent design principles for two-dimensional materials

Abstract The unique electronic and mechanical properties of two-dimensional (2D) materials make them promising next-generation candidates for a variety of applications. Large-scale searches for high-performing 2D materials are limited to calculating descriptors with computationally demanding first-principles density functional theory. In this work, we alleviate this issue by extending and generalizing crystal graph convolutional neural networks to systems with planar periodicity and train an ensemble of models to predict thermodynamic, mechanical and electronic properties. We carry out a screening of nearly 45,000 structures for two separate applications: mechanical strength and photovoltaics. By collecting statistics of the screened candidates, we investigate structural and compositional design principles that impact the properties of the structures surveyed. Our approach recovers some well-accepted design rules: hybrid organic-inorganic perovskites with lead and tin tend to be good candidates for solar cell applications and titanium based MXenes usually have high stiffness coefficients. Interestingly, other members of the group 4 elements also contribute to increasing the mechanical strength of MXenes. For all-inorganic perovskites, we discover some compositions that have not been deeply studied in the field of photovoltaics and thus open up paths for further investigation. We open-source the code-base to spur further development in this space.

Venturi, Victor (ORCID:0000000156727549)↗

DOE OSTI2022

BRST symmetry and the convolutional double copy

Motivated by the results of Anastasiou et al., we consider the convolutional double copy for BRST and anti-BRST covariant formulations of gravitational and gauge theories in more detail. We give a general BRST and anti-BRST invariant formulation of linearised $\mathcal{N}$ = 0 supergravity using superspace methods and show how this may be obtained from the square of linearised Yang-Mills theories. We demonstrate this relation for the Schwarzschild black hole and the ten-dimensional black string solution as two concrete examples.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Deep learning-based quasi-continuum theory for structure of confined fluids

Predicting the structural properties of water and simple fluids confined in nanometer scale pores and channels is essential in, for example, energy storage and biomolecular systems. Classical continuum theories fail to accurately capture the interfacial structure of fluids. In this work, we develop a deep learning-based quasi-continuum theory (DL-QT) to predict the concentration and potential profiles of a Lennard-Jones (LJ) fluid and water confined in a nanochannel. The deep learning model is built based on a convolutional encoder–decoder network (CED) and is applied for high-dimensional surrogate modeling to relate the fluid properties to the fluid–fluid potential. The CED model is then combined with the interatomic potential-based continuum theory to determine the concentration profiles of a confined LJ fluid and confined water. Further, we show that the DL-QT model exhibits robust predictive performance for a confined LJ fluid under various thermodynamic states and for water confined in a nanochannel of different widths. The DL-QT model seamlessly connects molecular physics at the nanoscale with continuum theory by using a deep learning model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Factorization at subleading power and endpoint-divergent convolutions in h → γγ decay

t is by now well known that, at subleading power in scale ratios, factorization theorems for high-energy cross sections and decay amplitudes contain endpoint-divergent convolution integrals. The presence of endpoint divergences hints at a violation of simple scale separation. At the technical level, they indicate an unexpected failure of dimensional regularization and the $\overline{MS}$ subtraction scheme. In this work, we start a detailed discussion of factorization at subleading power within the framework of soft-collinear effective theory. As a concrete example, we factorize the decay amplitude for the radiative Higgs-boson decay h → γγ mediated by a b-quark loop, for which endpoint-divergent convolution integrals require both dimensional and rapidity regulators. We derive a factorization theorem for the decay amplitude in terms of bare Wilson coefficients and operator matrix elements. We show that endpoint divergences caused by rapidity divergences cancel to all orders of perturbation theory, while endpoint divergences that are regularized dimensionally can be removed by rearranging the terms in the factorization theorem. We use our result to resum the leading double-logarithmic corrections of order $α^n_sln^{2n+2}(-M^2_h/m^2_b)$ to the decay amplitude to all orders of perturbation theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Understanding Twinning and Deformation in High Entropy Alloys

A combination of high strength and high ductility has been observed in multi-principal element alloys due to twin formation attributed to low stacking fault energy (SFE). In the pursuit of low SFE alloys, a key bottleneck is the lack of understanding of the composition–SFE cor- relations that would guide tailoring SFE via alloy composition. Using density functional theory (DFT), we show that dopant radius, which have been postulated as a key descriptor for SFE in dilute alloys, does not fully explain SFE trends across different host metals. Instead, charge density is a much more central descriptor. It allows us to (1) explain contrasting SFE trends in Ni and Cu host metals due to various dopants in dilute concentrations, (2) explain the large SFE variations observed in the literature even within a given alloy composition due to the nearest neighbor environments in “model” concentrated alloys, and (3) develop a machine learning model that can be used to predict SFEs in multi-elemental alloys. This model opens a possibility to use charge density as a descriptor for predicting SFE in alloys. Furthermore, a descriptor-less machine learning (ML) model based only on charge density images extracted from density functional theory (DFT) is developed to predict stacking fault energies (SFE) in concentrated alloys. The model is based on convolutional neural networks (CNNs) as one of the promising ML techniques for dealing with complex images and data. Identification of correct descriptors is a key bottleneck to develop ML models for predicting materials properties. Often, in most ML models, textbook physical descriptors such as atomic radius, valence charge and electronegativity are used as descriptors which have limitations because these properties change in concentrated alloys when multiple elements are mixed to form a solid solution. We illustrate that, within the scope of DFT, the search for descriptors can be circumvented by electronic charge density, which is the backbone of the Kohn-Sham DFT and describes the system completely. The performance of our model is demonstrated by predicting SFE of concentrated alloys with an RMSE and R2 of 6.18 mJ/m2 and 0.87, respectively, validating the accuracy of the proposed approach.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Factorization at subleading power and endpoint divergences in h → γγ decay. Part II. Renormalization and scale evolution

Building on the recent derivation of a bare factorization theorem for the b-quark induced contribution to the h → γγ decay amplitude based on soft-collinear effective theory, we derive the first renormalized factorization theorem for a process described at subleading power in scale ratios, where λ = m b /M h « 1 in our case. We prove two refactorization conditions for a matching coefficient and an operator matrix element in the endpoint region, where they exhibit singularities giving rise to divergent convolution integrals. The refactorization conditions ensure that the dependence of the decay amplitude on the rapidity regulator, which regularizes the endpoint singularities, cancels out to all orders of perturbation theory. We establish the renormalized form of the factorization formula, proving that extra contributions arising from the fact that “endpoint regularization” does not commute with renormalization can be absorbed, to all orders, by a redefinition of one of the matching coefficients. We derive the renormalization-group evolution equation satisfied by all quantities in the factorization formula and use them to predict the large logarithms of order $αα^2_sL^k$ in the three-loop decay amplitude, where $L=ln(-M^2_h/m^2_b)$ and k = 6, 5, 4, 3. We find perfect agreement with existing numerical results for the amplitude and analytical results for the three-loop contributions involving a massless quark loop. On the other hand, we disagree with the results of previous attempts to predict the series of subleading logarithms $~αα^n_sL^{2n+1}$

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

FeederGAN: Synthetic Feeder Generation via Deep Graph Adversarial Nets

This paper presents a novel, automated, generative adversarial networks (GAN) based synthetic feeder generation mechanism, abbreviated as FeederGAN. FeederGAN digests real feeder models represented by directed graphs via a deep learning framework powered by GAN and graph convolutional networks (GCN). Information of a distribution feeder circuit is extracted from its model input files so that the device connectivity is mapped onto the adjacency matrix and the device characteristics, such as circuit types (i.e., 3-phase, 2-phase, and 1-phase) and component attributes (e.g., length and current ratings), are mapped onto the attribute matrix. Then, Wasserstein distance is used to optimize the GAN and GCN is used to discriminate the generated graphs from the actual ones. A greedy method based on graph theory is developed to reconstruct the feeder using the generated adjacency and attribute matrices. Furthermore, our results show that the GAN generated feeders resemble the actual feeder in both topology and attributes verified by visual inspection and by empirical statistics obtained from actual distribution feeders.

42 ENGINEERING↗

DOE OSTI2023

Band-limited photodetection of temporal coherence

The quantum theory of optical coherence plays a ubiquitous role in identifying optical emitters. An unequivocal identification, however, presumes that the photon number statistics is resolved from timing uncertainties. We demonstrate from first principle that the observed nth-order temporal coherence is a n-fold convolution of the instrument responses and the expected coherence. The consequence is detrimental in which the photon number statistics is masked from the unresolved coherence signatures. The experimental investigations are thus far consistent with the theory developed. We envision the present theory will mitigate the false identification of optical emitters and enlarge the coherence deconvolution to an arbitrary order.

42 ENGINEERING↗

DOE OSTI2020

Prediction by Convolutional Neural Networks of CO 2 /N 2 Selectivity in Porous Carbons from N 2 Adsorption Isotherm at 77 K

Abstract Porous carbons are an important class of porous materials with many applications, including gas separation. An N 2 adsorption isotherm at 77 K is the most widely used approach to characterize porosity. Conventionally, textual properties such as surface area and pore volumes are derived from the N 2 adsorption isotherm at 77 K by fitting it to adsorption theory and then correlating it to gas separation performance (uptake and selectivity). Here the N 2 isotherm at 77 K was used directly as input (representing feature descriptors for the porosity) to train convolutional neural networks to predict gas separation performance (using CO 2 /N 2 as a test case) for porous carbons. The porosity space for porous carbons was explored for higher CO 2 /N 2 selectivity. Porous carbons with a bimodal pore‐size distribution of well‐separated mesopores (3–7 nm) and micropores (<2 nm) were found to be most promising. This work will be useful in guiding experimental research of porous carbons with the desired porosity for gas separation and other applications.

Wang, Song↗

DOE OSTI2020

Prediction by Convolutional Neural Networks of CO 2 /N 2 Selectivity in Porous Carbons from N 2 Adsorption Isotherm at 77 K

Wang, Song↗

DOE OSTI2024

Direct quarkonium production in DIS from a joint CGC and NRQCD framework

We compute the differential cross section for direct quarkonium production in high-energy electron-nucleus collisions at small 𝑥. Our computation is performed within the nonrelativistic QCD factorization formalism that separates the calculation into short distance coefficients and long distance matrix elements that depend on the color and spin of the state. We obtain the short distance coefficients of the production of the heavy quark pair within the framework of the color glass condensate effective field theory, which resums coherent multiple interactions of the heavy quark pair with the nucleus to all orders. Our results are expressed as the convolution of perturbatively calculable functions with multipoint lightlike Wilson line correlators. In the correlation limit, we establish the correspondence between our color glass condensate formulation with calculations employing the transverse momentum dependent (TMD) framework. We extend this correspondence by resumming kinematic power corrections within the improved TMD framework, which interpolates between the TMD formalism and 𝑘 ⊥ -factorization formalism. We present a detailed numerical analysis, focusing on 𝐽/𝜓 production in the kinematics accessible at the future Electron-Ion Collider, highlighting the importance of genuine higher-order saturation contributions when the electron collides with a large nucleus. Our results are also valid in the photoproduction limit where we expect the largest contribution from genuine higher-order saturation contributions which could be accessed in ultraperipheral collisions of relativistic heavy ions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Learning Optimal Multigrid Smoothers via Neural Networks

Multigrid methods are one of the most efficient techniques for solving large sparse linear systems arising from partial differential equations (PDEs) and graph Laplacians from machine learning applications. One of the key components of multigrid is smoothing, which aims at reducing high-frequency errors on each grid level. However, finding optimal smoothing algorithms is problem-dependent and can impose challenges for many problems. In this paper, we propose an efficient adaptive framework for learning optimized smoothers from operator stencils in the form of convolutional neural networks (CNNs). Here, the CNNs are trained on small-scale problems from a given type of PDEs based on a supervised loss function derived from multigrid convergence theories and can be applied to large-scale problems of the same class of PDEs. Numerical results on anisotropic rotated Laplacian problems and variable coefficient diffusion problems demonstrate improved convergence rates and solution time compared with classical hand-crafted relaxation methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Multi-task graph neural networks for simultaneous prediction of global and atomic properties in ferromagnetic systems *

Abstract We introduce a multi-tasking graph convolutional neural network, HydraGNN, to simultaneously predict both global and atomic physical properties and demonstrate with ferromagnetic materials. We train HydraGNN on an open-source ab initio density functional theory (DFT) dataset for iron-platinum with a fixed body centered tetragonal lattice structure and fixed volume to simultaneously predict the mixing enthalpy (a global feature of the system), the atomic charge transfer, and the atomic magnetic moment across configurations that span the entire compositional range. By taking advantage of underlying physical correlations between material properties, multi-task learning (MTL) with HydraGNN provides effective training even with modest amounts of data. Moreover, this is achieved with just one architecture instead of three, as required by single-task learning (STL). The first convolutional layers of the HydraGNN architecture are shared by all learning tasks and extract features common to all material properties. The following layers discriminate the features of the different properties, the results of which are fed to the separate heads of the final layer to produce predictions. Numerical results show that HydraGNN effectively captures the relation between the configurational entropy and the material properties over the entire compositional range. Overall, the accuracy of simultaneous MTL predictions is comparable to the accuracy of the STL predictions. In addition, the computational cost of training HydraGNN for MTL is much lower than the original DFT calculations and also lower than training separate STL models for each property.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Nonlocal Effective Field Theory and Its Applications

We review recent applications of nonlocal effective field theory, particularly focusing on nonlocal chiral effective theory and nonlocal quantum electrodynamics (QED), as well as an extension of nonlocal effective theory to curved spacetime. For the chiral effective theory, we discuss the calculation of generalized parton distributions (GPDs) of the nucleon at nonzero skewness, along with the corresponding gravitational (or mechanical) form factors, within the convolution framework. In the QED application, we extend the nonlocal formulation to construct the most general nonlocal QED interaction, in which both the propagator and fundamental QED vertex are modified due to the nonlocal Lagrangian, while preserving the Ward–Green–Takahashi identities. For consistency with the modified propagator, a solid quantization is proposed, and the nonlocal QED is applied to explain the lepton g−2 anomalies without the introduction of new particles beyond the standard model. Finally, with an extension of the chiral effective action to curved spacetime, we investigate the nonlocal energy–momentum tensor and gravitational form factors of the nucleon with a nonlocal pion–nucleon interaction.

chiral effective field theory↗

DOE OSTI2025

On finite-dimensional smoothed-particle Hamiltonian reductions of the Vlasov equation

The inclusion of spatial smoothing in finite-dimensional particle-based Hamiltonian reductions of the Vlasov equation and related models is considered. Here, this work investigates the underlying Hamiltonian structure of such smoothed particle-based methods for Hamiltonian systems and the small-scale regularization such methods implicitly make in approximating the continuum theory. In the context of the Vlasov–Poisson equation and other mean-field Lie–Poisson systems, of which Vlasov–Poisson is a special case, smoothing amounts to a convolutive regularization of the Hamiltonian. This regularization may be interpreted as a change of the inner product structure used to identify the dual space in the Lie–Poisson Hamiltonian formulation. In particular, the shape function used for spatial smoothing may be identified as the kernel function of a reproducing kernel Hilbert space whose inner product is used to define the Lie–Poisson Hamiltonian structure. It is likewise possible to introduce smoothing in the Vlasov–Maxwell system, but in this case the Poisson bracket must be modified rather than the Hamiltonian. The smoothing applied to the Vlasov–Maxwell system is incorporated by inserting smoothing in the map from canonical to kinematic coordinates. In the filtered system, the Lorentz force law and the current, the two terms coupling the Vlasov equation with Maxwell’s equations, are spatially smoothed.

Hamiltonian mechanics↗