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DOE OSTI2025

A review of low-rank methods for time-dependent kinetic simulations

Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised of a six–dimensional phase space, making simulations of such phenomena extremely expensive. In this article we demonstrate that in many situations, the solution to kinetics problems lives on a low dimensional manifold that can be described by a low-rank matrix or tensor approximation. We then review the recent development of so-called low-rank methods that evolve the solution on this manifold. The two classes of methods we review are the dynamical low-rank (DLR) method, which derives differential equations for the low-rank factors, and a Step-and-Truncate (SAT) approach, which projects the solution onto the low-rank representation after each time step. Thorough discussions of time integrators, tensor decompositions, and method properties such as structure preservation and computational efficiency are included. We further show examples of low-rank methods as applied to particle transport and plasma dynamics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Mechanisms of Metal Additive-Induced Ordering During SNIPS Membrane Formation

Isoporous membranes can be fabricated by combining self-assembly with nonsolvent induced phase separation (SNIPS) using an amphiphilic block copolymer like polystyrene-b-poly(4-vinylpyridine) (SV). Poly(4-vinylpyridine) (V) is known to complex with metal salts, which are hypothesized to stabilize solution ordering and preserve structure during casting. We explored how the molar ratio of metal additive to the poly(4-vinylpyridine) block affected the final membrane morphology via scanning electron microscopy (SEM). Dynamic light scattering (DLS), small-angle X-ray scattering (SAXS), and in situ grazing-incidence SAXS were used to track changes in solution ordering and chain conformation as a function of the molar ratio of the additive to the V block. Additives induced aggregation, promoted the formation of more compact conformations in solution, and facilitated micelle ordering onto lattices at optimal ratios. Furthermore, these experimental results were supported by random phase approximation calculations, which helped explain how the thermodynamic order–disorder transition shifts with additive binding strength. Stronger additive–polymer interactions reduced the block copolymer volume fraction required for ordering in solution, allowing ordered domains to form at lower polymer concentrations.

Additives↗

DOE OSTI2024

Neural network representations of multiphase Equations of State

Abstract Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general Equation of State model are adherence to the Laws of Thermodynamics, incorporation of phase transitions, and multiscale accuracy. Analytic models that adhere to all three are hard to develop and cumbersome to work with, often resulting in sacrificing one of these elements for the sake of efficiency. In this work, two deep-learning methods are proposed that provably satisfy the first and second conditions on a large-enough region of thermodynamic variable space. The first is based on learning the generating function (thermodynamic potential) while the second is based on structure-preserving, symplectic neural networks, respectively allowing modifications near or on phase transition regions. They can be used either “from scratch” to learn a full Equation of State, or in conjunction with a pre-existing consistent model, functioning as a modification that better adheres to experimental data. We formulate the theory and provide several computational examples to justify both approaches, highlighting their advantages and shortcomings.

Science & Technology - Other Topics↗

DOE OSTI2026

Counting topological interface modes using simplicial characteristic classes

A computational approach for predicting the number of topological interface modes (TIMs) in hermitian systems using the spectral flow—monopole correspondence is presented. The number of TIMs is determined by calculating the Chern number of a complex line bundle of local polarisation vectors over a phase space sphere surrounding a Weyl point. The Chern number is computed by constructing the simplicial first Chern class of a discrete vector bundle on a simplicial mesh. This approach is gauge invariant, derivative free, structure preserving, and robust to noise. The algorithm is shown to reproduce the expected number of TIMs for the case of equatorial fluid waves and the topological Langmuir cyclotron wave. The possibility of using this algorithm to analyse experimental measurements of bulk wave polarisations and predict the associated number of TIMs is explored in a synthetic example.

discrete vector bundles↗

DOE OSTI2025

Feature learning and generalization in deep networks with orthogonal weights

Fully-connected deep neural networks with weights initialized from independent Gaussian distributions can be tuned to criticality, which prevents the exponential growth or decay of signals propagating through the network. However, such networks still exhibit fluctuations that grow linearly with the depth of the network, which may impair the training of networks with width comparable to depth. We show analytically that rectangular networks with tanh activations and weights initialized from the ensemble of orthogonal matrices have corresponding preactivation fluctuations which are independent of depth, to leading order in inverse width. Moreover, we demonstrate numerically that, at initialization, all correlators involving the neural tangent kernel (NTK) and its descendants at leading order in inverse width—which govern the evolution of observables during training—saturate at a depth of ~20, rather than growing without bound as in the case of Gaussian initializations. We speculate that this structure preserves finite-width feature learning while reducing overall noise, thus improving both generalization and training speed in deep networks with depth comparable to width. We provide some experimental justification by relating empirical measurements of the NTK to the superior performance of deep non-linear orthogonal networks trained under full-batch gradient descent on the MNIST and CIFAR-10 classification tasks.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Quaternary MgSiN 2 -GaN alloy semiconductors for deep UV applications

Ultrawide direct band gap semiconductors hold great promise for deep ultraviolet optoelectronic applications. Here we evaluate the potential of MgSiN 2 -GaN alloys for this purpose. Although MgSiN 2 itself has an indirect gap ~0.4 eV below its direct gap of ~6.5 eV, its different sign lattice mismatch from GaN in two different basal plane directions could avoid the tensile strain which limits Al x Ga 1–x N on GaN for high x. Two octet-rule-preserving structures (with space groups Pmn2 1 and P1n1) of a 50% alloy of MgSiN 2 and GaN are investigated and are both found to have gaps larger than 4.75 eV using quasiparticle self-consistent GW calculations. Both are nearly direct gap in the sense that the indirect gap is less than 0.1 eV lower than the direct gap. Furthermore, their mixing energies are positive yet small, with values of 8 (31) meV/atom for Pmn2 1 (P1n1), indicating only a small driving force toward phase separation.

36 MATERIALS SCIENCE↗

DOE OSTI2025

In situ atomic-resolution imaging of water vapor–driven multistep oxidation dynamics in strontium cobaltite

Understanding how water vapor interacts with transition metal oxides (TMOs) is critical for tailoring material properties to improve performance and enable new technologies. Despite extensive research efforts, atomic-scale mechanisms underpinning dynamic reactions and reaction-induced phase transitions remain elusive. Here, we use in situ environmental transmission electron microscopy to investigate how water vapor oxidizes vacancy-ordered SrCoO 2.5 at moderately elevated temperatures, demonstrating that water molecules can initiate oxidation more effectively than oxygen under comparable conditions. We discover a distinct “staging” behavior during the oxidation process: A fully ordered intermediate phase, SrCoO 2.75 , forms before transitioning into a near-perovskite SrCoO 3−δ . In addition, antiphase boundaries, originating at step terraces of SrTiO 3 , alleviate strain by creating reversible nanoscale “gaps” during lattice contraction under oxidation, providing a pathway for preserving structural integrity throughout redox cycling. This work provides atomic-level guidance for engineering TMOs by leveraging water vapor to control their redox behavior and tailor functional properties.

Science & Technology - Other Topics↗

DOE OSTI2023

MrHyDE v.1.0

SAND2024-01324O MrHyDE, which stands for Multi-resolution Hybridized Differential Equations, is a general-purpose C++ package for the solution of coupled multiphysics and multiscale systems on massively parallel computing systems. MrHyDE is designed to enable moving beyond forward simulation for multiscale applications which includes optimization, control, uncertainty quantification, and stochastic inversion. The framework provides interfaces to several packages within the Trilinos framework and leverages automatic differentiation to enable adjoint capabilities for large-scale, gradient-based optimization. MrHyDE provides automated multiscale capabilities through a subgrid model interface and multiscale Dirichlet-to-Neumann maps. For extreme-scale applications, MrHyDE provides in situ data-compression algorithms to reduce memory requirements while maintaining performance. MrHyDE is a general-purpose, computational framework for the solution of multiscale and multiphysics applications. It uses a combination of structure-preserving, physics-compatible discretizations, fully implicit methods, multi-resolution schemes, or fully explicit methods. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗

DOE OSTI2021

Sandia / IBM Discussion on Machine Learning for Materials Applications [Slides]

This report includes a compilation of several slide presentations: 1) Interatomic Potentials for Materials Science and Beyond–Advances in Machine Learned Spectral Neighborhood Analysis Potentials (Wood); 2) Agile Materials Science and Advanced Manufacturing through AI/ML (de Oca Zapiain); 3) Machine Learning for DFT Calculations (Rajamanickam); 4) Structure-preserving ML discovery of a quantum-to-continuum codesign stack (Trask); and 5) IBM Overview of Accelerated Discovery Technology (Pitera)

36 MATERIALS SCIENCE↗

DOE OSTI2024

Small‐Molecule Mixed Ionic‐Electronic Conductors for Efficient N‐Type Electrochemical Transistors: Structure‐Function Correlations

Abstract The fundamental challenge in electron‐transporting organic mixed ionic‐electronic conductors (OMIECs) is simultaneous optimization of electron and ion transport. Beginning from Y6‐type/U‐shaped non‐fullerene solar cell acceptors, we systematically synthesize and characterize molecular structures that address the aforementioned challenge, progressively introducing increasing numbers of oligoethyleneglycol (OEG; g) sidechains from 1 g to 3 g, affording OMIECs 1gY, 2gY, and 3gY, respectively. The crystal structure of 1gY preserves key structural features of the Y n series: a U‐shaped/planar core, close π–π molecular stacking, and interlocked acceptor groups. Versus inactive Y6 and Y11, all of the new glycolated compounds exhibit mixed ion‐electron transport in both conventional organic electrochemical transistor (cOECT) and vertical OECT (vOECT) architectures. Notably, 3gY with the highest OEG density achieves a high transconductance of 16.5 mS, an on/off current ratio of ~10 6 , and a turn‐on/off response time of 94.7/5.7 ms in vOECTs. Systematic optoelectronic, electrochemical, architectural, and crystallographic analysis explains the superior 3gY‐based OECT performance in terms of denser n gY OEG content, increased crystallite dimensions with decreased long‐range crystalline order, and enhanced film hydrophilicity which facilitates ion transport and efficient redox processes. Finally, we demonstrate an efficient small‐molecule‐based complementary inverter using 3gY vOECTs, showcasing the bioelectronic applicability of these new small‐molecule OMIECs.

Cho, Yongjoon↗

DOE OSTI2024

Small‐Molecule Mixed Ionic‐Electronic Conductors for Efficient N‐Type Electrochemical Transistors: Structure‐Function Correlations

Cho, Yongjoon↗

DOE OSTI2023

The structural and functional integrities of porcine myocardium are mostly preserved by cryopreservation

Structural and functional studies of heart muscle are important to gain insights into the physiological bases of cardiac muscle contraction and the pathological bases of heart disease. While fresh muscle tissue works best for these kinds of studies, this is not always practical to obtain, especially for heart tissue from large animal models and humans. Conversely, tissue banks of frozen human hearts are available and could be a tremendous resource for translational research. It is not well understood, however, how liquid nitrogen freezing and cryostorage may impact the structural integrity of myocardium from large mammals. In this study, we directly compared the structural and functional integrity of never-frozen to previously frozen porcine myocardium to investigate the consequences of freezing and cryostorage. X-ray diffraction measurements from hydrated tissue under near-physiological conditions and electron microscope images from chemically fixed porcine myocardium showed that prior freezing has only minor effects on structural integrity of the muscle. Furthermore, mechanical studies similarly showed no significant differences in contractile capabilities of porcine myocardium with and without freezing and cryostorage. These results demonstrate that liquid nitrogen preservation is a practical approach for structural and functional studies of myocardium.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Fast relaxing sustainable soft vitrimer with enhanced recyclability

Soft, fully renewable vitrimers have been introduced to circumvent the lack of recyclability of traditional elastomers with permanent cross-linked structures, while preserving the advantages of rheo-structural stability, and mechanical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Reconstruction of the BNB and NuMI Neutrino Bunch Structure with ICARUS

ICARUS serves as the Far Detector of the Short Baseline Neutrino (SBN) program at Fermilab, sitting on-axis on the Booster Neutrino Beam (BNB) and 6$^\circ$ off-axis from the Neutrinos at the Main Injector (NuMI) beam. Neutrinos from both beams inherit the timing sub-structure of their parent proton spills, which is in turn derived from either the Booster's or the Main Injector's synchrotron acceleration. Since neutrino propagation introduces only a constant offset, their timing structure is preserved as they travel. Identifying this structure in data represents a powerful tool for selecting neutrino events and searching for physics beyond the Standard Model (BSM). This poster presents the preliminary reconstruction of the BNB and NuMI neutrino bunch structure with ICARUS data, exploiting only the precise timing of ICARUS optical readout system to both locate and assign a time to each interaction.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Reconstruction of the BNB and NuMI Neutrino Bunch Structure with ICARUS

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Argon broad ion beam sectioning and high resolution scanning electron microscopy imaging of hydrated alite

Highlights: • The native fibrous outer and dense inner C-S-H structure are preserved by using low energy argon broad ion beam sectioning. • Possible artefacts of the preparation and imaging of hydrated alite are shown and discussed. • An approach for a semi automated pore analysis of the obtained high resolution images is demonstrated. Scanning electron microscopy (SEM) imaging is able to visualize micro- to nano-structures of cement and concrete. A prerequisite is that the sample preparation preserves the native structure of the specimen. In this study, argon broad ion beam (BIB) sectioning is compared to state-of-the-art sample preparation (resin embedding, polishing) for hydrated alite. Additionally, it is investigated if during BIB, sample cooling is beneficial to avoid deterioration of cement hydrates. The aim is to quantitatively measure pore size distributions in hardened alite pastes. Therefore, not only optimized sample preparation but also optimized imaging conditions are investigated. Finally, it is demonstrated that by image analysis pores down to a diameter of 5 nm in hydrated alite pastes can be quantitatively analysed.

36 MATERIALS SCIENCE↗

DOE OSTI2025

CLPNets: Coupled Lie–Poisson neural networks for multi-part Hamiltonian systems with symmetries

To accurately compute data-based prediction of Hamiltonian systems, it is essential to utilize methods that preserve the structure of the equations over time. We consider a particularly challenging case of systems with interacting parts that do not reduce to pure momentum evolution. Such systems are essential in scientific computations, such as discretization of a continuum elastic rod, which can be viewed as the group of rotations and translations $SE(3)$. The evolution involves not only the momenta but also the relative positions and orientations of the particles. The presence of Lie group-valued elements, such as relative positions and orientations, poses a problem for applying previously derived methods for data-based computing. We develop a novel method of data-based computation and complete phase space learning of such systems. We follow the original framework of SympNets (Jin et al., 2020) and LPNets (Eldred et al., 2024), building the neural network from phase space mappings that preserve the Lie–Poisson structure. We derive a novel system of mappings that are built into neural networks describing the evolution of such systems. We call such networks Coupled Lie–Poisson Neural Networks, or CLPNets. We consider increasingly complex examples for the applications of CLPNets, starting with the rotation of two rigid bodies about a common axis, progressing to the free rotation of two rigid bodies, and finally to the evolution of two connected and interacting $SE(3)$ components, describing the discretization of an elastic rod into two elements. Our method preserves all Casimir invariants to machine precision, preserves energy to high accuracy, and shows good resistance to the curse of dimensionality, requiring only a few thousand data points for all cases studied (three to eighteen dimensions). Additionally, the method is highly economical in memory requirements, requiring only about 200 parameters for the most complex case considered.

Data-based modeling↗

DOE OSTI2025

Flux-Closure Domain Structures in Ferroelectric K 0.5 Na 0.5 NbO 3 Thin Films

Topological domain structures in ferroelectric materials have garnered increasing attention due to their intriguing physical properties and promising applications. While most existing topological structures in ferroelectric perovskite oxides originate from tetragonal or rhombohedral bulk phases, much less is understood about their counterparts in orthorhombic ferroelectrics. Here, in this work, we employ ferroelectric K 0.5 Na 0.5 NbO 3 (KNN) thin films as a model system and leverage phase-field simulations to theoretically predict the static structures and dynamic behaviors of three types of flux-closure domain configurations: in-plane (Type-I), out-of-plane (Type-II), and superdomain (Type-III) flux-closure structures. We systematically investigate the effects of finite size, misfit strains, and electrical boundary conditions on the formation and switching of these topological structures. For the Type-I structure, size reduction or small misfit strain facilitates a transition of the flux-closure pattern to polar vortices. Type-II structures emerge under open-circuit electrical boundary conditions of the film, forming at the junctions of specific domain walls with the film surface or the film–substrate interface. The formation mechanisms of these two flux-closure structures are rationalized from an energy perspective. We demonstrated switching capabilities of Type-II and Type-III structures by obtaining polarization–electric field hysteresis loops. Our simulations also reveal a reversible electric-field-induced transition between the orthorhombic and rhombohedral ferroelectric phases with a checkerboard domain pattern, during which the integrity of the flux-closure structure is preserved. These findings provide theoretical insights and practical guidance for identifying and manipulating topological structures in low-symmetry ferroelectrics, paving the way for developing energy-efficient microelectronic devices based on topological structures.

P-E loop↗