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DOE OSTI2025

Kernel Manifolds: Nonlinear‐Augmentation Dimensionality Reduction Using Reproducing Kernel Hilbert Spaces

This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections, augment linear dimensionality reduction with a nonlinear correction term in the reconstruction map to overcome approximation accuracy limitations of purely linear approaches. While feature map-based approaches typically learn a least squares optimal polynomial correction term, we generalize this approach by learning an optimal nonlinear correction from a user-defined reproducing kernel Hilbert space. Our approach allows one to impose arbitrary nonlinear structure on the correction term, including polynomial structure, and includes feature map and radial basis function-based corrections as special cases. Furthermore, our method has relatively low training cost and has monotonically decreasing error as the latent space dimension increases. In conclusion, we compare our approach to proper orthogonal decomposition and several recent QM approaches on data from several example problems.

kernel methods↗

DOE OSTI2020

Process optimization of complex geometries using feed forward control for laser powder bed fusion additive manufacturing

Additive manufacturing (AM) enables the fabrication of complex designs that are difficult to create by other means. Metal parts manufactured by laser powder bed fusion (LPBF) can incorporate intricate design features and demonstrate desirable mechanical properties. However, printing a part that is qualified for its intended application often involves reprinting and discarding many parts to eliminate defects, improve dimensional accuracy, and increase repeatability. The process of iteratively converging on the appropriate build parameters increases the time and cost of creating functional LPBF manufactured parts. This work describes a fast, scalable method for part-scale process optimization of arbitrary geometries. Additionally, the computational approach uses feature extraction to identify scan vectors in need of parameter adaptation and applies results from simulation-based feed forward control models. This method provides a framework to quickly optimize complex parts through the targeted application of models with a range of fidelity and by automating the transfer of optimization strategies to new part designs. The computational approach and algorithmic framework are described, a software package is implemented, the method is applied to parts with complex features, and parts are printed on a customized open architecture LPBF machine.

3D printing↗

DOE OSTI2020

Laser writing of nitrogen-doped silicon carbide for biological modulation

Conducting or semiconducting materials embedded in insulating polymeric substrates can be useful in biointerface applications; however, attainment of this composite configuration by direct chemical processes is challenging. Laser-assisted synthesis has evolved as a fast and inexpensive technique to prepare various materials, but its utility in the construction of biophysical tools or biomedical devices is less explored. Here, we use laser writing to convert portions of polydimethylsiloxane (PDMS) into nitrogen-doped cubic silicon carbide (3C-SiC). The dense 3C-SiC surface layer is connected to the PDMS matrix via a spongy graphite layer, facilitating electrochemical and photoelectrochemical activity. We demonstrate the fabrication of arbitrary two-dimensional (2D) SiC-based patterns in PDMS and freestanding 3D constructs. To establish the functionality of the laser-produced composite, we apply it as flexible electrodes for pacing isolated hearts and as photoelectrodes for local peroxide delivery to smooth muscle sheets.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Stochastic Modeling in a Multimaterial Continuum Mixture Shock Physics Code

Stochastic modelling approaches are presented to capture random effects at multiple time and length scales. Random processes that occur at the microscale produce nondeterministic effects at the macroscale. Here we present three stochastic modeling approaches that describe random processes at microscopic length scales and map these processes to the macroscopic length scale. The first stochastic modeling approach is based upon a particle based numerical technique to solve a Stochastic Differential Equation (SDE) using an arbitrary diffusion process to capture random processes at the microstructural level. The second approach prescribes a Probability Density Function (PDF) for the drift and diffusion of the random variable derived using the forward and backward Kolmogorov equations. This method requires mean and drift evolution PDF transport equations. The third approach is the coupling of multiple random variables which are dependent on each other. The relationship of the PDFs and a coupling function, known as a copula, produces a Joint Probability Density Function (JPDF). These stochastic modeling approaches are implemented into a Multiple Component (MC) shock physics computational code and used to model statistical fracture and reactive flow applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Design of a neutral thermal scattering (NeTS) module for hydrogen in light water

The accurate representation of thermal scattering law (TSL) data is integral to the design and characterization of many modern nuclear systems, particularly those using light water as a moderator/coolant. As a material-dependent distribution over energy-momentum phase space, the TSL may exhibit a variety of unique and relevant conditional (e.g., temperature, pressure) and compositional (e.g., porosity, stoichiometry, radiation damage) dependencies. Currently, there are various approaches to incorporate temperature dependence, which is especially important in coupled neutronic-thermal hydraulic simulations. In each approach, there is an inherent tradeoff between memory consumption and accuracy. Some techniques require tens to hundreds of MBs or more, while others fail to reproduce the underlying data to within 10% error over the considered input domain, despite having a reduced storage burden. This work aims to address both sides of the tradeoff simultaneously by implementing a novel deep learning (DL) approach to TSL representation. The neural thermal scattering (NeTS) concept, which is amenable to an arbitrary number of dependencies, is demonstrated via the inclusion of temperature dependence into a highly compact, highly accurate functional form of the multi- variate TSL (i.e., S(α, β, T)) for hydrogen in light water. Resulting storage requirements are on the order of 100 kB, and median and maximum percent deviations are on the order of 0.1% and 1%, respectively. These measures represent a step improvement over previous techniques. Notably, the developed neural network and feature methodology build on those employed in prior work on beryllium oxide. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Pick-and-Place Transfer of Arbitrary-Metal Electrodes for van der Waals Device Fabrication

Van der Waals electrode integration is a promising strategy to create nearly perfect interfaces between metals and 2D materials, with advantages such as eliminating Fermi-level pinning and reducing contact resistance. However, the lack of a simple, generalizable pick-and-place transfer technology has greatly hampered the wide use of this technique. Here, we demonstrate the pick-and-place transfer of prefabricated electrodes from reusable polished hydrogenated diamond substrates without the use of any sacrificial layers due to the inherent low-energy and dangling-bond-free nature of the hydrogenated diamond surface. The technique enables transfer of arbitrary-metal electrodes and an electrode array, as demonstrated by successful transfer of eight different elemental metals with work functions ranging from 4.22 to 5.65 eV. We also demonstrate the electrode array transfer for large-scale device fabrication. The mechanical transfer of metal electrodes from diamond to van der Waals materials creates atomically smooth interfaces with no interstitial impurities or disorder, as observed with cross-section high-resolution transmission electron microscopy and energy-dispersive X-ray spectroscopy. As a demonstration of its device application, we use the diamond transfer technique to create metal contacts to monolayer transition metal dichalcogenide semiconductors with high-work-function Pd, low-work-function Ti, and semimetal Bi to create n- and p-type field-effect transistors with low Schottky barrier heights. We also extend this technology to air-sensitive materials (trilayer 1T’ WTe 2 ) and other applications such as ambipolar transistors, Schottky diodes, and optoelectronics. This highly reliable and reproducible technology paves the way for new device architectures and high-performance devices.

2D materials↗

DOE OSTI2026

Dynamic Multipoles in the RCS

The Rapid Cycling Synchrotron (RCS) of the Electron--Ion Collider (EIC) will accelerate polarized electrons up to 18 GeV at a repetition rate of 1 Hz. Dynamic multipoles driven by eddy currents in the vacuum chamber can affect beam dynamics and polarization preservation during the energy ramp. Building on the analytical treatment of S.Y. Lee for a ramped normal-conducting dipole magnet, we use conformal transformations to derive compact expressions for dynamic multipoles in higher-order ramped magnets with circular beam pipes. We further derive analytical frequency-domain transfer functions for both self-response and cross-response multipoles, providing compact dynamical models for their evolution during arbitrary ramp waveforms. The resulting analytical predictions are benchmarked against finite-element simulations, including the effects of practical pole geometry and beam-pipe misalignment. Finally, the expected dynamic multipoles in the RCS magnets are estimated and their implications for beam dynamics and polarization preservation are discussed.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Triangle Method for Dense ReLU Layers [SWR-25-72]

This software is an implementation of the methods for initializing and training neural networks to be more efficient per parameter, described more fully below and in the related publication: In theory, depth should make a ReLU network EXPONENTIALLY more efficient by enabling it to produce an exponential number of piecewise linear sections in its output. This reasoning is largely based on the work of mathematicians that have hand-constructed networks that make good use of depth. In practice however, even very deep ReLU networks that have been randomly initialized will behave identically to their shallow counterparts - missing an entire exponential dimension of efficiency. The triangle method is a first attempt at realizing the exponential potential of deep networks. Instead of randomly setting weights, we force pairs of neurons in each layer learn to build triangles (i.e. functions from [0,1] -> [0,1] that look like triangles). This is a very efficient pattern for generating lots of linear pieces because composing two triangular functions doubles the number of pieces with each composition. The triangle method is more than just a different initialization, it is a new paradigm of training. Instead of making direct updates to the matrix weights, we do an extra step of backpropagation to collect the derivatives of the loss function with respect to the shapes of the triangles, training them to tilt left or right. This process essentially holds the networks hand throughout the loss landscape and forces it to always use depth effectively by producing triangular shapes internally. This can produce several orders of magnitude of improvement on convex one-dimensional regression problems. Much more theoretical work is needed to realize its full potential beyond this context, but the implementation in this repository will still work in arbitrary numbers of dimensions. The file Triangle_Method.py is a generalized form of the method that will build each neuron its own custom 1-d convex activation function (with exponential efficiency). Example usage on one dimensional problems can be found in Example_Usage.ipynb and an example of using this in a real neural network can be found in Example_VGG16_CIFAR10.ipynb.

Milkert, Max [National Renewable Energy Laboratory↗

DOE OSTI2022

Rotational symmetry relation for efficient response function generation in the coarse mesh transport method COMET

The coarse mesh transport code COMET is a continuous energy hybrid stochastic-deterministic neutronics solver with high fidelity and formidable computation speed in solving reactor core problems. Its method is based on the incident flux expansion theory. In this work, we take advantage of the local geometric symmetry in many reactor cores lattices (e.g., fuel lattices and reflector blocks) to develop relations among the flux response expansion coefficients for symmetric surfaces to further improve the computational efficiency of the COMET response function generation tool (method). This is done by a rigorous derivation of the transformation matrices for the angular and spatial expansion moments resulting from a rotation of a coarse mesh by an arbitrary angle. The relations for the response coefficients for the symmetric surfaces can be then written as the Kronecker product of those transformation matrices. The method is implemented into COMET and tested on two advanced high temperature reactor (AHTR) full-length single assembly benchmark problems. The COMET results using the response function library based on the symmetry relations were compared to those using the library directly generated by continuous energy Monte Carlo for all surfaces. It was found that the eigenvalues and stripe-wise fission densities using the two libraries are in statistical agreement as expected. This indicates that the new method maintains the high fidelity of the original COMET method while improving the computational efficiency in the response function generation by 270% to 400%, depending on the local geometric symmetry. This method also reduces the size of the response function library by the same magnitude (270% to 400%). (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2020

Porous cage-derived nanomaterial inks for direct and internal three-dimensional printing

The convergence of 3D printing techniques and nanomaterials is generating a compelling opportunity space to create advanced materials with multiscale structural control and hierarchical functionalities. While most nanoparticles consist of a dense material, less attention has been payed to 3D printing of nanoparticles with intrinsic porosity. Here, we combine ultrasmall (about 10 nm) silica nanocages with digital light processing technique for the direct 3D printing of hierarchically porous parts with arbitrary shapes, as well as tunable internal structures and high surface area. Thanks to the versatile and orthogonal cage surface modifications, we show how this approach can be applied for the implementation and positioning of functionalities throughout 3D printed objects. Furthermore, taking advantage of the internal porosity of the printed parts, an internal printing approach is proposed for the localized deposition of a guest material within a host matrix, enabling complex 3D material designs.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A general kinetic framework for dislocation mobility derived from probabilistic cellular automaton simulations of the kink-pair mechanism

Dislocation mobility laws are essential components of dislocation-density-based crystal plasticity models. For dislocations governed by the kink-pair mechanism, however, existing formulations are typically limited to specific regimes due to the com plex interplay between stochastic kink-pair nucleation and lateral kink migration. In this work, we develop a general kinetic framework that expresses the average dislocation velocity as a function of mechanism-level variables: positive/negative kink pair nucleation rates, kink migration velocity, dislocation segment length, critical kink-pair width, and kink height. Probabilis tic cellular automaton simulations are used to capture the behavior of conceptual dislocation segments between the limiting conditions of migration outpacing nucleation on the one end and nucleation outpacing migration on the other. An elemen tary functional form that captures the system dynamics is suggested and fitted against the simulation results. This framework remains valid for arbitrary combinations of the six variables and is, therefore, compatible with any admissible constitutive re lations that describe their stress and temperature dependence. Comparisons with established approaches and experimental results confirm the robustness and physical consistency of the formulation, making it broadly applicable to material systems in which dislocation motion is governed by the kink-pair mechanism.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Flow-driven spectral chaos (FSC) method for simulating long-time dynamics of arbitrary-order non-linear stochastic dynamical systems

Uncertainty quantification techniques such as the time-dependent generalized polynomial chaos (TD-gPC) use an adaptive orthogonal basis to better represent the stochastic part of the solution space (aka random function space) in time. However, because the random function space is constructed using tensor products, TD-gPC-based methods are known to suffer from the curse of dimensionality. Here, we introduce a new numerical method called the flow-driven spectral chaos (FSC) which overcomes this curse of dimensionality at the random-function-space level. The proposed method is not only computationally more efficient than existing TD-gPC-based methods but is also far more accurate. The FSC method uses the concept of enriched stochastic flow maps to track the evolution of a finite-dimensional random function space efficiently in time. To transfer the probability information from one random function space to another, two approaches are developed and studied herein. In the first approach, the probability information is transferred in the mean-square sense, whereas in the second approach the transfer is done exactly using a new theorem that was developed for this purpose. The FSC method can quantify uncertainties with high fidelity, especially for the long-time response of stochastic dynamical systems governed by ODEs of arbitrary order. Six representative numerical examples, including a nonlinear problem (the Van-der-Pol oscillator), are presented to demonstrate the performance of the FSC method and corroborate the claims of its superior numerical properties. Finally, a parametric, high-dimensional stochastic problem is used to demonstrate that when the FSC method is used in conjunction with Monte Carlo integration, the curse of dimensionality can be overcome altogether.

(nonlinear) stochastic dynamical systems↗

DOE OSTI2020

Mapped Moments to a Cartesian Grid (MMCG) Value-Added Product Report

Objective analysis (OA) is a method of mapping unstructured data to a structured grid. In the context of scanning radar data, OA is used to interpolate data in antenna coordinates (range, azimuth, and elevation) onto a regularly spaced Cartesian grid (Trapp and Doswell 2000). The U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility’s Mapped Moments to a Cartesian Grid (MMCG) Value-Added Product (VAP) uses the Python ARM Radar Toolkit (Py-ART), a data model-driven interactive architecture for working with weather radar data, to map the data to a Cartesian grid (Helmus and Collis 2016). MMCG, with Py-ART built in, has the ability to take radar data in antenna coordinates and map the gates to a Cartesian grid using inverse distance weight functions such as Cressman (square) and Barnes (exponential), but also can filter the data during the interpolation. MMCG also allows arbitrary formulations for the radius of influence, which are matched to particular radar scanning strategies. This creates a complex parameter space for optimizing the retention of storm structure detail while minimizing artifacts. MMCG takes data processed with ARM’s Corrected Precipitation Radar Moments in Antenna Coordinates (CMAC) VAP and maps it to a Cartesian grid as the output product. A variety of fields that have been mapped to the Cartesian grid are then saved to plots to complement each grid file.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

The eXtended virtual element method for elliptic problems with weakly singular solutions

This paper introduces a novel eXtended virtual element method, an extension of the conforming virtual element method. The X-VEM is formulated by incorporating appropriate enrichment functions in the local spaces. The method is designed to handle highly generic enrichment functions, including singularities arising from fractured domains. By achieving consistency on the enrichment space, the method is proven to achieve arbitrary approximation orders even in the presence of singular solutions. The paper includes a complete convergence analysis under general assumptions on mesh regularity, and numerical experiments validating the method’s accuracy on various mesh families, demonstrating optimal convergence rates in the L 2 - and H 1 - norms on fractured or L-shaped domains.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Approximating accelerator impedances with resonator networks

It is common in the accelerator community to use the impedance of accelerator components to describe wake interactions in the frequency domain. However, it is often desirable to understand such wake interactions in the time domain in a general manner for excitations that are not necessarily Gaussian in nature. Here, the conventional method for doing this involves taking the inverse Fourier Transform of the component impedance, obtaining the Green's Function, and then convolving it with the desired excitation distribution. This method can prove numerically cumbersome, for a convolution integral must be evaluated for each individual point in time when the wake function is desired. An alternative to this method would be to compute the wake function analytically, which would sidestep the need for repetitive integration. Only a handful of cases, however, are simple enough for this method to be tenable. One of these cases is the case where the component in question is an RLC resonator, which has a closed-form analytical wake function solution. This means that a component which can be represented in terms of resonators can leverage this solution. As it happens, common network synthesis techniques may be used to map arbitrary impedance profiles to RLC resonator networks in a manner the accelerator community has yet to take advantage of. In this work, we will use Foster Canonical Resonator Networks and partial derivative descent optimization to develop a technique for synthesizing resonator networks that well approximate the impedances of real-world accelerator components. We will link this synthesis to the closed-form resonator wake function solution, giving rise to a powerful workflow that may be used to streamline beam dynamics simulations.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Drell-Yan q T resummation of fiducial power corrections at N 3 LL

We consider Drell-Yan production pp → V*X → LX at small q T << Q, where q T and Q are the total transverse momentum and invariant mass of the leptonic final state L. Experimental measurements require fiducial cuts on L, which in general introduce enhanced, linear power corrections in q T /Q. We show that they can be unambiguously predicted from factorization, and resummed to the same order as the leading-power contribution. For the fiducial q T spectrum, they constitute the complete linear power corrections. We thus obtain predictions for the fiducial q T spectrum to N 3 LL and next-to-leading-power in q T /Q. Matching to full NNLO ($α$$^{2}_{s}$), we find that the linear power corrections are indeed the dominant ones, and once included by factorization, the remaining fixed-order corrections become almost negligible below q T ≲ 40 GeV. We also discuss the implications for more complicated observables, and provide predictions for the fiducial Φ* spectrum at N 3 LL+NNLO. We find excellent agreement with ATLAS and CMS measurements of q T and Φ*. We also consider the $p$$^{ℓ}_{T}$ spectrum. We show that it develops leptonic power corrections in q T /(Q – 2$p$$^{ℓ}_{T}$), which diverge near the Jacobian peak $p$$^{ℓ}_{T}$ ~ Q/2 and must be kept to all powers to obtain a meaningful result there. Doing so, we obtain for the first time an analytically resummed result for the $p$$^{ℓ}_{T}$ spectrum around the Jacobian peak at N 3 LL+NNLO. Our method is based on performing a complete tensor decomposition for hadronic and leptonic tensors. We show that in practice this is equivalent to often-used recoil prescriptions, for which our results now provide rigorous, formal justification. Our tensor decomposition yields nine Lorentz-scalar hadronic structure functions, which for Z/γ* → ℓℓ or W → ℓν directly map onto the commonly used angular coefficients, but also holds for arbitrary leptonic final states. In particular, for suitably defined Born-projected leptons it still yields a LO-like angular decomposition even when including QED final-state radiation. Finally, we also discuss the application to q T subtractions. Including the unambiguously predicted fiducial power corrections significantly improves their performance, and in particular makes them applicable near kinematic edges where they otherwise break down due to large leptonic power corrections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Medial axis and local thickness computation using the Fast Sweeping Method

This report describes an efficient and robust voxel-based methodology for computing the medial axis, local thickness, and distance-to-skeleton of arbitrary three-dimensional geometries. It is assumed that the object can be represented by an exact or approximate signed distance function on a discrete grid. The gradient of such function is used to formulate a hyperbolic partial differential equation (PDE) that models the collapse of the position vector in space. By exploiting the causality property of the PDE, the Fast Sweeping Method is able to obtain the solution in a finite number of sweeps independent of the mesh resolution. The intersection of characteristic lines leads to the formation of shocks and a discrete bisector function is used to identify the medial axis. The same PDE approach is used to compute the local thickness inside the object and obtain the distance-to-skeleton field. Multiple examples are given in two and three dimensions along with a resolution study. The methodology has optimal complexity and yields subsecond computational times for geometries with over a million zones on a single core. The methodology is also capable of parallelization across shared and distributed memory architectures.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Multiscale formulation of frictional contact mechanics at the pore scale

Direct numerical simulation (DNS) yields the highest fidelity predictions of mechanical deformation at the pore scale, but is prohibitively expensive for analyzing large or many samples. Discrete element methods (DEM) are an efficient alternative, but are limited to granular media and incapable of estimating or controlling prediction errors. We present a pore-level multiscale method (PLMM) that approximates DNS efficiently and with controllable accuracy. We focus on the linear elastic response of a consolidated geologic porous medium with arbitrary microstructure, heterogeneous mineralogy, containing cracks or defects. PLMM decomposes the solid phase into non-overlapping subdomains, on which local basis functions are constructed. The bases are then coupled with a global interface problem that accounts for slip or stick contact conditions between the subdomains. PLMM produces an initial, but accurate, approximation to DNS that can be iteratively improved. It is amenable to parallelism and allows for different mesh, models, and physics in each subdomain. An algebraic interpretation of PLMM as a preconditioner is also presented to allow non-intrusive implementation into existing solvers. Lastly, this work extends previous developments of PLMM in fluid dynamics to solid mechanics and enables future extensions towards modeling coupled flow and mechanics problems.

42 ENGINEERING↗