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At least 415 records · Page 23
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DOE OSTI2024

Assessment of the Impact of Realistic Sensor Physics and the Integration of Ex-Core Sensors on Reactor Power Synthesis

In the work documented in this report, a weighting function–based core power synthesis method was applied to multiple Monte Carlo N-Particle (MCNP) reactor models, which are informed based on simulated self-powered neutron detector (SPND) responses. The weighting function method used has been coined the point-based iterative (PBI) method. The goal of this application is to assess the impact of considering realistic sensor physics in the generation of the simulated SPND outputs as well as to consider how the synthesis is impacted based on the inclusion of ex-core detectors in the model. The NuScale small modular reactor (SMR) and Westinghouse AP1000 pressurized water reactor (PWR) are the models that served as the testbeds for the assessment of realistic sensor physics; this was achieved by using Geant4 SPND models in comparison with analytical models, such that the effect of electron transport in realistic SPND geometries in the Geant4 model can be understood in terms of synthesis error and convergence time. The comparison was considered for fuel burnup–induced perturbations, for a range of sensor string densities and synthesized power distribution axial fidelities. The Texas A&M Testing, Research, Isotopes, General Atomics Reactor (TAMU TRIGA) reactor MCNP model was used to assess the impact of ex-core sensors; this was done by performing synthesis with and without the ex-core detectors and by quantifying the synthesis error and number of iterations associated with Gaussian-type perturbations in many locations in the core. The TAMU TRIGA model was particularly pertinent for this study because of the interest in future experimental tests with SPNDs in this reactor, as well as the ease of modifying the MCNP model to include ex-core detectors with heterogeneously described response functions. Results from the comparison between the Geant4 and analytical SPND models indicate that similar average and maximum synthesis errors were obtained for burnup-induced perturbations in both the NuScale SMR and the AP1000. This was true for a range of sensor string densities and axial fidelities. However, there were marked differences between both the Geant4 and analytically informed models in terms of the iterations required to converge on the synthesized power distribution. Namely, the Geant4-informed models tended to lead to fewer iterations, except for a few sensor–core configurations that had particularly numerous iterations. Results from the ex-core sensor assessment with the TAMU TRIGA model indicate that the inclusion of ex-core sensors drastically reduces the synthesis error of Gaussian-type perturbations close to the edge of the core, and it slightly reduces synthesis errors for perturbations closer to the center of the core. This was achieved with a minimal increase in computational cost—that is, the number of iterations required for convergence. The errors were identified to be in the same location as the perturbation in the core, indicating that the methodology remains robust for unperturbed regions of the core. A secondary result from this study with the TAMU TRIGA was yielded by analysis of the neutron flux levels in the in-core and ex-core sensor locations of the core; these flux levels indicate that SPNDs could be used as both in-core and ex-core sensors, so long as the emitter material is sensitive to thermal neutrons. The results from these studies provide a quantitative understanding of the importance of considering realistic sensor physics and including ex-core sensors to perform accurate and timely power distribution synthesis of a reactor core.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Verification of numerical models for seismic fluid-structure interaction analysis of internal components in liquid-filled advanced reactors

Earthquake shaking of a liquid-filled advanced reactor induces fluid-structure interaction (FSI) between the reactor vessel (tank), its internal components, and the contained liquid. Seismic design, qualification, and risk assessment of such reactors must consider fluid-structure responses, their geometries and support conditions, and three-directional seismic inputs, all of which require numerical simulations. Numerical models used for analysis of safety-related nuclear equipment must be verified and validated. Here, this paper verifies numerical models of submerged components using analytical solutions. Seismic FSI analysis of the numerical models is performed using the Arbitrary Lagrangian-Eulerian (ALE) and Incompressible Computational Fluid Dynamics (ICFD) solvers in LS-DYNA. Prior analytical solutions are reworked in this paper, and calculation errors are identified and corrected. The solutions address frequencies of two concentric cylindrical pipes filled with liquid: the inner pipe is a submerged component, and the outer pipe contains the liquid. A unitless frequency coefficient is defined and presented for pipes of different materials, filled with different liquids, and with a range of dimensions for application to advanced reactors. The numerical models are verified here by comparing the lateral frequencies of submerged components with those calculated using the corrected analytical solutions. Recommendations for verification of numerical models of internal components in advanced reactors for seismic FSI analysis are provided. Although the unitless frequency coefficients and verification procedures are developed for application to advanced nuclear reactors, they are broadly applicable to FSI analysis of submerged components in liquid-filled vessels such as storage tanks, boilers, and steam generators.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Machine learning a molecular Hamiltonian for predicting electron dynamics

We develop a computational method to learn a molecular Hamiltonian matrix from matrix-valued time series of the electron density. As we demonstrate for three small molecules, the resulting Hamiltonians can be used for electron density evolution, producing highly accurate results even when propagating 1,000 time steps beyond the training data. As a more rigorous test, we use the learned Hamiltonians to simulate electron dynamics in the presence of an applied electric field, extrapolating to a problem that is beyond the field-free training data. We find that the resulting electron dynamics predicted by our learned Hamiltonian are in close quantitative agreement with the ground truth. Our method relies on combining a reduced-dimensional, linear statistical model of the Hamiltonian with a time-discretization of the quantum Liouville equation within time-dependent Hartree Fock theory. In conclusion, we train the model using a least-squares solver, avoiding numerous, CPU-intensive optimization steps. For both field-free and field-on problems, we quantify training and propagation errors, highlighting areas for future development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

A coupled multipoint stress–multipoint flux mixed finite element method for the Biot system of poroelasticity

In this work, we present a mixed finite element method for a five-field formulation of the Biot system of poroelasticity that reduces to a cell-centered pressure–displacement system on simplicial and quadrilateral grids. A mixed stress–displacement–rotation formulation for elasticity with weak stress symmetry is coupled with a mixed velocity–pressure Darcy formulation. The spatial discretization is based on combining the multipoint stress mixed finite element (MSMFE) method for elasticity and the multipoint flux mixed finite element (MFMFE) method for Darcy flow. It uses the lowest order Brezzi–Douglas–Marini mixed finite element spaces for the poroelastic stress and Darcy velocity, piecewise constant displacement and pressure, and continuous piecewise linear or bilinear rotation. A vertex quadrature rule is applied to the velocity, stress, and stress–rotation bilinear forms, which block-diagonalizes the corresponding matrices and allows for local velocity, stress, and rotation elimination. This leads to a cell-centered positive-definite system for pressure and displacement at each time step. We perform error analysis for the semidiscrete and fully discrete formulations, establishing first order convergence for all variables in their natural norms. The numerical tests confirm the theoretical convergence rates and illustrate the locking-free property of the method.

42 ENGINEERING↗
DOE OSTI2022

Co-optimized machine-learned manifold models for large eddy simulation of turbulent combustion

Many modeling approaches in large eddy simulation (LES) of turbulent combustion employ a projection of the thermochemical state onto a low-dimensional manifold within state space to reduce the number of transported variables and hence computational cost. Flamelet-generated manifolds (FGM) is an example of a well-established, physics-based approach, but increasingly, principal component analysis (PCA) is being used as a data-driven method for generating manifold models. For both approaches, the nonlinear relationship between the location on the predefined manifold and the outputs of interest, such as reaction rates, can be tabulated or encoded in a neural network. This work proposes a new approach for manifold modeling that extends these existing approaches. A modified neural network structure simultaneously encodes the definition of the manifold variables, the nonlinear mapping, and the subfilter closure for LES. This allows all three of these aspects of the model to be co-optimized, generating a model from any source of combustion thermochemical state data. The manifold parameterizing variables are constrained to be linear combinations of species, as in FGM and PCA-based models, to aid in interpretability and implementation. For LES, subfilter variances of the manifold variables are also included as inputs. Two types of a priori analysis are performed to evaluate the new approach. In the first, the model is trained on data from one-dimensional premixed flames. In this case, the approach recovers the behavior of flamelet-based manifold approaches, and in fact slightly improves performance by identifying an optimized progress variable. The approach is also applied to data from direct numerical simulations of spherical ignition kernels in isotropic turbulence. For any specified manifold dimensionality, the new approach provides substantially lower prediction errors than a PCA-based model developed from the same data set. Additionally, the LES formulation of the new approach can provide accurate predictions for filtered reaction rates across a variety of filter widths.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Debunking common myths in coastal circulation modeling

Despite tremendous progress in algorithm development, computational efficiency and transition into operations over the past two decades, coastal modeling still lacks scientific rigor due to proliferation of many ‘gray’ areas related to various modeling choices made by modelers. Here, in this paper, we propose some guiding principles for the modeling community to improve performance, and we also debunk commonly held myths that make the coastal modeling lack rigor. Using our own experience in developing seamless cross-scale unstructured-grid based models for the past two decades, we describe in unprecedented detail the end-to-end modeling process (i.e., from digital elevation models (DEMs) to mesh generation to post analysis), and demonstrate that defensible modeling is within reach for any end user by following three guiding principles: (1) Bathymetry is a first order forcing in coastal domains and thus should be respected in all aspects of modeling; (2) Oceanographic processes are driven across multiple spatial scales and so models should enable appropriate resolution as needed; and (3) Model assessment should focus on physical processes. Through qualitative and quantitative model assessments, we demonstrate the fundamental role played by bathymetry/topography as embedded in DEMs in making the results defensible, which is unfortunately glossed over in many modeling studies. Focusing on process-based assessment simplifies the calibration process. A major conclusion of this work is that model developers and operators should maximize the scientific rigor for in silico oceanography by avoiding some common pitfalls that rely on error compensation at the expense of representation of physical system processes. We present some best practice procedures for defensive and trustworthy numerical modeling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Assessing the source of error in the Thomas–Fermi–von Weizsäcker density functional

We investigate the source of error in the Thomas–Fermi–von Weizsäcker (TFW) density functional relative to Kohn–Sham density functional theory (DFT). In particular, through numerical studies on a range of materials, for a variety of crystal structures subject to strain and atomic displacements, we find that while the ground state electron density in TFW orbital-free DFT is close to the Kohn–Sham density, the corresponding energy deviates significantly from the Kohn–Sham value. Here, we show that these differences are a consequence of the poor representation of the linear response within the TFW approximation for the electronic kinetic energy, confirming conjectures in the literature. In so doing, we find that the energy computed from a non-self-consistent Kohn–Sham calculation using the TFW electronic ground state density is in very good agreement with that obtained from the fully self-consistent Kohn–Sham solution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

The hybrid topological longitudinal transmon qubit

We introduce a new hybrid qubit consisting of a Majorana qubit interacting with a transmon longitudinally coupled to a resonator. To do so, we equip the longitudinal transmon qubit with topological quasiparticles, supported by an array of heterostructure nanowires, and derive charge- and phase-based interactions between the Majorana qubit and the resonator and transmon degrees of freedom. Inspecting the charge coupling, we demonstrate that the Majorana self-charging can be eliminated by a judicious choice of charge offset, thereby maintaining the Majorana degeneracy regardless of the quasiparticles spatial arrangement and parity configuration. We perform analytic and numerical calculations to derive the effective qubit-qubit interaction elements and discuss their potential utility for state readout and quantum error correction. Further, we find that select interactions depend strongly on the overall superconducting parity, which may provide a direct mechanism to characterize deleterious quasiparticle poisoning processes.

36 MATERIALS SCIENCE↗
DOE OSTI2020

The virtual element method for linear elastodynamics models: Design, analysis, and implementation

We design the conforming virtual element method for the numerical simulation of two dimensional time-dependent elastodynamics problems. We investigate the performance of the method both theoretically and numerically. We prove the stability and the convergence of the semi-discrete approximation in the energy norm and derive optimal error estimates. We also show the convergence in the L 2 norm. The performance of the virtual element method is assessed on a set of different computational meshes, including non-convex cells up to order four in the h-refinement setting. Exponential convergence is also experimentally seen in the p-refinement setting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Physics-Informed Neural Network Solution of Point Kinetics Equations for a Nuclear Reactor Digital Twin

A digital twin (DT) for nuclear reactor monitoring can be implemented using either a differential equations-based physics model or a data-driven machine learning model. The challenge of a physics-model-based DT consists of achieving sufficient model fidelity to represent a complex experimental system, whereas the challenge of a data-driven DT consists of extensive training requirements and a potential lack of predictive ability. We investigate the performance of a hybrid approach, which is based on physics-informed neural networks (PINNs) that encode fundamental physical laws into the loss function of the neural network. We develop a PINN model to solve the point kinetic equations (PKEs), which are time-dependent, stiff, nonlinear, ordinary differential equations that constitute a nuclear reactor reduced-order model under the approximation of ignoring spatial dependence of the neutron flux. The PINN model solution of PKEs is developed to monitor the start-up transient of Purdue University Reactor Number One (PUR-1) using experimental parameters for the reactivity feedback schedule and the neutron source. The results demonstrate strong agreement between the PINN solution and finite difference numerical solution of PKEs. We investigate PINNs performance in both data interpolation and extrapolation. For the test cases considered, the extrapolation errors are comparable to those of interpolation predictions. Extrapolation accuracy decreases with increasing time interval.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Automatically adaptive stabilized finite elements and continuation analysis for compaction banding in geomaterials

Under compressive creep, viscoplastic solids experiencing internal mass transfer processes can accommodate singular cnoidal wave solutions as material instabilities at the stationary wave limit. These instabilities appear when the loading rate is significantly faster than the material's capacity to diffusive internal perturbations, leading to localized failure features (e.g., cracks and compaction bands). These cnoidal waves, generally found in fluids, have strong nonlinearities that produce periodic patterns. Due to the singular nature of the solutions, the applicability of the theory is currently limited. Additionally, practical simulation tools require proper regularization to overcome the challenges that singularity induces. We focus on the numerical treatment of the governing equation using a nonlinear approach building on a recent adaptive stabilized finite element method. This automatic refinement method provides an error estimate that drives mesh adaptivity, a crucial feature for the problem at hand. We compare the performance of this adaptive strategy against analytical and standard finite element solutions. We then investigate the sensitivity of the diffusivity ratio, the parameter controlling the process, and identify multiple possible solutions with several stress peaks. We also show the evolution of the spacing between peaks for all solutions as a function of that parameter.

42 ENGINEERING↗
DOE OSTI2020

Time-series machine-learning error models for approximate solutions to parameterized dynamical systems

This work proposes a machine-learning framework for modeling the error incurred by approximate solutions to parameterized dynamical systems. In particular, we extend the machine-learning error models (MLEM) framework proposed in Ref. Freno and Carlberg (2019) to dynamical systems. The proposed Time-Series Machine-Learning Error Modeling (T-MLEM) method constructs a regression model that maps features – which comprise error indicators that are derived from standard a posteriori error-quantification techniques – to a random variable for the approximate-solution error at each time instance. The proposed framework considers a wide range of candidate features, regression methods, and additive noise models. We consider primarily recursive regression techniques developed for time-series modeling, including both classical time-series models (e.g., autoregressive models) and recurrent neural networks (RNNs), but also analyze standard non-recursive regression techniques (e.g., feed-forward neural networks) for comparative purposes. Finally, numerical experiments conducted on multiple benchmark problems illustrate that the long short-term memory (LSTM) neural network, which is a type of RNN, outperforms other methods and yields substantial improvements in error predictions over traditional approaches.

42 ENGINEERING↗
DOE OSTI2020

Time-stepping DPG formulations for the heat equation

For a wide range of PDEs, the discontinuous Petrov–Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan provides discrete stability starting from a coarse mesh and minimization of the residual in a user-controlled norm, among other appealing features. Research on DPG for transient problems has mainly focused on spacetime discretizations, which has theoretical advantages, but practical costs for computations and software implementations. The sole examination of time-stepping DPG formulations was performed by Führer, Heuer, and Gupta, who applied Rothe’s method to an ultraweak formulation of the heat equation to develop an implicit time-stepping scheme; their work emphasized theoretical results, including error estimates in time and space. Here, we follow Führer, Heuer, and Gupta in examining the heat equation; our focus is on numerical experiments, examining the stability and accuracy of several formulations, including primal as well as ultraweak, and explicit as well as implicit and Crank–Nicolson time-stepping schemes. We are additionally interested in communication-avoiding algorithms, and we therefore include a highly experimental formulation that places all the trace terms on the right-hand side of the equation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A fast and accurate domain decomposition nonlinear manifold reduced order model

Here, this paper integrates nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD). NM ROMs approximate the full order model (FOM) state in a nonlinear-manifold by training a shallow, sparse autoencoder using FOM snapshot data. These NM-ROMs can be advantageous over linear-subspace ROMs (LS-ROMs) for problems with slowly decaying Kolmogorov n-width. However, the number of NM-ROM parameters that need to be trained scales with the size of the FOM. Moreover, for “extreme-scale” problems, the storage of high-dimensional FOM snapshots alone can make ROM training expensive. To alleviate the training cost, this paper applies DD to the FOM, computes NM-ROMs on each subdomain, and couples them to obtain a global NM-ROM. This approach has several advantages: Subdomain NM-ROMs can be trained in parallel, involve fewer parameters to be trained than global NM-ROMs, require smaller subdomain FOM dimensional training data, and can be tailored to subdomain specific features of the FOM. The shallow, sparse architecture of the autoencoder used in each subdomain NM-ROM allows application of hyper-reduction (HR), reducing the complexity caused by nonlinearity and yielding computational speedup of the NM-ROM. This paper provides the first application of NM-ROM (with HR) to a DD problem. In particular, this paper details an algebraic DD reformulation of the FOM, training a NM-ROM with HR for each sub domain, and a sequential quadratic programming (SQP) solver to evaluate the coupled global NM-ROM. Theoretical convergence results for the SQP method and a priori and a posteriori error estimates for the DD NM-ROM with HR are provided. The proposed DD NM-ROM with HR approach is numerically compared to a DD LS-ROM with HR on the 2D steady-state Burgers’ equation, showing an order of magnitude improvement in accuracy of the proposed DD NM-ROM over the DD LS-ROM.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Toward more mechanistic representations of biogeochemical processes in river networks: Implementation and demonstration of a multiscale model

A recently introduced multiscale model for representing the effects of small-scale hyporheic-zone biogeochemical processes is extended from the reach scale to river network scales. The model uses advection-dispersion-reaction equations for the channel network and one-dimensional advection-reaction subgrid models for the hyporheic zone. We summarize implementation in the integrated surface/subsurface hydrology modeling system Amanzi-ATS. The extension uses topologically defined meshes to represent stream/river networks and associates a hyporheic subgrid model with each channel grid cell. Biogeochemical reaction modeling capability residing in community software is accessed through an application programming interface. The implementation is verified against independent numerical solutions on a single reach. Mesh convergence studies show that commonly used semi-distributed representations can introduce significant spatial discretization error. Denitrification of farm runoff in a subbasin of the Portage River Basin in Ohio, USA is used to demonstrate the general-purpose reactive transport capability.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Dyn$\mathrm{AMO}$: Multi-agent reinforcement learning for dynamic anticipatory mesh optimization with applications to hyperbolic conservation laws

Here we introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost and solution accuracy in numerical methods for partial differential equations. However, traditional adaptive mesh refinement approaches for time-dependent problems typically rely only on instantaneous error indicators to guide adaptivity. As a result, standard strategies often require frequent remeshing to maintain accuracy. In the DynAMO approach, multi-agent reinforcement learning is used to discover new local refinement policies that can anticipate and respond to future solution states by producing meshes that deliver more accurate solutions for longer time intervals. By applying DynAMO to discontinuous Galerkin methods for the linear advection and compressible Euler equations in two dimensions, we demonstrate that this new mesh refinement paradigm can outperform conventional threshold-based strategies while also generalizing to different mesh sizes, remeshing and simulation times, and initial conditions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Covariance operator estimation via adaptive thresholding

This paper studies sparse covariance operator estimation for nonstationary processes with sharply varying marginal variance and small correlation lengthscale. We introduce a covariance operator estimator that adaptively thresholds the sample covariance function using an estimate of the variance component. Building on recent results from empirical process theory, we derive an operator norm bound on the estimation error in terms of the sparsity level of the covariance and the expected supremum of a normalized process. Furthermore, our theory and numerical simulations demonstrate the advantage of adaptive threshold estimators over universal threshold and sample covariance estimators in nonstationary settings.

Al-Ghattas, Omar [University of Chicago, IL (Unite↗
DOE OSTI2021

Data-driven learning of Mori–Zwanzig operators for isotropic turbulence

Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori–Zwanzig (MZ) formalism provides a mathematically exact procedure for constructing reduced-order representations of high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. Turbulence models based on MZ formalism have been scarce due to the limited knowledge of the MZ operators, which originates from the difficulty in deriving MZ kernels for complex nonlinear dynamical systems. In this work, we apply a recently developed data-driven learning algorithm, which is based on Koopman's description of dynamical systems and Mori's linear projection operator, on a set of fully resolved isotropic turbulence datasets to extract the Mori–Zwanzig operators. With data augmentation using known turbulence symmetries, the extracted Markov term, memory kernel, and orthogonal dynamics are statistically converged and the generalized fluctuation–dissipation relation can be verified. The properties of the memory kernel and orthogonal dynamics, and their dependence on the choices of observables are investigated to address the modeling assumptions that are commonly used in MZ-based models. A series of numerical experiments are then constructed using the extracted kernels to evaluate the memory effects on prediction. The results show that the prediction errors are strongly affected by the choice of observables and can be further reduced by including the past history of the observables in the memory kernel.

97 MATHEMATICS AND COMPUTING↗