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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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At least 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Emerging hierarchical dislocation structures: Insights from scanning electron microscopy-electron backscatter diffraction in situ tensile testing and multifractal analysis

Understanding the evolution of dislocation structures during plastic deformation is critical for predicting the mechanical performance of metallic materials. In this work, we applied in situ scanning electron microscopy/electron backscatter diffraction tensile testing combined with multifractal (MF) analysis to assess deformation-induced dislocation structure evolution in solution-annealed 304 L stainless steel, both in its as-received and neutron-irradiated states (5.4 displacements per atom). The analysis of kernel average misorientation patterns revealed the formation of hierarchical dislocation arrangements that exhibit clear MF scaling behavior. Despite pronounced visual differences between nonirradiated and irradiated specimens—most notably, the appearance of dislocation channels after irradiation—the singularity spectra suggest that both conditions give rise to similar underlying hierarchical structures. MF analysis provides a quantitative measure of the spatial complexity and self-organization of dislocation patterns, highlighting the accelerated emergence and evolution of the dislocation structures in irradiated polycrystalline materials, as well as the limitation of their spatial extent. The findings indicate that irradiation not only modifies microstructure but also alters correlation-driven dislocation organization. More generally, they demonstrate that MF analysis is a powerful tool for probing mesoscale deformation mechanisms.

Dislocation structures↗
DOE OSTI2024

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Experimental validation of the mechanistic scale-up methodology of gas–solid spouted beds using radioactive particle tracking (RPT)

The very high-temperature reactors (VHTRs) are highly ranked among candidates of Generation IV of nuclear reactors due to their high efficiency, safety, the resistance to proliferation, and reliability. The VHTRs are preferentially fueled by Tristructural-isometric (TRISO) coated fuel particles which has fuel kernels of fissile material coated by four coating layers: a porous buffer pyrolysis carbon layer (buffer PyC), an inner dense pyrolysis carbon layer (IPyC), a silicon carbide layer (SiC) and an outer dense pyrolysis carbon layer (OPyC). The heart of the operation and safety of the VHTRs significantly depends on the reliability of the coating layers of TRISO particles to retain metallic and gaseous fission products within the particles. The technique used for coating TRISO particles are gas-solids spouted beds via chemical vapor deposition (CVD). Fabrication of high-quality low-defect TRISO fuel particles fuel at larger scale spouted beds is required to support the commercialization of the VHTRs. In this work, our new developed mechanistic scale-up methodology of gas-solids spouted beds based on matching the radial profile of gas-holdup has been demonstrated and validated using radioactive particle tracking (RPT). Two spouted beds of small and larger scales were used in the study. Three sets of conditions were carried out which include the conditions of the reference case in the large scale, conditions that provide similar gas holdup radial profile to that of the reference case and conditions that provided dissimilar gas holdup radial in the small-scale spouted beds. The results confirm the validation of the scale-up methodology in terms of the dimensionless values of the spout diameter, cumulative probability distribution of the solids particles penetration into the spout, fraction of cycle time in each region of the bed, the radial profiles of the dimensionless values of the root-mean-square particle velocities and solids eddy diffusivity. Finally, the results further advance the knowledge and understanding of the gas-solids spouted beds provide deeper insight into their solids dynamics and presenting important benchmarking data for validating computational fluid dynamics codes and models. At last, procedures are established for the implementation of the new scale-up methodology.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Benchmarking FFTF LOFWOS Test# 13 using SAM code: Baseline model development and uncertainty quantification

The development and deployment of advanced reactors, such as the sodium-cooled fast reactor (SFR), relies on sophisticated modeling tools to ensure the safety of the design under various transients. The predictive capability of these advanced modeling tools requires validation to garner trust in supporting the licensing of the advanced reactors. For this reason, the International Atomic Energy Agency (IAEA) initiated a coordinated research project (CRP) in 2018 for the analysis of the Fast Flux Test Facility (FFTF) Loss of Flow Without Scram (LOFWOS) Test #13.In this study, we present and discuss the benchmarking efforts of the modern system code SAM on the FFTF LOFWOS Test #13. Further, the SAM baseline model was developed according to the benchmark specification, which included a detailed core model with reactivity feedback. Generally, good agreement was observed between the baseline results and benchmark measurements; however, discrepancies persisted, particularly in predicted fuel assembly coolant outlet temperatures. Utilizing the baseline model, uncertainty quantification (UQ) and sensitivity analysis (SA) were conducted with the assistance of various statistical learning and machine learning methods, including kernel density estimation, Gaussian processes, and Sobol indices. Following the baseline model prediction and UQ and SA results, we discuss the reasons for the simulation discrepancies and propose further improvements to the model. This benchmarking effort adheres to the best-estimate plus uncertainty approach and can serve as a valuable example for supporting risk-informed licensing of advanced reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Dynamics of disordered mechanical systems with large connectivity, free probability theory, and quasi-Hermitian random matrices

Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the systems studied in this paper have all their degrees of freedom coupled to each other. Thus, the problem of linearized small oscillations of such systems involves two full positive-definite and non-commuting matrices, as opposed to the sparse matrices associated with disordered crystals. Consequently, the familiar methods for determining the averaged vibrational spectra of disordered crystals, introduced many years ago by Dyson and Schmidt, are inapplicable for highly connected disordered systems. In this paper we apply random matrix theory (RMT) to calculate the averaged vibrational spectra of such systems, in the limit of infinitely large system size. At the heart of our analysis lies a calculation of the average spectrum of the product of two positive definite random matrices by means of free probability theory techniques. We also show that this problem is intimately related with quasi-hermitian random matrix theory (QHRMT), which means that the ‘hamiltonian’ matrix is hermitian with respect to a non-trivial metric. This extends ordinary hermitian matrices, for which the metric is simply the unit matrix. The analytical results we obtain for the spectrum agree well with our numerical results. The latter also exhibit oscillations at the high-frequency band edge, which fit well the Airy kernel pattern. We also compute inverse participation ratios of the corresponding amplitude eigenvectors and demonstrate that they are all extended, in contrast with conventional disordered crystals. Finally, we compute the thermodynamic properties of the system from its spectrum of vibrations. In addition to matrix model analysis, we also study the vibrational spectra of various multi-segmented disordered pendula, as concrete realizations of highly connected mechanical systems. A universal feature of the density of vibration modes, common to both pendula and the matrix model, is that it tends to a non-zero constant at vanishing frequency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Fluctuation–dissipation relation for a quantum Brownian oscillator in a parametrically squeezed thermal field

In this paper we study the nonequilibrium evolution of a quantum Brownian oscillator, modeling the internal degree of freedom of a harmonic atom or an Unruh–DeWitt detector, coupled to a nonequilibrium and nonstationary quantum field bath and inquire whether a fluctuation–dissipation relation (FDR) can exist after/if it approaches equilibration. This is a nontrivial issue because a squeezed field bath cannot reach equilibration and yet, as this work shows, the system oscillator indeed can, which is a necessary condition for FDRs. We discuss three different settings: (A) The bath field essentially remains in a squeezed thermal state throughout, whose squeeze parameter is a mode- and time-independent constant. This situation is often encountered in quantum optics and quantum thermodynamics. (B) The bath field is initially in a thermal state, but is subjected to a parametric process leading to mode- and time-dependent squeezing. This scenario is encountered in cosmology and dynamical Casimir effects. The squeezing in the bath in both types of processes will affect the oscillator’s nonequilibrium evolution. We show that at late times it approaches equilibration and this stationarity condition warrants the existence of a FDR. The trait of squeezing is marked by the oscillator’s effective equilibrium temperature, and the proportionality factor in the FDR is only related to the stationary component of the noise kernel of the bath field. Setting (C) is more subtle: A finite system–bath coupling strength can set the oscillator in a squeezed state even though the bath field is stationary and does not engage in any parametric process. The squeezing of the system in this case is in general time-dependent but becomes constant when the internal dynamics is fully relaxed. We begin with comments on the broad range of physical processes involving squeezed thermal baths and end with some remarks on the significance of FDRs in capturing the essence of quantum backreaction in nonequilibrium and stochastic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Creating values from wastes: Producing biofuels from waste cooking oil via a tandem vapor-phase hydrotreating process

Here, this study is focused on producing biofuels from waste oils via a tandem vapor-phase hydrotreating process in a pressurized two-stage fixed bed reactor over a bifunctional Ni/Al 2 O 3 -SiO 2 catalyst under 0.25 MPa H 2 . A 100% hydrodeoxygenation efficiency both in liquid and gas products was observed, yielding 83.9 wt% C 5 -C 19 n-alkanes which corresponds to a 7.4-fold increase compared with that obtained from non-catalytic conversion. The hydrodeoxygenation mechanism of waste cooking oil in the catalytic tandem hydrotreating process induced by Ni/Al 2 O 3 -SiO 2 was proposed. The hydropyrolysis temperature in the first reactor, hydrogenation temperature in the second reactor, reaction pressure, catalyst to waste cooking oil mass ratio, and gas hourly space velocity (GHSV) was optimized at 550 °C, 300 °C, 0.25 MPa, 3, and 56 s -1 , respectively. The application potential of this cascade vapor-phase hydrotreating process was evaluated by employing different waste oils such as palm kernel oil, woody oil (swida wilsoniana), soapstock, and waste lubricating oil as feedstock, giving C 5 to C 19 n-alkane yields ranging from 21.6 to 87.5 wt%. This work provides a novel and promising approach to upcycle waste oils into upgraded biofuels compared with conventional catalytic pyrolysis.

09 BIOMASS FUELS↗
DOE OSTI2025

A high-order computational framework for particle-resolved simulations of disperse multiphase flows

This work presents a high-order numerical approach for particle-resolved simulations of disperse multiphase flows, where the Navier-Stokes equations for fluid flow are solved using a high-order spectral element method in the Eulerian framework, and the particle phase is directly simulated with a discrete element method. The coupling between particles and fluids is explicitly handled using an adapted direct-forcing immersed boundary method. Unlike the conventional schemes, a high-order barycentric Lagrange interpolation method and a Gaussian projection kernel are used to ensure accurate momentum exchange between local boundary points and surrounding fluid nodes in the framework of high-order fluid solver. Benchmark tests of increasing complexity are conducted to demonstrate the accuracy and efficiency of our method. Here, it is found that our approach exhibits an excellent convergence performance, as the fluid element/grid is refined and the number of boundary points increases. Compared to conventional low-order methods, the proposed high-order framework enables the use of substantially larger fluid elements while maintaining high accuracy in modeling fluid-particle interactions, owing to the enhanced resolution of high-order basis functions. Moreover, since the primary unknowns are stored at element or grid nodes, the high-order approach offers improved efficiency in both CPU memory usage and total computational cost.

42 ENGINEERING↗
DOE OSTI2026

Polymer coatings on zirconia microspheres via rotating flow fluid dynamics

Conventional tristructural isotropic (TRISO) coatings for nuclear fuels require multi-step and expensive formation processes; any breakage of the coatings may lead to fission species release. Polymer derived ceramic (PDC) coatings can be a suitable alternative to address these issues. In this study, allylhydridopolycarbosilane (SMP-10) coatings were created on yttria stabilized zirconia (YSZ) microspheres using a Rotating Flow Fluid Dynamics (RFFD) coating method. The effects of curing temperature, rotation speed, and coating cycle/time on the coating were analyzed. Surface functionalization of YSZ microspheres with NaOH resulted in good adhesion between the polymer precursor and the YSZ kernel particles. Spectroscopy analysis revealed complete curing of SMP-10 coated YSZ at 160 °C. Rotation speed and coating time significantly affect the coating characteristics. After 3 cycles at lower rotation speed (50 rpm) for 10 min each, the coating obtained was uniform and homogeneous. In comparison, the coating showed almost 10 times less eccentricity at a high rotation speed of 300 rpm. Compared with the coatings prepared at 300 rpm condition, the coatings have higher sphericity and lower eccentricity at 50 rpm. Overall, this study provides a novel and effective route for fabricating and curing SMP-10 precursor coatings on YSZ microspheres.

Ravi, Nivetha [University of Alabama, Birmingham]↗
DOE OSTI2020

On The Use of Sectional Techniques for the Solution of Depolymerization Population Balances: Results on a Discrete-Continuous Mesh

To study the discrete bond-breaking phenomena of depolymerization, the use of a fully continuous Population Balance Equation (PBE) is inadequate to embody all the inherent characteristics of the process, thus resulting in the need for a discrete-continuous mesh. In this work, the performance of the three most state-of-the-art sectional techniques, i.e. the fixed pivot technique (FPT), cell average technique (CAT) and finite volume scheme (FVS) in approximating discrete depolymerization using discrete-continuous PBEs was extensively compared and evaluated. The solutions from these three methods show different accuracy depending on the breakage mechanisms. For chain-end scission, the FPT and the CAT satisfactorily predict the population densities and moments whereas the FVS fails to predict the population densities but preserves the zeroth and the first moments. In the application of a discrete-continuous model, we identified a previously-not-reported issue of a precipitous drop in the number density at the boundary of discrete and continuous region specifically for chain-end scission. We successfully fixed this problem by employing the alterations proposed in this paper, to the particle allocation functions at the boundary points. For random scission, all three sectional techniques predict the population densities and moments to a high degree of accuracy, even at a very coarse mesh, through the use of our new stoichiometric kernel which is able to closely approximate the inherently discrete bond-breaking depolymerization process. The assessments in this present work intends to provide a clear-cut direction to efficient and economical modelling of depolymerization processes.

Ahamed, Firnaaz↗
DOE OSTI2020

Dynamic Performance Enhancement for Nonlinear Stochastic Systems Using RBF Driven Nonlinear Compensation with Extended Kalman Filter

In this paper, a novel hybrid control method is proposed to enhance the control performance of the PI based control system for a class of nonlinear and non-Gaussian stochastic dynamic processes with unmeasurable states. Firstly, to enhance the tracking performance of the PI controller where the PI parameters are fixed in many actual control systems, the compensative signal is formed using the extended Kalman filter(EKF) based state estimator and driven by the radial basis function (RBF) neural network based compensator. In addition, the weights of RBF is trained to minimize the entropy criterion of tracking error as the process is subjected to non-Gaussian disturbances. Meanwhile, since the precise statistical property of noises is hard to obtain for many industrial processes, the kernel density estimation (KDE) technique is employed in this paper to estimate the entropy. The convergence of RBF network is discussed and the stability of the resulted closed-loop hybrid control system is analyzed in mean square sense. Finally, a numerical example and a practical system testing are given to illustrate the effectiveness of the proposed control method.

stochastic systems, PI Controller, Entropy, Extend↗
DOE OSTI2021

Multichannel Analysis of Surface Waves Accelerated (MASWAccelerated): Software for efficient surface wave inversion using MPI and GPUs

Multichannel Analysis of Surface Waves (MASW) is a technique frequently used in geotechnical engineering and engineering geophysics to infer 1D layered models of seismic shear wave velocities in the top tens to hundreds of meters of the subsurface. We aim to accelerate MASW calculations by capitalizing on modern computer hardware available in the workstations of most engineers: multiple cores and graphics processing units (GPUs). We propose new parallel and GPU accelerated algorithms for computing 1D MASW inversion, and provide software implementations in C using Message Passing Interface (MPI) and CUDA. These algorithms take advantage of sparsity that arises in the problem, and the work balance between processes considers typical data trends. We compare our methods to an existing open source Matlab MASW tool. Our serial C implementation achieves a 2x speedup over the Matlab software, and we continue to see improvements by parallelizing the problem with MPI. Here we see nearly perfect strong and weak scaling for uniform data, and improve strong scaling for realistic data by repartitioning the problem to process mapping. By utilizing GPUs available on most modern workstations, we observe an additional 1.3x speedup over the serial C implementation on the first use of the method. We typically repeatedly evaluate theoretical dispersion curves as part of an optimization procedure, and on the GPU the kernel can be cached for faster reuse on later runs. We observe a 3.2x speedup on the cached GPU runs compared to the serial C runs. This work is the first open-source parallel or GPU-accelerated software tool for MASW imaging, and should enable geotechnical engineers to fully utilize all computer hardware at their disposal.

58 GEOSCIENCES↗
DOE OSTI2021

Enhanced relaxed physical factorization preconditioner for coupled poromechanics

The relaxed physical factorization (RPF) preconditioner is a recent algorithm allowing for the efficient and robust solution to the block linear systems arising from the three-field displacement-velocity-pressure formulation of coupled poromechanics. For its application, however, it is necessary to invert blocks with the algebraic form C^ = (C + βFF T ), where C is a symmetric positive definite matrix, FF T a rank-deficient term, and β a real non-negative coefficient. The inversion of C^, performed in an inexact way, can become unstable for large values of β, as it usually occurs at some stages of a full poromechanical simulation. In this work, we propose a family of algebraic techniques to stabilize the inexact solve with C^. This strategy can prove useful in other problems as well where such an issue might arise, such as augmented Lagrangian preconditioning techniques for Navier-Stokes or incompressible elasticity. First, we introduce an iterative scheme obtained by a natural splitting of matrix C^. Second, we develop a technique based on the use of a proper projection operator annihilating the near-kernel modes of C^. Both approaches give rise to a novel class of preconditioners denoted as Enhanced RPF (ERPF). Furthermore, effectiveness and robustness of the proposed algorithms are demonstrated in both theoretical benchmarks and real-world large-size applications, outperforming the native RPF preconditioner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Generalized moving least squares vs. radial basis function finite difference methods for approximating surface derivatives

Approximating differential operators defined on two-dimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least squares (GMLS) and radial basis function finite differences (RBF-FD) have been shown to be effective for this task as they can give high orders of accuracy at low computational cost, and they can be applied to surfaces defined only by point clouds. However, there have yet to be any studies that perform a direct comparison of these methods for approximating surface differential operators (SDOs). The first purpose of this work is to fill that gap. For this comparison, we focus on an RBF-FD method based on polyharmonic spline kernels and polynomials (PHS+Poly) since they are most closely related to the GMLS method. Additionally, we use a relatively new technique for approximating SDOs with RBF-FD called the tangent plane method since it is simpler than previous techniques and natural to use with PHS+Poly RBF-FD. Further, the second purpose of this work is to relate the tangent plane formulation of SDOs to the local coordinate formulation used in GMLS and to show that they are equivalent when the tangent space to the surface is known exactly. The final purpose is to use ideas from the GMLS SDO formulation to derive a new RBF-FD method for approximating the tangent space for a point cloud surface when it is unknown. For the numerical comparisons of the methods, we examine their convergence rates for approximating the surface gradient, divergence, and Laplacian as the point clouds are refined for various parameter choices. We also compare their efficiency in terms of accuracy per computational cost, both when including and excluding setup costs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Linking spout fluidization hydrodynamics to pyrolytic carbon deposition characteristics in a fluidized bed chemical vapor deposition reactor

Spout fluidized bed chemical vapor deposition (SFB-CVD) is the dominant method for producing pyrolytic carbon (PyC) coatings on tristructural-isotropic (TRISO) fuel particles, yet the relationship between gas injector design, fluidization hydrodynamics, and resulting coating quality remains poorly quantified. Here, in this work, three spout fluidized bed (SFB) nozzle geometries were designed and fabricated to empirically investigate how injector-driven changes in particle circulation influence PyC deposition. The geometries were first evaluated in a room temperature fluidization apparatus using time-resolved particle image velocimetry, which highlighted distinct differences in particle velocity fields, circulation pathways, and overall fluidization quality. Graphite versions of each injector geometry were subsequently implemented in a laboratory-scale SFB-CVD reactor to deposit PyC onto surrogate fuel kernels under similar conditions. Post-deposition characterization included particle morphology, coating thickness, porosity distribution, optical anisotropy, and microindentation mechanical testing. Overall, the results show clear differences in coating microstructure as a function of changing injector geometry, despite mechanical testing indicating comparable elastic modulus values across all coatings. This study provides one of the first fully experimental, quantitative mappings between SFB nozzle geometry, fluidization hydrodynamics, and resulting PyC coating structure. The framework established here supports rational injector design and offers a pathway toward improved coating control in future pilot- and production-scale TRISO fuel fabrication systems.

Coated particle fuel↗
DOE OSTI2020

Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold

This paper introduces a surrogate modeling scheme based on Grassmannian manifold learning to be used for cost-efficient predictions of high-dimensional stochastic systems. The method exploits subspace-structured features of each solution by projecting it onto a Grassmann manifold. This point-wise linear dimensionality reduction harnesses the structural information to assess the similarity between solutions at different points in the input parameter space. The method utilizes a solution clustering approach in order to identify regions of the parameter space over which solutions are sufficiently similarly such that they can be interpolated on the Grassmannian. In this clustering, the reduced-order solutions are partitioned into disjoint clusters on the Grassmann manifold using the eigen-structure of properly defined Grassmannian kernels and, the Karcher mean of each cluster is estimated. Then, the points in each cluster are projected onto the tangent space with origin at the corresponding Karcher mean using the exponential mapping. For each cluster, a Gaussian process regression model is trained that maps the input parameters of the system to the reduced solution points of the corresponding cluster projected onto the tangent space. Using this Gaussian process model, the full-field solution can be efficiently predicted at any new point in the parameter space. In certain cases, the solution clusters will span disjoint regions of the parameter space. In such cases, for each of the solution clusters we utilize a second, density-based spatial clustering to group their corresponding input parameter points in the Euclidean space. The proposed method is applied to two numerical examples. Here, the first is a nonlinear stochastic ordinary differential equation with uncertain initial conditions where the surrogate is used to predict the time history solution. The second involves modeling of plastic deformation in a model amorphous solid using the Shear Transformation Zone theory of plasticity, where the proposed surrogate is used to predict the full strain field of a material specimen under large shear strains.

42 ENGINEERING↗
DOE OSTI2021

A compute-bound formulation of Galerkin model reduction for linear time-invariant dynamical systems

This work aims to advance computational methods for projection-based reduced-order models (ROMs) of linear time-invariant (LTI) dynamical systems. For such systems, current practice relies on ROM formulations expressing the state as a rank-1 tensor (i.e., a vector), leading to computational kernels that are memory bandwidth bound and, therefore, ill-suited for scalable performance on modern architectures. This weakness can be particularly limiting when tackling many-query studies, where one needs to run a large number of simulations. This work introduces a reformulation, called rank-2 Galerkin, of the Galerkin ROM for LTI dynamical systems which converts the nature of the ROM problem from memory bandwidth to compute bound. We present the details of the formulation and its implementation, and demonstrate its utility through numerical experiments using, as a test case, the simulation of elastic seismic shear waves in an axisymmetric domain. We quantify and analyze performance and scaling results for varying numbers of threads and problem sizes. In conclusion, we present an end-to-end demonstration of using the rank-2 Galerkin ROM for a Monte Carlo sampling study. We show that the rank-2 Galerkin ROM is one order of magnitude more efficient than the rank-1 Galerkin ROM (the current practice) and about 970 times more efficient than the full-order model, while maintaining accuracy in both the mean and statistics of the field.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Gaussian process regression constrained by boundary value problems

We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and boundary conditions, but for which only scattered observations of the source term are available. Scattered observations of the solution may also be used in the regression. The framework combines co-kriging with the linear transformation of a Gaussian process together with the use of kernels given by spectral expansions in eigenfunctions of the boundary value problem. Furthermore, it benefits from a reduced-rank property of covariance matrices. We demonstrate that the resulting framework yields more accurate and stable solution inference as compared to physics-informed Gaussian process regression without boundary condition constraints.

42 ENGINEERING↗