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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Variational Monte Carlo calculations of n + H 3 scattering

A paramount goal in nuclear physics is to unify ab initio treatments of bound and unbound states. The position-space quantum Monte Carlo (QMC) methods have a long history of successful bound-state calculations in light systems but have seen minimal implementation in unbound systems. Here, we introduce a numerical method to improve the efficiency and accuracy of unbound-state calculations in QMC. As an initial application, we compute scattering observables for the smallest system available to probe three-body forces, the neutron-triton system, using variational Monte Carlo (VMC) wave functions. The method involves inferring long-range amplitudes in the wave function from integrals over the short-range region where all the particles interact. This approach using integral relations is well established in the literature; here, we develop it for the QMC framework. We validate our approach with a consistency check between short-range spectroscopic overlap functions computed from direct evaluation and from the integral relations; scattering amplitudes are long-range asymptotics of those overlaps. Comparison against published benchmark calculations using the same potential demonstrates that when applied to the current VMC wave functions, the integral method produces more accurate scattering observables than direct evaluation from the same variational wave function. However, it still differs noticeably from the exact results. Using additional interactions, we then present phase shifts and mixing parameters for the n + 3 H system. In particular, we present one of the first applications of the Norfolk family of local coordinate-space chiral potentials in unbound systems of A > 2. The Norfolk results accurately describe s-wave scattering but predict p-wave cross sections too large. Compared with previous QMC scattering calculations, the integral method avoids difficulties associated with the precise computation of energy differences and with convergence outside the interaction region, which is particularly severe in the variational calculation. Application of the integral method here paves the way for its use in Green's function Monte Carlo (GFMC) calculations. In GFMC, the wave functions are more accurate, but the high-precision convergence of their tails is slow, and there are additional difficulties in reading out amplitudes. Here, the integral methods will address both of those remaining problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

MPACT Performance Improvements in VERA-CS

The report summarizes the initial profile of MPACT representative of the version that was distributed with VERA 3.4. It then describes several activities recently performed to increase the overall performance of the code. For the various improvements described in this report, several have been well known to the development team and reactor physics methods community for some time; while others proved novel in their combination of other existing ideas. Still, other improvements were the result of unanticipated breakthroughs in numerical methods research. These performance improvement activities focused on the following components of MPACT. Method of Characteristics Transport Kernel Iterative Methods for Coarse Mesh Finite Difference Linear System Macroscopic Cross Section and Effective Fission Spectrum Calculation Resonance self-shielding (Subgroup) calculation A summary of the overall improvement from this work as tested on a few representative problems is provided in the table below. The incremental improvements for various changes are shown in the figure below.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2013

The ICON-1.2 Hydrostatic Atmospheric Dynamical Core on Triangular Grids - Part 1: Formulation and Performance of the Baseline Version

A hydrostatic atmospheric dynamical core is developed for the purpose of global climate modelling. The model applies a finite difference method to discretize the primitive equations on spherical icosahedral grids, using C-type staggering with triangles as control volume for mass. This paper documents the numerical method employed in the baseline version of this model, discusses its properties, and presents results from idealized test cases. The evaluation shows that the new dynamical core is able to correctly represent the evolution of baroclinic eddies in the atmosphere and their role in meridional heat and momentum transport. The simulations compare well with the reference solutions, and converge as the horizontal resolution increases. First results from two aqua planet experiments are also presented, in which the equatorial wave spectra derived from tropical precipitation agree well with those simulated by a spectral transform model. The new dynamical core thus provides a good basis for further model development. Certain aspects of the model formulation that need further investigation and improvement are also pointed out.

atmospheric↗
DOE OSTI2017

Application of State Quantization-Based Methods in HEP Particle Transport Simulation

Simulation of particle-matter interactions in complex geometries is one of the main tasks in high energy physics (HEP) research. An essential aspect of it is an accurate and efficient particle transportation in a non-uniform magnetic field, which includes the handling of volume crossings within a predefined 3D geometry. Quantized State Systems (QSS) is a family of numerical methods that provides attractive features for particle transportation processes, such as dense output (sequences of polynomial segments changing only according to accuracy-driven discrete events) and lightweight detection and handling of volume crossings (based on simple root-finding of polynomial functions). In this work we present a proof-of-concept performance comparison between a QSS-based standalone numerical solver and an application based on the Geant4 simulation toolkit, with its default Runge-Kutta based adaptive step method. In a case study with a charged particle circulating in a vacuum (with interactions with matter turned off), in a uniform magnetic field, and crossing up to 200 volume boundaries twice per turn, simulation results showed speedups of up to 6 times in favor of QSS while it being 10 times slower in the case with zero volume boundaries.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Multiresolution quantum chemistry in multiwavelet bases: excited states from time-dependent Hartree–Fock and density functional theory via linear response

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using a numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2 , Be, N 2 , H 2 O, and C 2 H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Results of the Micromorphic Upscaling Workflow for the PSAAP III Year 3 Report

Predicting the mechanical response and failure of heterogeneous materials has proven difficult. Multiscale numerical methods based in higher order continuum theories attempt to bridge the gap between microscale and macroscale structural behavior. Micromorphic continuum theories have shown promise. The Tardigrade software package is an implementation of Eringen’s micromorphic continuum theory with capabilities to support multiscale material modeling workflows. These include homogenization through the Micromorphic Filter, calibration of micromorphic material models, and macroscale simulation in Tardigrade-MOOSE. This work discusses micromorphic upscaling efforts of the University of Colorado Boulder PSAAP III multidisciplinary simulation center (MSC). Verification studies are presented that compare the accuracy of the upscaling workflow with analytical solutions for a trivial stress state and homogeneous material using direct numerical simulations (DNS) conducted in the Ratel finite element method (FEM) and GEOS material point method (MPM) codes. These verification studies consider upscaling using the Micromorphic Filter for a “single filter domain”. Finally, DNS of a heterogeneous composite material is upscaled using a “multiple filter domain” method.

36 MATERIALS SCIENCE↗
DOE OSTI2022

First principles thermal transport modeling in GaN and related materials

Gallium nitride is a wide bandgap material utilized in a variety of technologies, including high-power electronics and light-emitting diodes, partly due to its favorable thermal properties. This chapter describes modern first-principles-based modeling of phonons and lattice thermal conductivity (k) of GaN, III-nitrides and related materials. In particular, we describe the theoretical underpinnings of calculating phonon dispersions, intrinsic phonon interactions, and other lattice dynamical properties from quantum perturbation theory and density functional theory (DFT) methods. Description of how these methods are then coupled with the Peierls-Boltzmann transport (PBT) equation to determine phonon distributions and lifetimes relevant for thermal transport is given. These theoretical and numerical methods have demonstrated quantitative accuracy and predictive power for calculating pristine k and defect-limited k from first principles for a variety of materials. We present a review of the literature utilizing DFT-PBT methods to understand novel k behaviors in III-nitrides and related materials.

Lindsay, Lucas↗
DOE OSTI2019

Development of an Ultra-Low Head Siphon Hydro Turbine Using Computational Fluid Dynamics

Structural simplification and efficient hydraulic performance are key to effectively utilizing ultra-low head water power resources and reducing hydroelectric unit costs. In this study, a computational fluid dynamics (CFD) method was used to predict hydraulic performance of an axial turbine at the Gaoliangjian power station. CFD results agreed well with field test data. Using the same numerical method, a new siphon turbine was then designed based on the original distributor and turbine runner equipment. This study investigated the effect of different siphon outlet passage geometry parameters, runner blade shapes, and distributors on the hydraulic performance of the siphon turbine. The maximum hydraulic efficiency increased to 87.9% under a head of 2.87 m. Finally, the hydraulic performance of the turbine was compared for four different distributor designs after adding an intake sump at the turbine entrance. The bell-shaped distributor with four guide vanes resulted in the highest power output at the lowest head. Therefore, the siphon turbine is a good option for energy conversion in ultra-low water head settings.

Zhou, Daqing↗
DOE OSTI2017

An Investigation into Solution Verification for CFD-DEM

This report presents the study of the convergence behavior of the computational fluid dynamicsdiscrete element method (CFD-DEM) method, specifically National Energy Technology Laboratory’s (NETL) open source MFiX code (MFiX-DEM) with a diffusion based particle-tocontinuum filtering scheme. In particular, this study focused on determining if the numerical method had a solution in the high-resolution limit where the grid size is smaller than the particle size. To address this uncertainty, fixed particle beds of two primary configurations were studied: i) fictitious beds where the particles are seeded with a random particle generator, and ii) instantaneous snapshots from a transient simulation of an experimentally relevant problem. Both problems considered a uniform inlet boundary and a pressure outflow. The CFD grid was refined from a few particle diameters down to 1/6 th of a particle diameter. The pressure drop between two vertical elevations, averaged across the bed cross-section was considered as the system response quantity of interest. A least-squares regression method was used to extrapolate the grid-dependent results to an approximate “grid-free” solution in the limit of infinite resolution. The results show that the diffusion based scheme does yield a converging solution. However, the convergence is more complicated than encountered in simpler, single-phase flow problems showing strong oscillations and, at times, oscillations superimposed on top of globally non-monotonic behavior. The challenging convergence behavior highlights the importance of using at least four grid resolutions in solution verification problems so that (over-determined) regression-based extrapolation methods may be applied to approximate the grid-free solution. The grid-free solution is very important in solution verification and VVUQ exercise in general as the difference between it and the reference solution largely determines the numerical uncertainty. By testing different randomized particle configurations of the same general problem (for the fictitious case) or different instances of freezing a transient simulation, the numerical uncertainties appeared to be on the same order of magnitude as ensemble or time averaging uncertainties. By testing different drag laws, almost all cases studied show that model form uncertainty in this one, very important closure relation was larger than the numerical uncertainty, at least with a reasonable CFD grid, roughly five particle diameters. In this study, the diffusion width (filtering length scale) was mostly set at a constant of six particle diameters. A few exploratory tests were performed to show that similar convergence behavior was observed for diffusion widths greater than approximately two particle diameters. However, this subject was not investigated in great detail because determining an appropriate filter size is really a validation question which must be determined by comparison to experimental or highly accurate numerical data. Future studies are being considered targeting solution verification of transient simulations as well as validation of the filter size with direct numerical simulation data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A progress update on selected AREVA NP advanced BWR methodologies

This article presents an overview of select advances in AREVA NP methods concerning 3 topics: Analytical fuel rod model, Transient and accident simulation, and ATWSi post dryout treatment. Concerning the first topic, the analytical fuel rod model relies heavily on first-principles closed-form solutions instead of ever finer nodalization and higher dimensions of standard numerical methods such as finite differences or finite elements. This analytical fuel rod model takes full account of the complications that made numerical analysis necessary, e.g. variation of pellet thermal conductivity with temperature and burnup, and the radial dependence of fission power deposition in pellets. The model also calculates thermo-mechanical parameters such as clad stress and strain, fission gas release, pellet sintering and swelling, and pellet-clad gap size and thermal resistance. The model is suited for innovative fuel designs such as doped pellets. Concerning the second topic, the BWR evaluation model, AURORA-B, is an advanced transient and accident simulator including SRELAP5, a two fluid thermal hydraulic code comprehensively reviewed by international safety authorities for BWR and PWR applications; RODEX4, a best estimate fuel performance code used to evaluate the local thermal-mechanical behavior of fuel rods during postulated transients and accidents; and MB2-K, a neutron kinetics extension of the steady state core simulator MICROBURN-B2. The analytical domains will include transients as well as control rod drop and loss of coolant accidents. Extension of RODEX4 have been made to accommodate analysis of chromium-doped fuel. Concerning the third issue,The new AREVA post-dryout models can accurately predict dryout/re-wet followed by an ultimate failure to re-wet under oscillatory ATWSi (Anticipated Transient Without SCRAM with core instability) conditions. These models, while not a boiling curve based method, can qualitatively reproduce the characteristics of the boiling curve.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Numerical investigation of the role of free-stream turbulence in boundary-layer separation

The aerodynamic performance of lifting surfaces operating at low Reynolds number conditions is impaired by laminar separation. In most cases, transition to turbulence occurs in the separated shear layer as a result of a series of strong hydrodynamic instability mechanisms. Although the understanding of these mechanisms has been significantly advanced over the past decades, key questions remain unanswered about the influence of external factors such as free-stream turbulence (FST) and others on transition and separation. The present study is driven by the need for more accurate predictions of separation and transition phenomena in ‘real world’ applications, where elevated levels of FST can play a significant role (e.g. turbomachinery). Numerical investigations have become an integral part in the effort to enhance our understanding of the intricate interactions between separation and transition. Due to the development of advanced numerical methods and the increase in the performance of supercomputers with parallel architecture, it has become feasible for low Reynolds number application ( $O(10^{5})$ ) to carry out direct numerical simulations (DNS) such that all relevant spatial and temporal scales are resolved without the use of turbulence modelling. Because the employed high-order accurate DNS are characterized by very low levels of background noise, they lend themselves to transition research where the amplification of small disturbances, sometimes even growing from numerical round-off, can be examined in great detail. When comparing results from DNS and experiment, however, it is beneficial, if not necessary, to increase the background disturbance levels in the DNS to levels that are typical for the experiment. For the current work, a numerical model that emulates a realistic free-stream turbulent environment was adapted and implemented into an existing Navier–Stokes code based on a vorticity–velocity formulation. The role FST plays in the transition process was then investigated for a laminar separation bubble forming on a flat plate. FST was shown to cause the formation of the well-known Klebanoff mode that is represented by streamwise-elongated streaks inside the boundary layer. Increasing the FST levels led to accelerated transition, a reduction in bubble size and better agreement with the experiments. Moreover, the stage of linear disturbance growth due to the inviscid shear-layer instability was found to not be ‘bypassed’.

Mechanics↗
DOE OSTI2020

RELAP-7 Application and Enhancement for FLEX Strategies and ATF Behavior under Extended Loss of AC Power Conditions

This report summarizes the results of a three-year research project sponsored by the U.S. Department of Energy (DOE) Nuclear Energy University Program (NEUP) to enhance and apply the RELAP-7 code by adding and improving several important components (e.g., a mechanistic Reactor Core Isolation Cooling (RCIC) system model) for thermal hydraulic studies of LWRs under ELAP conditions and evaluating the time available for transition to portable FLEX equipment. The project team included University of Massachusetts–Lowell, The Ohio State University, Texas A&M University, Idaho National Laboratory and Oak Ridge National Laboratory. In the Fukushima accident, it was found that the RCIC system played a crucial role in delaying core meltdown by almost three days in Fukushima Daiichi Unit 2, because of self-regulated operation of the steam driven RCIC turbine-pump injection system. Steam flow in the convergent-divergent nozzles of the RCIC Terry turbine is two-phase non-equilibrium transonic flow with homogenous nucleation condensation. To more accurately predict the dynamic process and behavior of the transonic compressible steam flow, a one-dimensional transient two-phase analytical model is presented. A simplified four-fluid model was employed in the present work with the consideration of four separate fluid fields: vapor, liquid film, entrained droplets and condensed droplets. The mass, momentum and energy interactions between the fluids were considered and modeled. An extended seven-equation non-equilibrium critical flow model was developed to obtain the critical pressure and velocities of each phase at the nozzle throat. To predict the wetness in the divergent section, a mechanistic nucleation condensation model was integrated in the nozzle analysis model, considering the generation and consequent growth of droplets. The governing differential equations on a staggered grid were discretized using the second-order Lax-Wendroff scheme with a flux limiter, and the Semi-Implicit Method for Pressure-Linked Equation (SIMPLE) algorithm was employed to solve the discrete linear system. To demonstrate the predictability and reliability of the physical models and the numerical method proposed in the present work, three representative nozzles were modeled and simulated. The results show good agreement with the available experimental data, even for condensation shock. Then, the 1D nozzle model was employed to obtain nozzle flow tables of the Terry turbine nozzle for different working pressures which can cover the operation pressure range of the RCIC system. A mechanistic RCIC turbine-pump system model was developed and implemented in the system code TRACE to simulate dynamic responses of the RCIC system under Beyond Design Basis Accident (BDBA) conditions. The turbine-pump governing equations are based on the control volume approach of the angular momentum balance. The physics based mechanistic RCIC model was developed using the TRACE control system components (i.e., signal variables, control blocks, and tables), and incorporated into a TRACE boiling water reactor (BWR) model. The TRACE model in this report has a detailed nodalization of the reactor pressure vessel (RPV), and all of the major flow paths and system components, including the safety relief valves (SRVs) and the containment suppression pool and drywell. Based on the nozzle flow tables generated from the 1D nozzle model developed, the turbine drive torque can be calculated from table lookup. Since the detailed specifications of the RCIC pump are unavailable, the homologous curves for a Bingham pump were used in the current pump component. A station black-out (SBO) accident test problem was selected to demonstrate the TRACE RCIC model. The short-term SBO simulations were performed for two cladding materials: Zircaloy and FeCrAl, to demonstrate the effect of the accident tolerant fuel cladding on fuel heat-up under BDBA accident conditions. The wetwell plays a vital safety role in SBO and other BWR accident scenarios in that it can reduce containment pressure and supply additional core make-up water. The suppression pool temperature distribution has a very large impact on both RPV and containment pressure. Thus, another novel contribution of the project comes mainly from an improved, systems-level wetwell model which can capture buoyancy-induced thermal stratification effects due to steam injection and condensation. A two-zone stratified wetwell model has been implemented in RELAP-7 and some results from that model are presented. This wetwell model is capable of simulating thermal stratification due to a low steam mass injection rate. With a low mass flow rate, the model assumes that all the steam condenses within the pipe and the resulting plume can be approximated with a purely buoyant, heat-source driven model. The wetwell model developed with these assumptions is adequate to simulate slow transients such as extended SBO transients.

42 ENGINEERING↗
DOE OSTI2017

The mimetic finite difference method for the Landau–Lifshitz equation

The Landau–Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which poses interesting challenges in developing numerical methods. We develop and analyze explicit and implicit mimetic finite difference schemes for this equation. These schemes work on general polytopal meshes which provide enormous flexibility to model magnetic devices with various shapes. A projection on the unit sphere is used to preserve the magnitude of the magnetization. We also provide a proof that shows the exchange energy is decreasing in certain conditions. The developed schemes are tested on general meshes that include distorted and randomized meshes. As a result, the numerical experiments include a test proposed by the National Institute of Standard and Technology and a test showing formation of domain wall structures in a thin film.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Effect of squeeze on electrostatic Trivelpiece-Gould wave damping

We present a theory for increased damping of Trivelpiece-Gouid plasma modes on a nonneutral plasma column, due to application of a Debye shielded cylindrically symmetric squeeze potential φ{sub 1}. We present two models of the effect this has on the plasma modes: a 1D model with only axial dependence, and a 2D model that also keeps radial dependence in the squeezed equilibrium and the mode. We study the models using both analytical and numerical methods. For our analytical studies, we assume that φ{sub 1}/T≪1, and we treat the Debye shielded squeeze potential as a perturbation in the equilibrium Hamiltonian. Our numerical simulations solve the 1D Vlasov-Poisson system and obtain the frequency and damping rate for a self-consistent plasma mode, making no assumptions as to the size of the squeeze. In both the 1D and 2D models, damping of the mode is caused by Landau resonances at energies E{sub n} for which the particle bounce frequency ω{sub b}(E{sub n}) and the wave frequency ω satisfy ω=nω{sub b}(E{sub n}). Particles experience a non-sinusoidal wave potential along their bounce orbits due to the squeeze potential. As a result, the squeeze induces bounce harmonics with n > 1 in the perturbed distribution. The harmonics allow resonances at energies E{sub n}≤T that cause substantial damping, even when wave phase velocities are much larger than the thermal velocity. In the regime ω/k≫√(T/m) (k is the wave number) and T≫φ{sub 1}, the resonance damping rate has a |φ{sub 1}|{sup 2} dependence. This dependence agrees with the simulations and experimental results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms

We develop efficient numerical methods for fractional order PDEs, and employ them to investigate viscoelastic constitutive laws for arterial wall mechanics. Recent simulations using one-dimensional models [1] have indicated that fractional order models may offer a more powerful alternative for modeling the arterial wall response, exhibiting reduced sensitivity to parametric uncertainties compared with the integer-calculus-based models. Here, we study three-dimensional (3D) fractional PDEs that naturally model the continuous relaxation properties of soft tissue, and for the first time employ them to simulate flow structure interactions for patient-specific brain aneurysms. To deal with the high memory requirements and in order to accelerate the numerical evaluation of hereditary integrals, we employ a fast convolution method [2] that reduces the memory cost to O(log(N)) and the computational complexity to O(N log(N)). Furthermore, we combine the fast convolution with high-order backward differentiation to achieve third-order time integration accuracy. We confirm that in 3D viscoelastic simulations, the integer order models strongly depends on the relaxation parameters, while the fractional order models are less sensitive. As an application to long-time simulations in complex geometries, we also apply the method to modeling fluid-structure interaction of a 3D patient-specific compliant cerebral artery with an aneurysm. Taken together, our findings demonstrate that fractional calculus can be employed effectively in modeling complex behavior of materials in realistic 3D time-dependent problems if properly designed efficient algorithms are employed to overcome the extra memory requirements and computational complexity associated with the non-local character of fractional derivatives.

Computer Science↗
DOE OSTI2019

Spectral Galerkin solver for intense beam Vlasov equilibria in nonlinear constant focusing channels

Here a numerical method is described for producing stationary solutions of the Vlasov-Poisson system describing a relativistic charged-particle beam in a constant focusing accelerator channel, confined transversely by a general (linear or nonlinear) focusing potential. The method utilizes a variant of the spectral Galerkin algorithm to solve a nonlinear partial differential equation (PDE) in two degrees of freedom for the beam space charge potential in equilibrium. Numerical convergence with an increasing number of computed spectral modes is investigated for several benchmark problems. Preservation of the stationary phase space density is verified using a strongly nonlinear focusing channel based on the Integrable Optics Test Accelerator at Fermi National Accelerator Laboratory.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Nonlinear manifold reduced order model

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, e.g., any advection-dominated flow phenomena such as in traffic flow, atmospheric flows, and air flow over vehicles, a lowdimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physics-informed neural network ROM, namely nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs. Our software takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 1D and 2D Burgers' equations. A speedup of up to 2.6 for 1D Burgers' and a speedup of 11.7 for 2D Burgers' equations are achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique.

Choi, Youngsoo↗
DOE OSTI2025

$\mathrm{SageNet}$: Fast Neural Network Emulation of the Stiff-amplified Gravitational Waves from Inflation

Accurate modeling of the inflationary gravitational waves (GWs) requires time-consuming, iterative numerical integrations of differential equations to take into account their backreaction on the expansion history. To improve computational efficiency while preserving accuracy, we present the Stiff-amplified Gravitational-wave Emulator Network (SageNet), a deep learning framework designed to replace conventional numerical solvers (code available at https://github.com/YifangLuo/SageNet). SageNet employs a long short-term memory architecture to emulate the present-day energy density spectrum of the inflationary GWs with possible stiff amplification, Ω GW (f). Trained on a data set of 25,689 numerically generated solutions, SageNet allows accurate reconstructions of Ω GW (f) and generalizes well to a wide range of cosmological parameters; 90.9% of the test emulations with randomly distributed parameters exhibit errors of under 4%. In addition, SageNet demonstrates its ability to learn and reproduce the artificial, adaptive sampling patterns in numerical calculations, which implement denser sampling of frequencies around changes in spectral indices in Ω GW (f). The dual capability of learning both physical and artificial features of the numerical GW spectra establishes SageNet as a robust alternative to exact numerical methods. Finally, our benchmark tests show that SageNet reduces the computation time from tens of seconds to milliseconds, achieving a speedup of ∼10 4 times over standard CPU-based numerical solvers with the potential for further acceleration on GPU hardware. These capabilities make SageNet a powerful tool for accelerating Bayesian inference procedures for extended cosmological models. In a broad sense, the SageNet framework offers a fast, accurate, and generalizable solution to modeling cosmological observables whose theoretical predictions demand costly differential equation solvers.

Astronomy data modeling↗