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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2022

A Note on the Probability of Initiation Problem

The purpose of this note is to draw attention to Pál’s derivation of the Pál Bell equation which is used by LLNL and LANL to model Probability of Initiation (POI) problems. Both laboratories credit the equation to Bell and Lee. Although the equation formulated by Bell and Lee and the equation derived by Pál appear to be the same, the derivation by Bell and Lee is flawed. Scattering, which was absent in Bell’s original formulation of a POI problem, was later introduced by Bell and Lee by simply replacing a fission term with a scattering term. Such a replacement, however, leads to an inaccurate average number v̅ of neutrons that is produced by a fission event. By approaching a POI problem from probabilistic point of view, Pál formulates the problem as a branching process that determines v̅ correctly. There are six reasons for writing this report. The first is to clarify the failing in Bell and Lee’s derivation. The second is to establish the origin of the equation used by the laboratories. The third is to elucidate the fixed point technique formulated by Mokhtar-Kharroubi for solving the Pál-Bell equation. The fourth is to derive the α eigenvalue that is associated with a time dependent Pál-Bell equation. The fifth is to show in Appendix A that the non-linear fission operator of the Pál-Bell equation is descended from the operator of the Galton-Watson process of stochastic theory. The sixth is to describe in Appendix B a second order positivity preserving technique that accelerates the convergence of the first order fixed point method developed by Mokhtar-Kharroubi.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Spectrally Stabilized Interface Capturing Formulation and Implementation in Nek5000/NekRS

This report documents the formulation of a novel level-set method for incompressible two-phase flows in the continuous Galerkin (CG) high order spectral element framework. The overall method hinges on a novel implementation of the spectral vanishing viscosity (SVV) operator for the stabilization of linear/non-linear hyperbolic problems. The multidimensional SVV convolution kernels, which in essence, have a similar effect as a high pass filter applied to the derivatives, are formulated by exploiting the tensor product form, analogous to the construction of the usual stiffness matrix system. The resulting kernels are directionally decoupled and ensure a linear, symmetric positive definite, elliptic matrix operator. The SVV formulation is demonstrated to provide a robust stabilizing mechanism through challenging linear and non-linear hyperbolic problems, including problems pertinent to the level-set formulation. The two-phase framework conceptualized herein is based on the conservative level-set (CLS) method which represents the interface between the fluids by the 0.5 iso-contour of the smoothed Heaviside function. The CLS method is augmented with a preconditioning procedure for interface normals using the signed distance function which precludes the manifestation of spurious oscillations in the vicinty of the interface. Further, the existing mixed explicit-implicit approach for the solution of Navier-Stokes equations in Nek5000, as described in Tomboulides et al, is augmented with a pressure coefficient splitting approach for the Poisson equation, which greatly accelerated the convergence of pressure solver for two-phase systems with large density ratio. The robustness and accuracy of the overall two-phase method is demonstrated through canonical challenging problems involving high density and viscosity ratios, with and without surface tension. The two-phase formulation is wholly implemented in Nek5000 and the SVV stabilization method is implemented in NekRS, which is the essential precursor to the two-phase framework, undergoing active development.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Application of linear prolongation to coarse mesh finite difference acceleration in CASMO5

The Coarse-Mesh Finite Difference (CMFD) method has been used for over a decade to accelerate the convergence of the Method of Characteristics (MOC) solution to the two- dimensional particle transport equation in CASMO5. Numerical testing, along with widespread use in production-level calculations, have shown that the current CMFD implementation provides stability and robustness for a wide range of realistic reactor physics problems. However, the recent development of linear prolongation has attracted attention from the community as a way to further improve the performance and stability of CMFD. Two interpolation methods for linear prolongation are presented in this work and implemented into a test version of CASMO5. The performance of the proposed interpolations, referred to as the bilinear and linear directional schemes, is evaluated in terms of runtime relative to the default constant or uniform scaling update. Numerical results indicate that the use of linear prolongation can reduce the transport solver runtime on average by approximately 10% when tested with two hundred randomly selected cases. The new directional linear interpolation, combined with default constant boundary updates, is found to provide the highest reduction in runtime for the cases analyzed. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

A fast two-stage algorithm for non-negative matrix factorization in smoothly varying data

This article reports the study of algorithms for non-negative matrix factorization (NMF) in various applications involving smoothly varying data such as time or temperature series diffraction data on a dense grid of points. Utilizing the continual nature of the data, a fast two-stage algorithm is developed for highly efficient and accurate NMF. In the first stage, an alternating non-negative least-squares framework is used in combination with the active set method with a warm-start strategy for the solution of subproblems. In the second stage, an interior point method is adopted to accelerate the local convergence. The convergence of the proposed algorithm is proved. The new algorithm is compared with some existing algorithms in benchmark tests using both real-world data and synthetic data. Furthermore, the results demonstrate the advantage of the algorithm in finding high-precision solutions.

interior point method↗
DOE OSTI2022

Accelerating amorphous polymer electrolyte screening by learning to reduce errors in molecular dynamics simulated properties

Polymer electrolytes are promising candidates for the next generation lithium-ion battery technology. Large scale screening of polymer electrolytes is hindered by the significant cost of molecular dynamics (MD) simulation in amorphous systems: the amorphous structure of polymers requires multiple, repeated sampling to reduce noise and the slow relaxation requires long simulation time for convergence. Here, we accelerate the screening with a multi-task graph neural network that learns from a large amount of noisy, unconverged, short MD data and a small number of converged, long MD data. We achieve accurate predictions of 4 different converged properties and screen a space of 6247 polymers that is orders of magnitude larger than previous computational studies. Further, we extract several design principles for polymer electrolytes and provide an open dataset for the community. Our approach could be applicable to a broad class of material discovery problems that involve the simulation of complex, amorphous materials.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Elucidating ion capture and transport mechanisms of Preyssler anions in aqueous solutions using biased MACE-accelerated MD simulations

Equilibrium and biased multi-atomic cluster expansion (MACE) accelerated molecular dynamics (MD) simulations in aqueous solutions are performed to investigate the ion capture and transport mechanisms of the {P 5 W 30 } Preyssler anion (PA) as the smallest representative member of the extended polyoxometalate (POM) family with an internal cavity. The unique interatomic interactions present in the internal cavity vs the exterior of PA are carefully investigated using equilibrium MACE MD simulations for two representative Na(H 2 O)@PA and Na@PA complexes in aqueous solutions. Our careful analyses of radial distribution functions and coordination numbers show that the presence of confined water in Na(H 2 O)@PA has profound modulating effects on the nature of the interactions of the encapsulated ion with the oxygens of the PA cavity. Using well-converged MACE-accelerated multiple walker well-tempered metadynamics simulations with nanosecond timescales, two different associative (ion exchange) and dissociative (ion ejection) ion transport mechanisms were carefully investigated for Na + as one of the most abundant and representative ions present in seawater and saline solutions. By comparing systems with and without confined water, it was found that the presence of only one pre-encapsulated confined water in Na(H 2 O)@PA dramatically changes the free energy landscape of ion transport processes. It was also found that the contraction and dilation of the two windows present in PA directly influence the Na + and H 2 O transport. Furthermore, the results from this work are helpful, as they show a viable path toward tuning the ion exchange and transport phenomena in aqueous solutions of POM molecular clusters and frameworks.

25 ENERGY STORAGE↗
DOE OSTI2021

Accelerated basis adaptation in homogeneous chaos spaces

Polynomial chaos expansions (PCE) provide an efficient approach to uncertainty quantification (UQ) and have been adapted to diverse applications across the spectrum of science and engineering. For situations involving large stochastic parameterizations, the curse of dimensionality renders PCE-based methods computationally prohibitive. A basis adaptation approach for PCE was proposed by Tipireddy and Ghanem (2014) which transforms the input random variables through an isometry such that sufficient probabilistic characterization of specific quantities of interest (QoI) is concentrated in an algebraic manifold embedded in the linear span of the dominant transformed variables. While quite versatile, that original version of the PCE basis adaptation exhibited slow convergence for a number of problems of practical significance. In the present paper, we propose two novel methods to accelerate the convergence of the original basis adaptation approach, thus expanding its reach while also providing insight into its performance. In the first method, information gained from a pilot PCE representation is used to correct the mean and Gaussian coefficients in the adapted space. By taking advantages of probabilistic information in higher dimensional adaptation gleaned from an initial adaptation, the second method updates the rotation matrix used to identify the dominant transformed variables. In this manner, the new rotation matrix concentrates even more probabilistic information in its first few dimensions. These two method can be combined to achieve even better performance, the combined method is referred to as sequentially optimized adaptation method. Here, the methods are demonstrated on an analytical test function and a model of a space structure with several sub-components and a non-smooth quantity of interest representing the maximum acceleration over time. Both methods achieve accelerated convergence of the basis adaptation approach with negligible additional costs.

Accelerated convergence↗
DOE OSTI2022

aphBO-2GP-3B: a budgeted asynchronous parallel multi-acquisition functions for constrained Bayesian optimization on high-performing computing architecture

High-fidelity complex engineering simulations are often predictive, but also computationally expensive and often require substantial computational efforts. The mitigation of computational burden is usually enabled through parallelism in high-performance cluster (HPC) architecture. Optimization problems associated with these applications is a challenging problem due to the high computational cost of the high-fidelity simulations. In this paper, an asynchronous parallel constrained Bayesian optimization method is proposed to efficiently solve the computationally expensive simulation-based optimization problems on the HPC platform, with a budgeted computational resource, where the maximum number of simulations is a constant. The advantage of this method are three-fold. Firstly, the efficiency of the Bayesian optimization is improved, where multiple input locations are evaluated parallel in an asynchronous manner to accelerate the optimization convergence with respect to physical runtime. This efficiency feature is further improved so that when each of the inputs is finished, another input is queried without waiting for the whole batch to complete. Second, the proposed method can handle both known and unknown constraints. Third, the proposed method samples several acquisition functions based on their rewards using a modified GP-Hedge scheme. The proposed framework is termed aphBO-2GP-3B, which means asynchronous parallel hedge Bayesian optimization with two Gaussian processes and three batches. The numerical performance of the proposed framework aphBO-2GP-3B is comprehensively benchmarked using 16 numerical examples, compared against other 6 parallel Bayesian optimization variants and 1 parallel Monte Carlo as a baseline, and demonstrated using two real-world high-fidelity expensive industrial applications. The first engineering application is based on finite element analysis (FEA) and the second one is based on computational fluid dynamics (CFD) simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Divide and conquer: Learning chaotic dynamical systems with multistep penalty neural ordinary differential equations

Forecasting high-dimensional dynamical systems is a fundamental challenge in various fields, such as geosciences and engineering. Neural Ordinary Differential Equations (NODEs), which combine the power of neural networks and numerical solvers, have emerged as a promising algorithm for forecasting complex nonlinear dynamical systems. However, classical techniques used for NODE training are ineffective for learning chaotic dynamical systems. In this work, we propose a novel NODE-training approach that allows for robust learning of chaotic dynamical systems. Here, our method addresses the challenges of non-convexity and exploding gradients associated with underlying chaotic dynamics. Training data trajectories from such systems are split into multiple, non-overlapping time windows. In addition to the deviation from the training data, the optimization loss term further penalizes the discontinuities of the predicted trajectory between the time windows. The window size is selected based on the fastest Lyapunov time scale of the system. Multi-step penalty(MP) method is first demonstrated on Lorenz equation, to illustrate how it improves the loss landscape and thereby accelerates the optimization convergence. MP method can optimize chaotic systems in a manner similar to least-squares shadowing with significantly lower computational costs. Our proposed algorithm, denoted the Multistep Penalty NODE, is applied to chaotic systems such as the Kuramoto-Sivashinsky equation, the two-dimensional Kolmogorov flow, and ERA5 reanalysis data for the atmosphere. It is observed that MP-NODE provide viable performance for such chaotic systems, not only for short-term trajectory predictions but also for invariant statistics that are hallmarks of the chaotic nature of these dynamics.

Chaotic dynamical systems↗
DOE OSTI2026

Two-Level Sketching Alternating Anderson Acceleration for Complex Physics Applications

We present a novel two-level sketching extension of the Alternating Anderson–Picard (AAP) method for accelerating fixed-point iterations in challenging single- and multiphysics simulations governed by discretized PDEs. Our approach combines a static, physics-based projection that reduces the least-squares (LS) problem to the most informative field (e.g., via Schur-complement insight) with a dynamic, algebraic sketching stage driven by a backward stability analysis under Lipschitz continuity. We introduce inexpensive estimators for stability thresholds and cache-aware randomized selection strategies to balance computational cost against memory access overhead. The resulting algorithm solves reduced LS systems in place, minimizes memory footprints, and seamlessly alternates between low-cost Picard updates and Anderson mixing. Implemented in Julia, our two-level sketching AAP achieves up to 50% time-to-solution reductions compared to standard Anderson acceleration—without degrading convergence rates—on benchmark problems including Stokes, 𝑝-Laplacian, bidomain, and Navier–Stokes formulations at varying problem sizes. These results demonstrate the method’s robustness, scalability, and potential for integration into high-performance scientific computing frameworks. Our implementation is available open source in the AAP.jl library.

Barnafi, Nicolas [University of Chile, Santiago]↗
DOE OSTI2023

Fully Implicit Conjugate Heat Transfer Analysis of the ARC-Class Vacuum Vessel

The coupled simulation of fusion reactor blankets including neutronics, thermal-hydraulics and thermo-mechanics is expected to speed up the design cycle of fusion reactor design concepts. In this work we demonstrate tight implicit coupling of conjugate heat transfer using the open-source Computational Fluid Dynamics software OpenFOAM for thermo-fluid mechanics and Diablo for thermo-solid mechanics. The heat transfer analysis is augmented by volumetric energy deposition from neutronic calculations using the Monte Carlo N-particle code on both solid and fluid parts of the vacuum vessel. An additional heat flux is imposed on the first wall estimated from the design power of the reactor. The tight coupling is realized through the open-source coupling library, preCICE, and tested on the vacuum vessel of the affordable, robust, compact reactor design by Commonwealth Fusion Systems. The features of the coupling and the influence of different coupling parameters such as coupling schemes, acceleration techniques and convergence criterion are discussed. The coupled simulation results are compared to a thermal-hydraulics simulation which includes only the fluid domains (the liquid immersion molten salt blanket and cooling channel) to demonstrate usefulness of a coupled simulation. Further analysis is performed to identify regions of hot spots for subsequent design improvement. This introduces the outline for integrating conjugate electromagnetics and fluid/solid mechanics (e.g., allow for deformation of the cooling channel walls) with our present approach for future analysis.

Sircar, Arpan↗
DOE OSTI2022

Fed-DeepONet: Stochastic Gradient-Based Federated Training of Deep Operator Networks

The Deep Operator Network (DeepONet) framework is a different class of neural network architecture that one trains to learn nonlinear operators, i.e., mappings between infinite-dimensional spaces. Traditionally, DeepONets are trained using a centralized strategy that requires transferring the training data to a centralized location. Such a strategy, however, limits our ability to secure data privacy or use high-performance distributed/parallel computing platforms. To alleviate such limitations, in this paper, we study the federated training of DeepONets for the first time. That is, we develop a framework, which we refer to as Fed-DeepONet, that allows multiple clients to train DeepONets collaboratively under the coordination of a centralized server. To achieve Fed-DeepONets, we propose an efficient stochastic gradient-based algorithm that enables the distributed optimization of the DeepONet parameters by averaging first-order estimates of the DeepONet loss gradient. Then, to accelerate the training convergence of Fed-DeepONets, we propose a moment-enhanced (i.e., adaptive) stochastic gradient-based strategy. Finally, we verify the performance of Fed-DeepONet by learning, for different configurations of the number of clients and fractions of available clients, (i) the solution operator of a gravity pendulum and (ii) the dynamic response of a parametric library of pendulums.

Moya, Christian↗
DOE OSTI2021

Revisiting the ODE Method for Recursive Algorithms: Fast Convergence Using Quasi Stochastic Approximation

Several decades ago, Profs. Sean Meyn and Lei Guo were postdoctoral fellows at ANU, where they shared interest in recursive algorithms. It seems fitting to celebrate Lei Guo's 60th birthday with a review of the ODE Method and its recent evolution. The method has been regarded as a technique for algorithm analysis. It is argued that this viewpoint is backwards: The original stochastic approximation method was surely motivated by an ODE, and tools for analysis came much later (based on establishing robustness of Euler approximations). The paper presents a brief survey of recent research in machine learning that shows the power of algorithm design in continuous time, following by careful approximation to obtain a practical recursive algorithm. While these methods are usually presented in a stochastic setting, this is not a prerequisite. In fact, recent theory shows that rates of convergence can be dramatically accelerated by applying techniques inspired by quasi Monte-Carlo. Subject to conditions, the optimal rate of convergence can be obtained by applying the averaging technique of Polyak and Ruppert. The conditions are not universal, but theory suggests alternatives to achieve acceleration. The theory is illustrated with applications to gradient-free optimization, and policy gradient algorithms for reinforcement learning.

learning and adaptive systems in artificial intell↗
DOE OSTI2021

Analysis of a New Implicit Solver for a Semiconductor Model

Here, we present and analyze a new iterative solver for implicit discretizations of a simplified Boltzmann--Poisson system. The algorithm builds on recent work that incorporated a sweeping algorithm for the Vlasov--Poisson equations as part of nested inner-outer iterative solvers for the Boltzmann--Poisson equations. The new method eliminates the need for nesting and requires only one transport sweep per iteration. It arises as a new fixed-point formulation of the discretized system which we prove to be contractive for a given electric potential. We also derive an accelerator to improve the convergence rate for systems in the drift-diffusion regime. We numerically compare the efficiency of the new solver, with and without acceleration, against a recently developed nested iterative solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Effect of Nozzle Curvature on Supersonic Gas Jets Used in Laser-Plasma Acceleration

Supersonic gas jets produced by converging-diverging (C-D) nozzles are commonly used as targets for laser-plasma acceleration (LPA) experiments. A major point of interest for these targets is the gas density at the region of interaction where the laser ionizes the gas plume to create a plasma, providing the acceleration structure. Tuning the density profiles at this interaction region is crucial to LPA optimization. A "flat-top" density profile is desired at this line of interaction to control laser propagation and high energy electron acceleration, while a short high-density profile is often preferred for acceleration of lower-energy tightly-focused laser-plasma interactions. A particular design parameter of interest is the curvature of the nozzle's diverging section. We examine three nozzle designs with different curvatures: the concave "bell", straight conical and convex "trumpet" nozzles. We demonstrate that, at mm-scale distances from the nozzle exit, the trumpet and straight nozzles, if optimized, produce "flat-top" density profiles whereas the bell nozzle creates focused regions of gas with higher densities. An optimization procedure for the trumpet nozzle is derived and compared to the straight nozzle optimization process. We find that the trumpet nozzle, by providing an extra parameter of control through its curvature, is more versatile for creating flat-top profiles and its optimization procedure is more refined compared to the straight nozzle and the straight nozzle optimization process. Furthermore, we present results for different nozzle designs from computational fluid dynamics (CFD) simulations performed with the program ANSYS Fluent and verify them experimentally using neutral density interferometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

The Impact of High-Dimensional Phase Space Correlations on the Beam Dynamics in a Linear Accelerator

Hadron beams develop intensity-dependent transverse-longitudinal correlations within radio-frequency quadrupole (RFQ) accelerating structures. These correlations are only visible in six-dimensional phase space and are destroyed by reconstructions from low-dimensional projections. In this work, we estimate the effect of artificial decorrelation on the beam dynamics in the Spallation Neutron Source (SNS) linac and Beam Test Facility (BTF). We show that the evolution of a realistic initial distribution and its decorrelated twin converge during the early acceleration stages; thus, low-dimensional projections are probably sufficient for detailed predictions in high-power linacs.

Hoover, Austin↗
DOE OSTI2020

thornado-transport: Anderson- and GPU-accelerated nonlinear solvers for neutrino-matter coupling

Algorithms for neutrino-matter coupling in core-collapse supernovae (CCSNe) are investigated in the context of a spectral two-moment model, which is discretized in space with the discontinuous Galerkin method, integrated in time with implicit-explicit (IMEX) methods, and implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado). The model considers electron neutrinos and antineutrinos and tabulated opacities from Bruenn (1985), which includes neutrino-electron scattering and pair processes. The nonlinear system arising from implicit time discretization of the equations governing neutrino-matter coupling is iterated to convergence using Anderson-accelerated fixed-point methods, which avoid formation of Jacobians and inversion of dense linear systems. Numerical experiments show that, for a given tolerance, a nested iteration scheme which aims to reduce opacity evaluations can lower the computational cost. Our initial port to GPUs, using both OpenMP and OpenACC, shows an overall speedup of up to ~ 100× when compared to results using a single CPU core. These results indicate that the algorithms implemented in thornado are well-suited to GPU acceleration.

Laiu, Paul↗
DOE OSTI2025

Surrogate optimization of variational quantum circuits

Variational quantum eigensolvers are touted as a near-term algorithm capable of impacting many applications. However, the potential has not yet been realized, with few claims of quantum advantage and high resource estimates, especially due to the need for optimization in the presence of noise. Finding algorithms and methods to improve convergence is important to accelerate the capabilities of near-term hardware for VQE or more broad applications of hybrid methods in which optimization is required. To this goal, we look to use modern approaches developed in circuit simulations and stochastic classical optimization, which can be combined to form a surrogate optimization approach to quantum circuits. Using an approximate (classical CPU/GPU) state vector simulator as a surrogate model, we efficiently calculate an approximate Hessian, passed as an input for a quantum processing unit or exact circuit simulator. This method will lend itself well to parallelization across quantum processing units. We demonstrate the capabilities of such an approach with and without sampling noise and a proof-of-principle demonstration on a quantum processing unit utilizing 40 qubits.

Gustafson, Erik J. [RIACS, Mtn. View] (ORCID:00000↗