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DOE OSTI2024

Hutchinson Trace Estimation for high-dimensional and high-order Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by seamlessly blending data and physics. However, extending PINNs to high-dimensional and even high-order PDEs encounters significant challenges due to the computational cost associated with automatic differentiation in the residual loss function calculation. Herein, we address the limitations of PINNs in handling high-dimensional and high-order PDEs by introducing the Hutchinson Trace Estimation (HTE) method. Starting with the second-order high-dimensional PDEs, which are ubiquitous in scientific computing, HTE is applied to transform the calculation of the entire Hessian matrix into a Hessian vector product (HVP). This approach not only alleviates the computational bottleneck via Taylor-mode automatic differentiation but also significantly reduces memory consumption from the Hessian matrix to an HVP’s scalar output. We further showcase HTE’s convergence to the original PINN loss and its unbiased behavior under specific conditions. Comparisons with the Stochastic Dimension Gradient Descent (SDGD) highlight the distinct advantages of HTE, particularly in scenarios with significant variability and variance among dimensions. We further extend the application of HTE to higher-order and higher-dimensional PDEs, specifically addressing the biharmonic equation. By employing tensor-vector products (TVP), HTE efficiently computes the colossal tensor associated with the fourth-order high-dimensional biharmonic equation, saving memory and enabling rapid computation. The effectiveness of HTE is illustrated through experimental setups, demonstrating comparable convergence rates with SDGD under memory and speed constraints. Additionally, HTE proves valuable in accelerating the Gradient-Enhanced PINN (gPINN) version as well as the Biharmonic equation. Overall, HTE opens up a new capability in scientific machine learning for tackling high-order and high-dimensional PDEs.

Curse of dimensionality↗

DOE OSTI2020

A numerical-homogenization based phase-field fracture modeling of linear elastic heterogeneous porous media

Most porous media, such as geomaterials and biomaterials are highly heterogeneous in nature, and they contain large variations of microscopic pore structures, such as pore sizes, pore distribution, and pore shapes. The oscillation of microscopic structures is a substantial challenge in theoretical characterization and is usually ignored in continuous modeling. However, mechanical behavior of porous media such as deformation and failure, are essentially impacted by the microscopic heterogeneity which needs to be considered in modeling a porous media. Here, this research proposes a numerical modeling framework with a capability to investigate the effect of microscopic heterogeneity on the macroscopic fracture behavior in porous media by using a numerical homogenization technique, combined with the phase-field fracture modeling method. This numerical modeling strategy computes a homogenized elasticity tensor based on microscopic heterogeneous pore structures heterogenous porous domain by solving boundary value problems at microscopic domain. The strain energy and subsequent propagation of macroscopic fractures will be updated using homogenized stiffness information. Using this numerical scheme, the microscopic pore structure’s impact on the fracture behavior through the homogenized elastic tensor will be taken into account. This multiscale technique is benchmarked against classical problems. Finally, the results highlight the importance of the underlying pore structure and reveal that both fracture strength and propagation path can be influenced by the microscopic heterogeneity.

36 MATERIALS SCIENCE↗

DOE OSTI2024

The use of digital thread for reconstruction of local fiber orientation in a compression molded pin bracket via deep learning

A deep convolutional neural network (DCNN) was used for microstructure reconstruction using artificial intelligence (MR-AI) by predicting local average fiber orientation distributions (FOD) in a 3D prepreg platelet molded composite (PPMC) pin bracket. To train the MR-AI model, surface strain fields from residual stresses simulated in PPMC plates were used as the input to the DCNN. A training dataset included PPMC plates with various degrees of global fiber alignment, based on the information obtained from high-fidelity flow simulation of a pin bracket. Further, the MR-AI model was then deployed to analyze FOD in the 3D pin bracket by conducting thermo-elastic residual stress analysis. Initially, the MR-AI model was established entirely on the synthetic simulation data. Then, a μCT scan of a physically molded pin bracket was used to create a finite element model that provided data for additional validation of the DCNN model. For the μCT scan finite element pin bracket the MR-AI model predicted the distribution of fiber orientation tensor components with MAE of 0.10 indicating a global prediction error of 10%. For the flow simulated pin bracket, the MR-AI model predicted the distribution of fiber orientation tensor components with a global prediction error of 11%. The MR-AI model showed the ability to predict regions of varying alignment in the base and flange of the pin bracket. The proposed MR-AI methodology allows for rapid prediction of FOD in geometrically complex parts and offers a promising path to detecting unique fiber orientation states in molded components.

42 ENGINEERING↗

DOE OSTI2022

Field validation of data-driven BSDF and peak extraction models for light-scattering fabric shades

Shading and daylighting systems affect cooling, heating, and lighting energy use by modulating solar radiation through the building façade. Characterizing shading systems holistically and accurately helps designers and engineers evaluate shading systems to achieve energy and non-energy performance goals. These complex fenestration systems can be modeled using Bidirectional Scattering Distribution Functions (BSDF), which map incident radiation to hemispherical distributions of outgoing radiation. Data-driven, tabulated BSDFs are derived from interpolated goniophotometer measured data, then sampled during the raytracing calculation. A peak extraction (PE) algorithm was developed to circumvent limits in BSDF angular resolution, where the specular peak is extracted during simulation by evaluating the BSDF in the through direction and surrounding region. The objective of this study was to validate this measurement and modeling workflow using field monitored data from a full scale testbed with eleven installed fabrics of different weaves, openness factors, and colors and assess the accuracy of the workflow under different adaptation and contrast conditions. Test conditions were limited to clear sky conditions with the sun in the field of view. Results showed that, for tensor tree datasets, vertical illuminance, solar luminance (2.5° apex), and daylight glare probability (DGP) were predicted to within a mean bias error (MBE) error of -456 lx (-12.3%), -3.46e5 (-38.4%), and -0.042 (-7.8%) when full PE occurred. With a binary classification of glare/ no glare, DGP was predicted accurately with a true positive rate of 0.98 and true negative rate of 1.0 using tensor tree data and less accurately with Klems BSDF data, particularly for cases of no glare. The workflow may be of insufficient accuracy to distinguish borderline performance between fabrics using the four-point glare scale, particularly under low adaptation, high contrast daylit conditions. Errors were due to reductions in peak shape and intensity across the BSDF interpolation and data reduction workflow. Future work is needed to better preserve measurement fidelity during interpolation and sampling, which in turn will improve PE performance.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

A collision operator for describing dissipation in noncanonical phase space

The phase space of a noncanonical Hamiltonian system is partially inaccessible due to dynamical constraints (Casimir invariants) arising from the kernel of the Poisson tensor. When an ensemble of noncanonical Hamiltonian systems is allowed to interact, dissipative processes eventually break the phase space constraints, resulting in a thermodynamic equilibrium described by a Maxwell–Boltzmann distribution. However, the time scale required to reach Maxwell–Boltzmann statistics is often much longer than the time scale over which a given system achieves a state of thermal equilibrium. Examples include diffusion in rigid mechanical systems, as well as collisionless relaxation in magnetized plasmas and stellar systems, where the interval between binary Coulomb or gravitational collisions can be longer than the time scale over which stable structures are self-organized. Here, we focus on self-organizing phenomena over spacetime scales such that particle interactions respect the noncanonical Hamiltonian structure, but yet act to create a state of thermodynamic equilibrium. We derive a collision operator for general noncanonical Hamiltonian systems, applicable to fast, localized interactions. This collision operator depends on the interaction exchanged by colliding particles and on the Poisson tensor encoding the noncanonical phase space structure, is consistent with entropy growth and conservation of particle number and energy, preserves the interior Casimir invariants, reduces to the Landau collision operator in the limit of grazing binary Coulomb collisions in canonical phase space, and exhibits a metriplectic structure. We further show how thermodynamic equilibria depart from Maxwell–Boltzmann statistics due to the noncanonical phase space structure, and how self-organization and collisionless relaxation in magnetized plasmas and stellar systems can be described through the derived collision operator.

Boltzmann equation↗

DOE OSTI2026

Solid state 59 Co NMR study of a Np(VII) compound

Np(VII) compounds with [Co(NH 3 ) 6 ] 3+ cations were synthesized and structurally examined using powder X-ray diffraction. Multiple phases were observed, consisting of octahedral [Co(NH 3 ) 6 ] 3+ cations, discrete tetragonal bipyramidal [NpO 4 (OH) 2 ] 3− anions, and waters of hydration. Electric field gradient tensors at Co sites were measured by solid state 59 Co nuclear magnetic resonance (NMR) spectroscopy and compared with theoretical calculations. The relative contributions of the chemical shift and electric field tensors to the NMR lineshape were determined by recording spectra at field strengths of 7.04 and 11.74 Tesla. Further, the evolution of structure and morphology as a function of sample age and the effects on NMR spectral parameters has also been investigated. These results demonstrate the use of NMR at multiple fields to expand understanding of the stability and electronic structure of high valent neptunium compounds.

heptavalent neptunium↗

DOE OSTI2020

Energy conservative SBP discretizations of the acoustic wave equation in covariant form on staggered curvilinear grids

In this work, we develop a numerical method for solving the acoustic wave equation in covariant form on staggered curvilinear grids in an energy conserving manner. The use of a covariant basis decomposition leads to a rotationally invariant scheme that outperforms a Cartesian basis decomposition on rotated grids. The discretization is based on high order Summation-By-Parts (SBP) operators and preserves both symmetry and positive definiteness of the contravariant metric tensor. To improve accuracy and decrease computational cost, we also derive a modified discretization of the metric tensor that leads to a conditionally stable discretization. Bounds are derived that yield a point-wise condition that can be evaluated to check for stability of the modified discretization. This condition shows that the interpolation operators should be constructed such that their norm is close to one.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

An arbitrarily high-order three-dimensional Cartesian-grid method for reconstructing interfaces from volume fraction fields

Here Tthis work describes a newly developed, arbitrarily high-order Cartesian-grid method for reconstructing material interfaces from a volume fraction field. The method begins by identifying all of the grid cells in the volume fraction field that are intersected by the interface and need to be approximated by the reconstruction scheme. Finite-differences are used to calculate the gradient of the volume fraction field and provide an estimate of the surface normal in all of the interfacial grid cells. Groups of connected grid cells are then identified which all have the same dominant component of the normal vector. This grouping by orientation determines the proper dependent variable to use in the surface reconstruction (e.g. for a 2D curve, this step determines if the surface will be approximated by a function of x or y). A cumulative integral over the surface is constructed and fit using b-splines for two-dimensional problems or tensor-product b-splines for three-dimensional problems. This construction allows for the interface to be recovered through application of the second fundamental theorem of calculus. Fitting the cumulative integral with $\mathscr{N}$ th-order b-splines (or tensor-product b-splines) yields an ($\mathscr{N}$-1) th-order convergence rate of the interface shape. Differentiation of the b-spline interface function(s) allows for the high-order approximation of the normal vector and curvature to be obtained directly anywhere along b-spline. Together, the proposed reconstruction technique can achieve arbitrarily high mesh convergence rates. Validation tests are presented with mesh convergence rates ranging from fourth- to tenth-order.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗

DOE OSTI2024

In situ measurement of three-dimensional intergranular stress localizations and grain yielding under elastoplastic axial-torsional loading

The three-dimensional grain-averaged response of solid bar samples under non-proportional (NP) elastoplastic axial-torsional loading was investigated using in situ high energy diffraction microscopy (HEDM) and companion crystal plasticity finite element (CPFE) modeling. Important stress metrics including applied shear (σ θZ ) and axial (σ ZZ ) stress tensor components, stress and stress deviator tensor invariants (I 1 , J 2 , and J 3 ), von Mises equivalent stress (σ$^{grain}_{VM}$), maximum resolved shear stress (mRSS), stress triaxiality (η), and lode angle parameter ($\barθ$) values were tracked for ~300 grains under two different loading conditions: (1) Torsion-dominated loading (low NP) and (2) Tension-torsion loading (high NP) in equiatomic NiCoCr, a representative multicomponent face-centered cubic (FCC) superalloy. Overall, significant stress localizations existed within both samples as evidenced by the radial dependence of grain-resolved σ θZ , σ$^{grain}_{VM}$, and J 2 ; by comparison, I 1 , J 3 , η, and $\barθ$ metrics did not show discernible trends within the volume. These stress localizations reveal a complex interplay between axial and shear stress components (e.g., stress coupling) resulting in grain yielding near the sample surface largely driven by shear stress, whereas internal grain yielding was largely accommodated by axial stress. Grain-resolved stress localization trends were described well by the CPFE model, although some discrepancies in magnitude occurred, particularly for volumetric stress metrics (I 1 and η) due to initial type II residual stress distributions. The superposition of initial residual stress states onto CPFE grain-resolved data significantly improved model accuracy for η. This suggests that residual stresses more strongly influence the simulation of volumetric rather than deviatoric (yield) stress metrics.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Determination of single crystal thermal expansion in Uranium-6wt%Niobium shape memory alloy using in-situ diffraction and modeling of textured polycrystalline samples

In-situ neutron diffraction and ex-situ dilatometry experiments were performed on a chemically banded, quenched uranium-6wt% niobium shape memory alloy to study the impact of deformation-(detwinning-) induced texture on the evolution of thermally induced strains (and associated stresses). Thermal heating and cooling cycles between 5K and 473K were performed in-situ with neutron diffraction, and the lattice strain evolution is reported for the observed monoclinic α" phase. Comparisons between the measured diffraction strains and macroscopic dilatometry experiments reveal relationships between micro- and macro-level thermal expansion. Softening of the texture during heating suggests that twin boundary motion can accommodate the large internal thermal strains which are approximately 2% greater than that typically observed during the 175K heating interval used to age more randomly oriented polycrystalline material. Assuming weak constraint of neighboring grains in randomly textured polycrystals, the single crystal thermal expansion tensor is extracted from measurements of lattice strains over the range 5K to 473K. Predictions of polycrystalline thermal expansion, based upon this single crystal thermal expansion tensor, are shown to compare favorably with bulk thermal expansion observations of the as quenched microstructure. However, such a lower-bound estimate is insufficient to explain all aspects of the behavior of the textured material, where the matrix is not isotropic. In conclusion, it is hypothesized that relaxation processes which occur within the quenched microstructure during heating are responsible for the distinct thermal expansion behavior observed during the initial heating cycle compared to cooling and subsequent cycling.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Low rank approximation in simulations of quantum algorithms

Simulating quantum algorithms on classical computers is challenging when the system size, i.e., the number of qubits used in the quantum algorithm, is moderately large. However, some quantum algorithms and the corresponding quantum circuits can be simulated efficiently on a classical computer if the input quantum state is a low rank tensor and all intermediate states of the quantum algorithm can be represented or approximated by low rank tensors. Here, in this paper, we examine the possibility of simulating a few quantum algorithms by using low-rank canonical polyadic (CP) decomposition to represent the input and all intermediate states of these algorithms. Two rank reduction algorithms are used to enable efficient simulation. We show that some of the algorithms preserve the low rank structure of the input state and can thus be efficiently simulated on a classical computer. However, the rank of the intermediate states in other quantum algorithms can increase rapidly, making efficient simulation more difficult. To some extent, such difficulty reflects the advantage or superiority of a quantum computer over a classical computer. As a result, understanding the low rank structure of a quantum algorithm allows us to identify algorithms that can benefit significantly from quantum computers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Graph neural networks for mechanical property prediction of 2D fiber composites

This work investigates the ability of graph neural networks (GNNs) to homogenize 2D fiber composite microstructures. We use different inhomogeneity and anisotropy indices to motivate and show that the Volume Elements (VEs) used in ML methods should ideally be far from their Representative Volume Element (RVE) size limit and, consequently, are notably anisotropic. Hence, training only the isotropic limit properties may not be acceptable. Another aspect is the need to normalize elastic stiffness values for ML, especially when high elastic contrast ratios are encountered between composite phases or in the material set. We introduce a normalization technique based on the mean-field method (MFM) to handle such high contrast ratios and train for the entire stiffness tensor. We show that the proposed GNN approaches exhibit high accuracy and efficiency compared to traditional methods and convolutional neural networks, utilizing unstructured graphs constructed from microstructure topology. Our model successfully predicts the stiffness tensor, peak strength under bulk damage, and brittle fracture initiation strength across diverse microstructure configurations while maintaining high accuracy even for extreme material contrasts and volume fractions. We also present a method to improve prediction accuracy for small dataset sizes using Voronoi partitioning.

Brittle strength↗

DOE OSTI2023

ECCE sensitivity studies for single hadron transverse single spin asymmetry measurements

Here, we performed feasibility studies for various single transverse spin measurements that are related to the Sivers effect, transversity and the tensor charge, and the Collins fragmentation function. The processes studied include semi-inclusive deep inelastic scattering (SIDIS) where single hadrons (pions and kaons) were detected in addition to the scattered DIS lepton. The data were obtained in pythia6 and geant4 simulated e+p collisions at 18 GeV on 275 GeV, 18 on 100, 10 on 100, and 5 on 41 that use the ECCE detector configuration. Typical DIS kinematics were selected, most notably Q 2 >1 GeV 2 , and cover the x range from 10 -4 to 1. The single spin asymmetries were extracted as a function of x and Q 2 , as well as the semi-inclusive variables z, which corresponds to the momentum fraction the detected hadron carries relative to the struck parton, and P T , which corresponds to the transverse momentum of the detected hadron relative to the virtual photon. They are obtained in azimuthal moments in combinations of the azimuthal angles of the hadron transverse momentum and transverse spin of the nucleon relative to the lepton scattering plane. In order to extract asymmetries, the initially unpolarized MonteCarlo was re-weighted in the true kinematic variables, hadron types and parton flavors based on global fits of fixed target SIDIS experiments and e + e – annihilation data. The expected statistical precision of such measurements is extrapolated to 10 fb –1 and potential systematic uncertainties are approximated given the deviations between true and reconstructed yields. Similar neutron information is obtained by comparing the ECCE e+p pseudo-data with the same from the EIC Yellow Report and scaling the corresponding Yellow Report e+ 3 He pseudo-data uncertainties accordingly. The impact on the knowledge of the Sivers functions, transversity and tensor charges, and the Collins function has then been evaluated in the same phenomenological extractions as in the Yellow Report. Finally, the impact is found to be comparable to that obtained with the parametrized Yellow Report detector and shows that the ECCE detector configuration can fulfill the physics goals on these quantities.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Weyl-ambient geometries

Weyl geometry is a natural extension of conformal geometry with Weyl covariance mediated by a Weyl connection. We generalize the Fefferman-Graham (FG) ambient construction for conformal manifolds to a corresponding construction for Weyl manifolds. We first introduce the Weyl-ambient metric motivated by the Weyl-Fefferman-Graham (WFG) gauge. From a top-down perspective, we show that the Weyl-ambient space as a pseudo-Riemannian geometry induces a codimension-2 Weyl geometry. Then, from a bottom-up perspective, we start from promoting a conformal manifold into a Weyl manifold by assigning a Weyl connection to the principal R+-bundle realizing a Weyl structure. We show that the Weyl structure admits a well-defined initial value problem, which determines the Weyl-ambient metric. Through the Weyl-ambient construction, we also investigate Weyl-covariant tensors on the Weyl manifold and define extended Weyl-obstruction tensors explicitly.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Evolution of tensile and shear cracking in crystalline rocks under compression

Here we performed laboratory-scale unconfined compression experiments on Barre granite specimen with a single pre-existing flaw to study the evolution of tensile and shear cracking that occurs during different stress levels. Moment tensor inversion of acoustic emission (AE) events in combination with the nonelastic strain component obtained through the 2D digital image correlation (DIC) technique are used to track the changes in the source mechanisms of the stress-induced cracks. The mode of deformation computed from the image based strain profiles, enables visual comparison of the nucleation, growth and interaction of the tensile and shear cracks with the microseismic source mechanism observed by moment tensor inversion of the AE events. Comparing the results obtained from the two techniques on the same dataset demonstrates a quantitative correlation between the acoustic and visual observations in terms of the cracking mechanisms obtained at different stages of cracking from crack initiation at the flaw tips to the failure of the rock specimen.

58 GEOSCIENCES↗

DOE OSTI2021

Hamiltonian kinetic-Hall magnetohydrodynamics with fluid and kinetic ions in the current and pressure coupling schemes

We present two generalized hybrid kinetic-Hall magnetohydrodynamics (MHD) models describing the interaction of a two-fluid bulk plasma, which consists of thermal ions and electrons, with energetic, suprathermal ion populations described by Vlasov dynamics. The dynamics of the thermal components are governed by standard fluid equations in the Hall MHD limit with the electron momentum equation providing an Ohm's law with Hall and electron pressure terms involving a gyrotropic electron pressure tensor. The coupling of the bulk, low-energy plasma with the energetic particle dynamics is accomplished through the current density (current coupling scheme; CCS) and the ion pressure tensor appearing in the momentum equation (pressure coupling scheme; PCS) in the first and the second model, respectively. The CCS is a generalization of two well-known models, because in the limit of vanishing energetic and thermal ion densities, we recover the standard Hall MHD and the hybrid kinetic-ions/fluid-electron model, respectively. This provides us with the capability to study in a continuous manner, the global impact of the energetic particles in a regime extending from vanishing to dominant energetic particle densities. The noncanonical Hamiltonian structures of the CCS and PCS, which can be exploited to study equilibrium and stability properties through the energy-Casimir variational principle, are identified. As a first application here, we derive a generalized Hall MHD Grad–Shafranov–Bernoulli system for translationally symmetric equilibria with anisotropic electron pressure and kinetic effects owing to the presence of energetic particles using the PCS.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Ten-moment fluid modeling of the Weibel instability

We investigate the one-dimensional non-relativistic Weibel instability through the capture of anisotropic pressure tensor dynamics using an implicit 10-moment fluid model that employs the electromagnetic Darwin approximation. The results obtained from the 10-moment model are compared with an implicit particle-in-cell simulation. The linear growth rates obtained from the numerical simulations are in good agreement with the theoretical fluid and kinetic dispersion relations. The fluid dispersion relations are derived using Maxwell’s equations and the Darwin approximation. We also show that the magnetohydrodynamic approximation can be used to model the Weibel instability if one accounts for an anisotropic pressure tensor and unsteady terms in the generalised Ohm’s law. In addition, we develop a preliminary theory for the saturation magnetic field strength of the Weibel instability, showing good agreement with the numerical results.

Kuldinow, D. A. (ORCID:0000000319730196)↗