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DOE OSTI2024

The soaring kite: a tale of two punctured tori

We consider the 5-mass kite family of self-energy Feynman integrals and present a systematic approach for constructing an ε-form basis, along with its differential equation pulled back onto the moduli space of two tori. Each torus is associated with one of the two distinct elliptic curves this family depends on. We demonstrate how the locations of relevant punctures, which are required to parametrize the full image of the kinematic space onto this moduli space, can be extracted from integrals over maximal cuts. A boundary value is provided such that the differential equation is systematically solved in terms of iterated integrals over g-kernels and modular forms. Then, the numerical evaluation of the master integrals is discussed, and important challenges in that regard are emphasized. In an appendix, we introduce new relations between g-kernels.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Predictive numerical modeling of plasma-induced surface roughness and wettability evolution in LM-PAEK/CF tape

Plasma surface modification effectively enhances adhesion in thermoplastic composites, yet its impacts on high-performance polymers like low-melting polyaryletherketone (LM-PAEK) remain inadequately quantified. Here, this study integrates experimental analysis and numerical modeling to characterize surface roughness and wettability changes in LM-PAEK/carbon fiber composites treated with atmospheric plasma. Atomic Force Microscopy quantified surface topography (n = 10 per condition for contact angles), while static contact-angle assessments measured wettability. Roughness rapidly increased from ∼0.2 nm to 1.6 nm, and contact angle reduced from ∼90° to 24°, both stabilizing after 25–30 s of exposure. A semi-empirical, physics-informed framework was calibrated to these data, coupling surface chemistry via the Owens–Wendt decomposition with topography via the Wenzel roughness factor, and evaluated using out-of-sample (cross-validated) tests, while static contact angle assessments measured wettability. Numerical predictions matched experimental results closely (RMSE <5%, R 2 > 0.95). Incorporating material-specific parameters, the calibrated model supports plasma-treatment optimization and provides quantitative guidance for improving interfacial adhesion in thermoplastic composite manufacturing.

Atomic Force Microscopy↗

DOE OSTI2024

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. Here, this study introduces NeuroSEM, a hybrid framework integrating PINNs with the highfidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh-B´enard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU-CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.

42 ENGINEERING↗

DOE OSTI2026

Fast Fourier transform evaluation of the Fresnel integral for gravitational-wave lensing

Gravitational waves (GWs) exhibit wave-optics effects when their wavelength is comparable to the scale of the gravitational lens. This may occur in lensing from galactic subhalos in GWs emitted by binary black-hole mergers and is gaining interest as a novel probe of dark matter. Predictions for observables in these cases ultimately rely on evaluating a Fresnel integral that quantifies the effect of lensing on the amplitude of a GW at a given frequency. However, numerical evaluation of this Fresnel integral is tricky, and several algorithms and publicly available codes that implement it have been developed. Here, we show that the dependence of this integral on the lens position can be written as a two-dimensional Fourier transform. Modern FFT techniques then enable rapid evaluation at all-sky positions simultaneously for general lenses without symmetry. Vectorization of FFT routines allows for derivatives with respect to model parameters to be obtained with only incremental additional computational cost. If the lens is axisymmetric, further speedups can be achieved with recently developed techniques for nonuniform fast Hankel transforms. To demonstrate, we make available Fresnel Integral Optimization with Nonuniform Transforms (fiona), an efficient and accurate code that is significantly faster than current methods for dense source grids, reaching 2 orders of magnitude speedups for ∼10 6 GW-emitting points. As part of FIONA , we developed code that provides vectorized nonuniform fast Hankel transforms that may have other uses (e.g., calculation of cosmological two-point correlation functions) beyond those considered here.

dark matter↗

DOE OSTI2025

Quasi-optical beam tracing module development for millimeter-wave high-wavenumber collective scattering on the NSTX-U and EAST tokamaks

A Python3-based beam tracing code utilizing Quasi-Optics has been developed to track both incident and receiving beams in high-k collective millimeter wave scattering systems within magnetic fusion plasmas. In contrast to existing ray tracing codes that solely consider refraction, this beam tracing code incorporates diffraction phenomena, providing a more comprehensive calculation. Here, this enhanced capability allows for a more accurate calculation of the scattering volume and spatial resolution in high-k collective scattering systems, crucial for evaluating system performance and facilitating data analysis. Unlike Geometrical Optics, Quasi-Optics employs the complex eikonal method, representing a Gaussian beam as a collection of coupled rays to accurately preserve diffraction characteristics. The developed code is intended for application in NSTX-Upgrade and EAST high-k beam tracing analyses, targeting frequencies of 693 GHz and 270 GHz, respectively. The high-k system's primary objective is the observation of electron-scale instabilities. Employing a symplectic integrator, the code ensures numerical accuracy, assessed through the conservation of the Hamiltonian. With its precision and efficiency, the code facilitates rapid inter-shot analyses.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

A machine-learning approach to measure 3D sample properties from 2D Transmission Electron Microscopy images

Transmission Electron Microscopy (TEM) is a powerful tool for the characterization of materials at the nanoscale; however, its inherent two-dimensional (2D) nature poses significant challenges to accurately measure three-dimensional (3D) properties. We introduce a supervised machine-learning model that predicts 3D structural information, such as sample thickness and curvature, from a series of conventional 2D TEM images. The model, a U-Net convolutional neural network, is trained on a large synthetic dataset generated from dynamical diffraction simulations that model TEM’s complex, nonlinear image formation, accounting for sample thickness and curvature. This physically realistic framework enables exploration of a broad parameter space impractical to sample experimentally. We demonstrate that the trained model has accurate predictions for experimental single-crystal silicon samples, achieving performance comparable to established measurement techniques. This work highlights the critical role of robust, simulation-based training in overcoming the limitations of real-world imaging artifacts and inconsistent sample geometries. By integrating machine learning with numerical simulations, we offer an efficient and scalable framework for quantitative TEM analysis, paving the way for more sophisticated 3D characterization of complex materials.

Dynamical diffraction↗

DOE OSTI2025

A review on the state of thermal hydraulics research on air ingress scenarios in High-Temperature Gas-cooled Reactors following a D-LOFC

With the expectation of near-immediate carbon neutrality, widespread implementation of proven High-Temperature Gas-cooled Reactors (HTGRs) embodies a viable solution pathway given their inherent, passive safety features and high thermal efficiency. This study provides an overview of the current state of research involving the thermal hydraulics associated with air ingress from a depressurized loss of forced cooling (D-LOFC) in HTGRs. Accurately characterizing and predicting the physical phenomena underlying air ingress is of paramount concern, as the integrity of the fuel and core graphite support structures are threatened by the presence of oxygen. Broadly speaking, the air ingress scenario can be delineated into three main stages: (1) Depressurization, (2) Density-Driven Flow, and (3) Natural Convection. In tandem with the underlying fundamental theory, this review collates and synthesizes the existing body of contemporary research concerning the air ingress scenario following a D-LOFC. As evinced by this review, our current understanding and predictive abilities have benefited from extensive research, predominantly concentrated on the rate of air ingestion into the core. Here, additional research is necessary to holistically capture the phenomenology of an air ingress scenario following a D-LOFC by considering an additional variable: the oxygen content of the ingressing air. The latter variable requires investigation into the complex interactions of the fully integrated system. Additionally, while numerical tools are evolving domestically through the Nuclear Energy Advanced Modeling and Simulation program, a sufficiently validated code remains absent.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2026

Harnessing the Second-Order Metal−Insulator Transition for Neuromorphic Computing

Vanadium oxides are widely studied phase change materials for brain-inspired computing architectures. Systems like VO 2 and V 2 O 3 exhibit first-order metal−insulator transitions (MITs) with hysteresis and percolative switching, increasing stochasticity and device variability. Here, we focus on the less explored Magnéli phase V 4 O 7 , which undergoes a continuous, non-hysteretic, second-order MIT. This surprisingly enables highly reproducible volatile resistive switching in spiking-neuron-type devices. We synthesize V 4 O 7 films, characterize their structural and transport properties, and demonstrate voltage and current-driven threshold switching with electrothermal feedback. In a Pearson–Anson oscillator, V 4 O 7 devices produce stable, tunable spiking across 20–200 kHz, with consistent operation among multiple devices. We introduce a numerical analog leaky-integrate-and-fire (aLIF) model that captures waveform shapes and their dependence on load resistance, temperature, and voltage. Furthermore, these findings suggest that second-order MIT materials like V 4 O 7 are promising for deterministic, scalable spiking neuron arrays for neuromorphic computing.

V4O7↗

DOE OSTI2025

2025 Continuing Incubator Final Report: Active Hybrid Mooring

This project advanced the development of an active hybrid mooring system integrating experimental testing with numerical simulation to capture complex mooring dynamics not feasible in existing wave basins, including deep-water and shared mooring interactions. Verification testing of the complete hybrid system yielded good agreement in mooring tension and platform translation responses, though discrepancies in platform pitch response indicate that further refinement may be needed in future work.

16 TIDAL AND WAVE POWER↗

DOE OSTI2026

Data Center Market Report

The data center market is poised to explode in the coming decade due to undeniable drivers such as continued adoption of generative AI, increased data storage needs, and enterprise integration of AI in numerous industries [1] [2] [3]. Scalable power and increased computational capacity are at the forefront of considerations for hyperscalers, the major cloud service providers in this space. Lawrence Livermore National Laboratory is uniquely poised to help with informed decision making for data center market leaders during this phase of explosive expansion. National grid modeling expertise and cutting edge innovations in computer cooling systems place LLNL in an enviable position for creating economic impact in the data center industry by leveraging its expertise in these areas which can help the data center market keep up with growing demand.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Manufactured solutions for an electromagnetic slot model

The accurate modeling of electromagnetic penetration is an important topic in computational electromagnetics. Electromagnetic penetration occurs through intentional or inadvertent openings in an otherwise closed electromagnetic scatterer, which prevent the contents from being fully shielded from external fields. To efficiently model electromagnetic penetration, aperture or slot models can be used with surface integral equations to solve Maxwell's equations. A necessary step towards establishing the credibility of these models is to assess the correctness of the implementation of the underlying numerical methods through code verification. Surface integral equations and slot models yield multiple interacting sources of numerical error and other challenges, which render traditional code-verification approaches ineffective. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources for the method-of-moments implementation of the electric-field integral equation with a slot model. Finally, we demonstrate the effectiveness of these approaches for a variety of cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Level 2 Milestone: Develop and Incorporate Novel Code Verification of Fundamental Equations in Gemma and Set Up Appropriate Tests

For computational physics simulations, code verification plays a major role in establishing the credibility of the results by assessing the correctness of the implementation of the underlying numerical methods. In computational electromagnetics, surface integral equations, such as the method-of-moments implementations of the electric-, magnetic-, and combinedfield integral equations, are frequently used to solve Maxwell’s equations on the surfaces of electromagnetic scatterers. These electromagnetic surface integral equations yield many code-verification challenges due to the various sources of numerical error and their possible interactions. In this report, we provide approaches to separately measure the numerical errors arising from these different error sources. We demonstrate the effectiveness of these approaches in Gemma.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Rethinking materials simulations: Blending direct numerical simulations with neural operators

Abstract Materials simulations based on direct numerical solvers are accurate but computationally expensive for predicting materials evolution across length- and time-scales, due to the complexity of the underlying evolution equations, the nature of multiscale spatiotemporal interactions, and the need to reach long-time integration. We develop a method that blends direct numerical solvers with neural operators to accelerate such simulations. This methodology is based on the integration of a community numerical solver with a U-Net neural operator, enhanced by a temporal-conditioning mechanism to enable accurate extrapolation and efficient time-to-solution predictions of the dynamics. We demonstrate the effectiveness of this hybrid framework on simulations of microstructure evolution via the phase-field method. Such simulations exhibit high spatial gradients and the co-evolution of different material phases with simultaneous slow and fast materials dynamics. We establish accurate extrapolation of the coupled solver with large speed-up compared to DNS depending on the hybrid strategy utilized. This methodology is generalizable to a broad range of materials simulations, from solid mechanics to fluid dynamics, geophysics, climate, and more.

36 MATERIALS SCIENCE↗

DOE OSTI2026

New Time Integrators and Capabilities in SUNDIALS Versions 6.2.0-7.4.0

SUNDIALS is a well-established numerical library that provides robust and efficient time integrators and nonlinear solvers. This article overviews several significant improvements and new features added over the last 3 years to support scientific simulations run on high-performance computing systems. Notably, three new classes of one-step methods have been implemented: low storage Runge–Kutta, symplectic partitioned Runge–Kutta, and operator splitting. In addition, we describe new timestep adaptivity support for multirate methods, adjoint sensitivity analysis capabilities for explicit Runge–Kutta methods, additional options for Anderson acceleration in nonlinear solvers, and improved error handling and logging.

Computer science↗

DOE OSTI2026

Computational capacity in hydrodynamic real-time hybrid simulation applied to simulate the dynamic response of floating offshore wind turbines

Real-time hybrid simulation (RTHS) mitigates similitude distortions in model-scale tests of floating offshore wind turbines (FOWTs) by coupling physical experiments with numerical models in real time. The coupling requires faster-than-real-time numerical computations to satisfy temporal similitude with the physical experiment, presenting a bottleneck for using more complex numerical models in RTHS. This paper presents a hydrodynamic-RTHS (hydro-RTHS) framework for FOWTs that simulates the hydrodynamics physically and the aerodynamics numerically with sensor feedback from the physical testing. The framework adapts the three-loop hardware architecture to leverage greater computational resources and mitigate strict temporal requirements, enabling more computationally demanding numerical analyses in hydro-RTHS. The three-loop hardware architecture integrates multiple machines, each dedicated to either numerical analysis or RTHS controls, with a rate-transition algorithm to synchronize the tasks executed across the different machine processors. Virtual and physical tests verified and validated the hydro-RTHS framework, respectively. The ”virtual” tests, which approximates the physical domain numerically, verified the RTHS framework with respect to a numerical full-scale complete FOWT model simulated in the open-source software, OpenFAST. The virtual tests were able to maintain comparable control signals while enabling greater computational resources for the numerical calculations. Real-world physical tests demonstrated that the hydro-RTHS framework computes aerodynamic forces similar to the complete OpenFAST model, validating the hydro-RTHS framework using the three-loop hardware architecture. Findings show that the hydro-RTHS framework with the three-loop hardware architecture is computationally efficient, with reserve capacity to simulate more complex problems due to the customized software, hardware, and rate-transition algorithm.

17 WIND ENERGY↗

DOE OSTI2025

A double copy from twisted (co)homology at genus g

We study a family of generalized hypergeometric integrals defined on punctured Riemann surfaces of genus g. These integrals are closely related to g-loop string amplitudes in chiral splitting, where one leaves the loop-momenta, moduli and all but one puncture un-integrated. We study the twisted homology groups associated to these integrals, and determine their intersection numbers. We make use of these homology intersection numbers to write a double-copy formula for the "complex" version of these integrals -- their closed-string analogues. To verify our findings, we develop numerical tools for the evaluation of the integrals in this work. This includes the recently introduced Enriquez kernels -- integration kernels for higher-genus polylogarithms.

Pokraka, Andrejz [Brown University; Amsterdam Univ↗

DOE OSTI2024

A numerical study of process complexity in permafrost dominated regions

Numerical modeling of permafrost dynamics requires adequate representation of atmospheric and surface processes, a reasonable parameter estimation strategy, and site-specific model development. The three main research objectives of the study are: (i) to propose a novel methodology that determines the required level of surface process complexity of permafrost models by conducting parameter sensitivity and calibration, (ii) to design and compare three numerical models of increasing surface process complexity, and (iii) to calibrate and validate the numerical models at the Yakou catchment on the Qinghai-Tibet Plateau as an exemplary study site. The calibration was carried out by coupling the Advanced Terrestrial Simulator (numerical model) and PEST (calibration tool). Simulation results showed that (i) A simple numerical model that considers only subsurface processes can simulate active layer development with the same accuracy as other more complex models that include surface processes. (ii) Peat and mineral soil layer permeability, Van Genuchten alpha, and porosity are highly sensitive. (iii) Liquid precipitation aids in increasing the rate of permafrost degradation. (iv) Deposition of snow insulated the subsurface during the thaw initiation period. We have developed and released an integrated code that couples the numerical software ATS to the calibration software PEST. The numerical model can be further used to determine the impacts of climate change on permafrost degradation.

Calibration↗

DOE OSTI2025

Integral X-ray diffuse scattering for studying irradiation-induced dislocation loops in single crystals

Numerical diffuse scattering cross-section calculations are used to establish a rigorous basis for determining the concentration and size distribution of dislocation loops in irradiated single crystals from integral X-ray diffuse scattering (XRDS) measurements. Differential XRDS intensities for prismatic {111} type dislocation loops are numerically calculated as a function of loop radius R and wavevectors q relative to Bragg reflections in tungsten. The results show the well known 1/q 2 Huang scattering form at small q that transitions to a ∼1/q 4 dependence associated with the Stokes–Wilson approximation for q ≳ 1/R. More importantly, they show further that the 1/q 4 falloff is not the asymptotic large-q form of the diffuse scattering for small loops (R < 200 Å) as has often been assumed. Rather, for loop sizes as small as R ≃ 5 Å with strong curvature, the calculations show definitively that the scattering transitions to a robust 1/q 5 falloff at larger q that arises due to the local strains near the dislocation core defining the circumference of the dislocation loops. The presence of this 1/q 5 asymptotic form for both small and large loops is experimentally confirmed using an integral XRDS measurement around the 110 reflection on self-ion-irradiated tungsten combined with numerically calculated integral XRDS cross-sections. Accordingly, the historical two-region theoretical treatment of the cross-sections for integral XRDS is extended to a three-region model that has direct sensitivity to the (first-moment) dislocation line lengths of dislocation loops. In conclusion, these developments enable the use of both numerical and analytically modeled cross-sections to make accurate integral XRDS determinations of dislocation loop sizes and concentrations using modest-intensity laboratory X-ray sources.

42 ENGINEERING↗