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DOE OSTI2026

Enabling probabilistic learning on manifolds through double diffusion maps

Here, we present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.

Double diffusion maps↗

DOE OSTI2021

An FFT-based approach for Bloch wave analysis: application to polycrystals

A method based on the Fast Fourier Transform is proposed to obtain the dispersion relation of acoustic waves in heterogeneous periodic media with arbitrary microstructures. The microstructure is explicitly considered using a voxelized Representative Volume Element (RVE). The dispersion diagram is obtained solving an eigenvalue problem for Bloch waves in Fourier space. To this aim, two linear operators representing stiffness and mass are defined through the use of differential operators in Fourier space. The smallest eigenvalues are obtained using the implicitly restarted Lanczos and the subspace iteration methods, and the required inverse of the stiffness operator is done using the conjugate gradient with a preconditioner. The method is used to study the propagation of acoustic waves in elastic polycrystals, showing the strong effect of crystal anistropy and polycrystaline texture on the propagation. It is shown that the method combines the simplicity of classical Fourier series analysis with the versatility of Finite Elements to account for complex geometries proving an efficient and general approach which allows the use of large RVEs in 3D.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Space-time dependent thermal conductivity in nonlocal thermal transport

Nonlocal thermal transport is generally described by the Peierls-Boltzmann transport equation (PBE). However, solving the PBE for a general space-time dependent problem remains a challenging task due to the high dimensionality of the integro-differential equation. In this work, we present a direct solution to the space-time dependent PBE with a linearized collision matrix using an eigendecomposition method. We show that there exists a generalized Fourier-type relation that links heat flux to the local temperature, and this constitutive relation defines a thermal conductivity that depends on both time and space. Combining this approach with ab initio calculations of phonon properties, we demonstrate that the space-time dependent thermal conductivity gives rise to an oscillatory response in temperature in a transient grating geometry in high thermal conductivity materials. The present solution method allows us to extend the reach of our computational capability for heat conduction to space-time dependent nondiffusive transport regimes. Here, this capability will not only enable a more accurate interpretation of thermal measurements that observe nonlocal thermal transport, but also enhance our physical understanding of nonlocal thermal transport in high thermal conductivity materials that are promising candidates for nanoscale thermal management applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Frequency domain assurance criterion for defect detection in additively manufactured parts

Additive manufacturing (AM) is a very desirable manufacturing method for industries such as aerospace and automotive due to its ability to create internal features and complex geometries, however, these characteristics also present challenges for nondestructive evaluation (NDE) and defect detection. Dynamic analysis and modal analysis have shown promise for NDE and identifying flaws in AM parts. Frequency Domain Assurance Criterion (FDAC) is a method of dynamic evaluation that represents the degree of correlation between two sets of operational deflection shapes (ODS) at each spectral line. Using colormaps to display the results allows for quick and easy interpretation of parts’ similarities and differences. This method appears to show promise in identifying parts with minor defects and can be used to differentiate nominal and defective parts. This paper explores the use of FDAC on various AM parts with and without intentional defects.

Deonarain, G↗

DOE OSTI2023

Behavior of Hydrogarnet‐Type Defects in Hydrous Stishovite at Various Temperatures and Pressures

Abstract Dense polymorphs of silica have been demonstrated experimentally to incorporate from 1.5 wt% to as much as 11.6 wt% H 2 O as OH groups, with implications for the hydrogen budgets of Earth and other planets. This OH is thought to enter the SiO 2 structure via a charge‐balanced substitution in which silicon vacancies (V Si ) are compensated by protonating four of the surrounding six oxygen atoms, often referred to as a hydrogarnet‐type defect. There are many possible configurations for this defect structure in dense silica, but the nature of these configurations and whether they can be distinguished experimentally is unknown. We present here density functional theory calculations that systematically assess the possible configurations of a hydrogarnet‐type defect in stishovite (rutile‐type SiO 2 ), with direct comparisons to experimental vibrational spectroscopy data. We predict that stishovite synthesized at 450 K and 10 GPa quenched to room temperature is dominated by a single defect type with tetrahedral geometry. This leads to OH stretching modes (2,500–3,000 cm −1 ) and SiOH bending modes (∼1,400–1,450 cm −1 ) largely consistent with experimentally observed modes. One remaining issue is that our calculations produce results compatible with experimental data on H to D exchange, but do not explain why a considerable fraction of the 1,420 cm −1 mode shifts by only 40 cm −1 in deuterated samples. At elevated pressures and temperatures, we find that a second square planar defect configuration also becomes favorable, leading to modes that should allow differentiation from the tetrahedral configuration.

Geochemistry & Geophysics↗

DOE OSTI2026

Magnus force induced magnetic diode effect in skyrmion systems

We show that skyrmions can exhibit a “magnetic diode effect,” where there is a nonreciprocal response in the transport when the magnetic field is reversed. This effect can be achieved for skyrmions moving in channels with a sawtooth potential on one side and a reversed sawtooth potential on the other side. We consider the cases of both spin-transfer torque (STT) and spin–orbit torque (SOT). When the magnetic field is held fixed, the velocity response of the skyrmion is the same for current applied in either direction for both torques, so there is no current diode effect. When the magnetic field is reversed, under STT driving the velocity of the skyrmion reverses and its absolute value changes. Under SOT driving, the velocity remains in the same direction but drops to a much lower value, resulting in negative differential conductivity. For a fixed current, we find a nonreciprocal skyrmion velocity as a function of the applied field’s sign, in analogy to the velocity–current curves observed in the usual diode effect. The nonreciprocity is generated by the Magnus force, which causes skyrmions to interact preferentially with one side of the channel. Since the channel sides have opposite asymmetry, a positive magnetic field can cause the skyrmion to interact with the “hard” asymmetry side of the channel, while a negative magnetic field causes the skyrmion to interact with the “easy” asymmetry side. This geometry could be used to create new kinds of magnetic-field-induced diode effects that can be harnessed in new types of skyrmion-based devices.

36 MATERIALS SCIENCE↗

DOE OSTI2021

The PENELOPE Physics Models and Transport Mechanics. Implementation into Geant4

A translation of the PENELOPE physics subroutines to C++, designed as an extension of the GEANT4 toolkit, is presented. The Fortran code system PENELOPE performs Monte Carlo simulation of coupled electron-photon transport in arbitrary materials for a wide energy range, nominally from 50 eV up to 1 GeV. PENELOPE implements the most reliable interaction models that are currently available, limited only by the required generality of the code. In addition, the transport of electrons and positrons is simulated by means of an elaborate class II scheme in which hard interactions (involving deflection angles or energy transfers larger than pre-defined cutoffs) are simulated from the associated restricted differential cross sections. After a brief description of the interaction models adopted for photons and electrons/positrons, we describe the details of the class-II algorithm used for tracking electrons and positrons. The C++ classes are adapted to the specific code structure of GEANT4. They provide a complete description of the interactions and transport mechanics of electrons/positrons and photons in arbitrary materials, which can be activated from the G4ProcessManager to produce simulation results equivalent to those from the original PENELOPE programs. The combined code, named PENG4, benefits from the multi-threading capabilities and advanced geometry and statistical tools of GEANT4.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Slow manifold reduction as a systematic tool for revealing the geometry of phase space

Many non-dissipative reduced plasma models can be derived from more fundamental non-dissipative models by restricting to an approximate invariant manifold. I present a general systematic procedure for finding the Hamiltonian formulation of a plasma model that can be derived in this manner. Several illustrative examples are considered in detail.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Tip-based proximity ferroelectric switching and piezoelectric response in wurtzite multilayers

Proximity ferroelectricity is a paradigm for inducing ferroelectricity when a nonferroelectric polar material (such as Al⁢ N), which is unswitchable with an external field below the dielectric breakdown field, becomes a practically switchable ferroelectric in direct contact with a thin switchable ferroelectric layer (such as Al 1−𝑥 ⁢Sc 𝑥 ⁢N). Here, we develop a Landau-Ginzburg-Devonshire approach to study the proximity effect of local piezoelectric response and polarization reversal in wurtzite ferroelectric multilayers under a sharp electrically biased tip. Using finite-element modeling, we analyze the probe-induced nucleation of nanodomains, the features of local polarization hysteresis loops and coercive fields in the Al 1−𝑥 ⁢Sc 𝑥 ⁢N/Al⁢ N bilayers and three-layers. Similar to the wurtzite multilayers sandwiched between two parallel electrodes, the regimes of “proximity switching” (when all layers collectively switch) and the regime of “proximity suppression” (when they collectively do not switch) are the only two possible regimes in the probe-electrode geometry. However, the parameters and asymmetry of the local piezoresponse and polarization hysteresis loops depend significantly on the sequence of the layers with respect to the probe. The physical mechanism of proximity ferroelectricity in the local probe geometry is a depolarizing electric field determined by the polarization of the layers and their relative thickness. The field, whose direction is opposite to the polarization vector in the layer(s) with the larger spontaneous polarization (such as Al⁢ N), renormalizes the double-well ferroelectric potential to lower the steepness of the switching barrier in the “otherwise unswitchable” polar layers. Tip-based control of domains in otherwise nonferroelectric layers using proximity ferroelectricity can provide nanoscale control of domain reversal in memory, actuation, sensing, and optical applications. The ability of the tip-induced proximity switching to differentially switch multilayers, based on the order of the layers, provides a powerful tool for selective domain engineering.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Computational Modeling of Graphite Degradation due to Molten Salt Infiltration and Wear

Molten-salt reactors (MSRs) represent a promising next-generation reactor design, with graphite serving as a moderator and/or reflector in several designs. However, due to limited experimental data and operational experience, a technical understanding of the structural integrity of graphite in molten salt environments remains incomplete. This report presents a modeling-based evaluation of graphite degradation in MSR environments, focusing on the effects of salt infiltration in fuel salt-based designs and surface wear in pebble bed reactor designs. The objective of this study is to enhance understanding of the structural integrity challenges posed by these degradation mechanisms and to provide a framework for assessing graphite behavior in MSRs. The first part of the report investigates the phenomenon of molten salt infiltration into graphite. This infiltration occurs when molten salt permeates the interconnected pore structure of the graphite moderator, driven by factors such as pressure differentials and the physical properties of both the salt and graphite. The infiltration process is influenced by characteristics of the pore structure, viscosity of the molten salt, and the interfacial energies between the graphite, salt, and the atmosphere within the graphite pore. Utilizing a coupled multiphysics modeling approach with Grizzly software, the study evaluates the stress induced by internal heat sources due to infiltration, which can lead to structural concerns. This evaluation is crucial for understanding how infiltration affects the mechanical integrity of graphite components in MSRs. The study considers the Molten-Salt Reactor Experiment (MSRE) graphite stringer geometry due to the availability of relevant data. Through detailed finite element analysis, the study examines stress distributions at varying infiltration percentages, revealing that stress levels increase with higher amounts of infiltration. Rare-event simulations, using the parallel subset simulation (PSS) framework, further quantify the failure probabilities under input uncertainties, with a user-specified failure metric. The PSS framework also identifies critical input parameters that significantly affect the stress values, including infiltration amount, thermal conductivity, and power density. Additionally, considering realistic reactor scenarios, the analysis was performed to account for the combined effects of radiation and infiltration, and modeling strategies on how to analyze new reactor designs or new graphite grades are discussed. The second part of the report focuses on wear mechanisms in pebble bed-based MSRs. As graphite fuel pebbles interact with the graphite reflector block, wear can result in material loss and the formation of surface defects, which may act as stress concentrators. A similar multiphysics modeling framework is employed to assess the impact of wear on the structural integrity of graphite components. This study considers a generic fluoride-cooled high-temperature reactor (gFHR) design due to the availability of comprehensive data. Worst-case scenario dimensions of the reflector blocks were analyzed under thermal and radiation conditions. Subsequently, wear in the form of idealized pits and grooves is modeled on the inner surface of the graphite block, with the maximum stress from previous simulations. The simulations show that groove-type defects are more detrimental than pits, leading to higher stress concentrations. Considering worst-case simulation scenarios and experimental wear rates, it was determined that the formation of a surface defect critical enough to affect the stress may not be possible in a gFHR design. Overall, the findings of this research contribute to the development of robust modeling tools for predicting graphite behavior under various operational conditions in MSRs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

VALVE TIMING AND AREA PROFILE SELECTION FOR HYDRAULIC PUMPS AND MOTORS

A significant amount of research has been conducted to select valve timing and area profiles that create efficient and quiet hydraulic pumps and motors. Numerous active valve architectures have been modeled and optimized, but the rationale for the final solution is often unclear. The solution is usually highly dependent on the modeled valve geometry constraints and the duty cycle of the pump or motor for which the valve was optimized. This paper first presents an ideal valve area profile and what compromises are made to design for a working pressure and speed range. The ideal valve area profile is resolved using a piston-cylinder model with a pressure dependent bulk modulus and variable valve openings. The piston-cylinder is first modeled as a pump with passive (check) valves and a specified pressure drop across the valves to determine the ideal area profile. A generalization of the ideal timing is demonstrated for positive pressure differential and positive rotation direction, also known as the first quadrant. The effects on valve timing when varying pressure are shown for the first quadrant, but the trends can be extrapolated for all quadrants of operation. The ideal valve profile is implemented as fixed valve timing, meaning the valve area is only a function of the timing angle, in a pump-motor. The pump-motor is simulated in one rotation direction through a pressure range. Performance is high in pumping operation, but when the pressure differential is reversed, cylinder pressure spikes ensue. Two strategies to modify an ideal valve area profile are presented: timing grooves and a pressure shifted valve timing. Timing grooves reduce pressure spikes and cavitation in the cylinder but generally increase throttling losses. A pressure shifted valve timing has lower throttling energy losses, making it the favored solution.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Cartesian equivariant representations for learning and understanding molecular orbitals

Qualitative and quantitative orbital properties such as bonding/antibonding character, localization, and orbital energies are critical to how chemists understand reactivity, catalysis, and excited-state behavior. Despite this, representations of orbitals in deep learning models have been very underdeveloped relative to representations of molecular geometries and Hamiltonians. Here, we apply state-of-the-art equivariant deep learning architectures to the task of assigning global labels to orbitals, namely energies characterizations, given the molecular coefficients from Hartree–Fock or density functional theory. The architecture we have developed, the Cartesian Equivariant Orbital Network (CEONET), shows how molecular orbital coefficients are readily featurized as equivariant node features common to all graph-based machine-learned potentials. We find that CEONET performs well at predicting difficult quantitative labels such as the orbital energy and orbital entropy. Furthermore, we find that the CEONET representation provides an intuitive latent space for differentiating orbital character for the qualitative assignment of e.g. bonding or antibonding character. In addition to providing a useful representation for further integrating deep learning with electronic structure theory, we expect CEONET to be useful for automatizing and interpreting the results of advanced electronic structure methods such as complete active space self-consistent field theory. In particular, the ability of CEONET to infer multireference character via the orbital entropy paves the way toward the machine-learned selection of active spaces.

chemical reactions↗

DOE OSTI2024

AMReX v2024

The software framework, AMReX, supports the development of block-structured adaptive mesh refinement (AMR) algorithms for solving systems of partial differential equations. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving the essential local descriptions of different physical processes in complex multiphysics algorithms. AMR uses a hierarchical representation of the solution at multiple levels of resolution where the solution on each level is defined on the union of data containers at that resolution. These data containers, which represent the solution over a logically rectangular subregion of the domain, can contain field data defined on a mesh, Lagrangian particles or combinations of both. In addition to these basic data types, AMReX supports a multilevel embedded boundary representation of complex geometry; linear solvers for cell-centered and nodal data; asynchronous I/O in a native format readable by ParaView, VisIt and yt; and interfaces to hypre and PETSc solvers. AMReX enables applications to run on distributed memory architectures with multicore CPUs and with GPU accelerators. AMReX uses a lightweight abstraction layer that effectively hides the details of the architecture from the application. The framework currently supports CUDA, HIP and SYCL for GPU acceleration and OpenMP for multi-core CPU architectures.

Almgren, Ann↗

DOE OSTI2021

Fracture Network Localization Preceding Catastrophic Failure in Triaxial Compression Experiments on Rocks

We quantify the spatial distribution of fracture networks throughout six in situ X-ray tomography triaxial compression experiments on crystalline rocks at confining stresses of 5–35 MPa in order to quantify how fracture development controls the final macroscopic failure of the rock, a process analogous to those that control geohazards such as earthquakes and landslides. Tracking the proportion of the cumulative volume of fractures with volumes >90th percentile to the total fracture volume, ∑ v 90 / v t o t indicates that the fracture networks tend to increase in localization toward these largest fractures for up to 80% of the applied differential stress. The evolution of this metric also matches the evolution of the Gini coefficient, which measures the deviation of a population from uniformity. These results are consistent with observations of localizing low magnitude seismicity before large earthquakes in southern California. In both this analysis and the present work, phases of delocalization interrupt the general increase in localization preceding catastrophic failure, indicating that delocalization does not necessarily indicate a reduction of seismic hazard. However, the proportion of the maximum fracture volume to the total fracture volume does not increase monotonically. Experiments with higher confining stress tend to experience greater localization. To further quantify localization, we compare the geometry of the largest fractures, with volumes >90th percentile, to the best fit plane through these fractures immediately preceding failure. The r 2 scores and the mean distance of the fractures to the plane indicate greater localization in monzonite than in granite. The smaller mean mineral diameter and lower confining stress in the granite experiments may contribute to this result. Tracking these various metrics of localization reveals a close association between macroscopic yielding and the acceleration of fracture network localization. Near yielding, ∑ v 90 / v t o t and the Gini coefficient increase while the mean distance to the final failure plane decreases. Macroscopic yielding thus occurs when the rate of fracture network localization increases.

58 GEOSCIENCES↗

DOE OSTI2025

Solving sparse finite element problems on neuromorphic hardware

The finite element method (FEM) is one of the most important and ubiquitous numerical methods for solving partial differential equations (PDEs) on computers for scientific and engineering discovery. Applying the FEM to larger and more detailed scientific models has driven advances in high-performance computing for decades. Here we demonstrate that scalable spiking neuromorphic hardware can directly implement the FEM by constructing a spiking neural network that solves the large, sparse, linear systems of equations at the core of the FEM. We show that for the Poisson equation, a fundamental PDE in science and engineering, our neural circuit achieves meaningful levels of numerical accuracy and close to ideal scaling on modern, inherently parallel and energy-efficient neuromorphic hardware, specifically Intel’s Loihi 2 neuromorphic platform. We illustrate extensions to irregular mesh geometries in both two and three dimensions as well as other PDEs such as linear elasticity. Our spiking neural network is constructed from a recurrent network model of the brain’s motor cortex and, in contrast to black-box deep artificial neural network-based methods for PDEs, directly translates the well-understood and trusted mathematics of the FEM to a natively spiking neuromorphic algorithm.

Applied mathematics↗

DOE OSTI2020

Detection, monitoring, and determination of location of changes in metallic structures using multimode acoustic signals

Methods for detection, monitoring, and determination of location of changes in rigid structures with arbitrarily complex geometries are described. Implementations include locating acoustic transducers that generate and receive acoustic signals at multiple locations along a surface of the rigid structure, wherein longitudinal spacing between the transducer locations define measurement zones. Acoustic signals with chosen amplitude-time-frequency characteristics excite multiple vibration modes in the structure within each zone. Small mechanical changes in the inspection zones lead to scattering and attenuation of broadband acoustic signals, which are detectable as changes in received signal characteristics as part of a through-transmission technique. Additional use of short, narrowband pulse acoustic signals as part of a pulse-echo technique allows determination of the relative location of the mechanical change within each zone based on the differential delay profiles.

42 ENGINEERING↗

DOE OSTI2020

Deep Minima in the Triply Differential Cross Section for Ionization of Atomic Hydrogen by Electron and Positron Impact

We investigate ionization of atomic hydrogen by electron- and positron-impact. We apply the Coulomb–Born (CB1) approximation, various modified CB1 approximations, the three body distorted wave (3DW) approximation, and the time-dependent close-coupling (TDCC) method to electron-impact ionization of hydrogen. For electron-impact ionization of hydrogen for an incident energy of approximately 76.45 eV, we obtain a deep minimum in the CB1 triply differential cross section (TDCS). However, the TDCC for 74.45 eV and the 3DW for 74.46 eV gave a dip in the TDCS. For positron-hydrogen ionization (breakup) we apply the CB1 approximation and a modified CB1 approximation. We obtain a deep minimum in the TDCS and a zero in the CB1 transition matrix element for an incident energy of 100 eV with a gun angle of 56.13 °. Corresponding to a zero in the CB1 transition matrix element, there is a vortex in the velocity field associated with this element. For both electron- and positron-impact ionization of hydrogen the velocity field rotates in the same direction, which is anticlockwise. All calculations are performed for a doubly symmetric geometry; the electron-impact ionization is in-plane and the positron-impact ionization is out-of-plane.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Fluoropolymer Aging Phenomena

This project aims to investigate structural and morphological changes in fluoropolymers induced by both processing and aging phenomena such as heat, time, and irradiation. Fluoropolymers are an important class of thermoplastics that are broadly used in industry as o-rings and seals when chemical resistance and thermal performance are important. They are also often used in thin film geometries as binders in batteries, insulation layers, water barriers, and anti-fouling coatings. For all of these applications, mechanical integrity and aging are important aspects of their use. Changes in the crystalline morphology are known to impact the mechanical properties of the polymer and can lead to failure. The broad goals of this project are to correlate compositional changes, morphological changes, and mechanical changes. report focuses on the morphological changes that are correlated with nuclear magnetic resonance (NMR), calorimetry and mechanical testing. We plan to compare structure and morphology measurements across complementary bulk and surface techniques. We use in situ atomic force microscopy (AFM) to measure domain shape and crystallization kinetics; in situ NMR to measure crystalline composition; and differential scanning calorimetry (DSC) to measure melting temperatures.

36 MATERIALS SCIENCE↗