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At least 253 records · Page 14

Krylov complexity in mixed phase space

We investigate the Krylov complexity of thermofield double states in systems with mixed phase space, uncovering a direct correlation with the Brody distribution, which interpolates between Poisson and Wigner statistics. Our analysis spans two-dimensional random matrix models featuring (I) GOE-Poisson and (II) GUE-Poisson transitions and extends to higher-dimensional cases, including a stringy matrix model (GOE-Poisson) and the mass-deformed SYK model (GUE-Poisson). Krylov complexity consistently emerges as a reliable marker of quantum chaos, displaying a characteristic peak in the chaotic regime that gradually diminishes as the Brody parameter approaches zero, signaling a shift toward integrability. These results establish Krylov complexity as a powerful diagnostic of quantum chaos and highlight its interplay with eigenvalue statistics in mixed phase systems.

chaos & nonlinear dynamics↗

Improving Predictive Capability in REHEDS Simulations with Fast, Accurate, and Consistent Non-Equilibrium Material Properties

Predictive design of REHEDS experiments with radiation-hydrodynamic simulations requires knowledge of material properties (e.g. equations of state (EOS), transport coefficients, and radiation physics). Interpreting experimental results requires accurate models of diagnostic observables (e.g. detailed emission, absorption, and scattering spectra). In conditions of Local Thermodynamic Equilibrium (LTE), these material properties and observables can be pre-computed with relatively high accuracy and subsequently tabulated on simple temperature-density grids for fast look-up by simulations. When radiation and electron temperatures fall out of equilibrium, however, non-LTE effects can profoundly change material properties and diagnostic signatures. Accurately and efficiently incorporating these non-LTE effects has been a longstanding challenge for simulations. At present, most simulations include non-LTE effects by invoking highly simplified inline models. These inline non-LTE models are both much slower than table look-up and significantly less accurate than the detailed models used to populate LTE tables and diagnose experimental data through post-processing or inversion. Because inline non-LTE models are slow, designers avoid them whenever possible, which leads to known inaccuracies from using tabular LTE. Because inline models are simple, they are inconsistent with tabular data from detailed models, leading to ill-known inaccuracies, and they cannot generate detailed synthetic diagnostics suitable for direct comparisons with experimental data. This project addresses the challenge of generating and utilizing efficient, accurate, and consistent non-equilibrium material data along three complementary but relatively independent research lines. First, we have developed a relatively fast and accurate non-LTE average-atom model based on density functional theory (DFT) that provides a complete set of EOS, transport, and radiative data, and have rigorously tested it against more sophisticated first-principles multi-atom DFT models, including time-dependent DFT. Next, we have developed a tabular scheme and interpolation methods that compactly capture non-LTE effects for use in simulations and have implemented these tables in the GORGON magneto-hydrodynamic (MHD) code. Finally, we have developed post-processing tools that use detailed tabulated non-LTE data to directly predict experimental observables from simulation output.

36 MATERIALS SCIENCE↗

Nuclear Safeguards: Feature Extraction for Machine Learning Enrichment Analysis of UF 6 Cylinders

With the increasing international interest in using nuclear material as sources of energy, comes the growing concern that we may see an increase in proliferation threats. Uranium hexafluoride (UF 6 ) is used in the nuclear fuel cycle for uranium enrichment. Inspectors from the International Atomic Energy Agency (IAEA) monitor the enrichment levels of UF 6 stored in transportation cylinders, to ensure the enrichments match that of a facility operator’s declarations. However, only a characteristic subset of UF 6 cylinders can be measured by inspectors from the IAEA during these inspections. In turn, the inspector may not identify a cylinder whose enrichment levels do not match the facility declarations. Therefore, our team attempts to develop a machine learning network that could determine the enrichment percentage of cylinders as they enter and exit facilities. The machine learning model must be robust against spectral variations due to factors that are internal and external to the UF 6 cylinder. Such factors include but are not limited to the speed and distance of the moving vehicle, cylinder type, cylinder orientation, and fill level. Many features in the spectral continuum can be used to identify and correct for some of these variations. As a consequence, the model must extract numerous features in the continuum. We investigate new approaches in continuum subtraction to verify enrichment percentage: interpolation and extrapolation of lines at the notable characteristic spectral peaks. It was determined that there was no clear answer on which method proved superior, therefore the decision was made to implement both new methods into the current codebase. We currently rely on synthetic training and testing data to analyze the results and fine tune our models but hope to test the system on measured data soon.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Advanced Cross Section Library Generation using Reduced Order Models

Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which consist of databases of tabulated values, used to calculate the neutron cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of microscopic cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. In order to address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multigroup cross section data across isotopes, reaction types, and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs have been trained for all isotopes in this work and systematic Griffin testing is ongoing to ensure the feasibility of this ROM technique for predicting cross section and reducing memory requirements without a significant sacrifice in computational performance.

42 - ENGINEERING↗

Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: Comparison with linear subspace techniques

Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of CO 2 sequestration). Here, we extend and present a non-intrusive reduced order model of natural convection in porous media employing deep convolutional autoencoders for the compression and reconstruction and either radial basis function (RBF) interpolation or artificial neural networks (ANNs) for mapping parameters of partial differential equations (PDEs) on the corresponding nonlinear manifolds. To benchmark our approach, we also describe linear compression and reconstruction processes relying on proper orthogonal decomposition (POD) and ANNs. Further, we present comprehensive comparisons among different models through three benchmark problems. The reduced order models, linear and nonlinear approaches, are much faster than the finite element model, obtaining a maximum speed-up of 7 × 10 6 because our framework is not bound by the Courant–Friedrichs–Lewy condition; hence, it could deliver quantities of interest at any given time contrary to the finite element model. Our model’s accuracy still lies within a relative error of 7% in the worst-case scenario. We illustrate that, in specific settings, the nonlinear approach outperforms its linear counterpart and vice versa. We hypothesize that a visual comparison between principal component analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE) could indicate which method will perform better prior to employing any specific compression strategy.

97 MATHEMATICS AND COMPUTING↗

Solvable time-like cosets and holography beyond AdS

We build a novel time-like coset sigma-model describing type-II superstring theory in a charged rotating black-brane background that interpolates between a local AdS 3 in the IR and a linear-dilaton geometry in the UV. This allows one to peform a systematic study of holography in non-AdS backgrounds which are smoothly connected to AdS 3 . We construct massless closed string states vertex operators in the NS-NS sector, calculate the corresponding two-point correlation functions, and discuss holographic interpretation of our results from 4+1 dimensional boundary field theory point of view. Compactifying the theory on T 4 , we show that the spectrum of a single long string with unit winding agrees with the spectrum of a CFT 2 deformed by TT¯. We also calculate correlation functions of operators of the dual 1+1 dimensional non-conformal boundary field theory using worldsheet techniques.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Surface 3D Electrical Resistivity Tomography Inversion of 2005 BC Cribs and Trenches Datasets

Hydrogeophysics, Inc. (HGI) conducted an electrical resistivity tomography (ERT) dataset at the BC Cribs and Trenches site, located in the Central Plateau of the Hanford Site. The 20 trenches and 6 cribs received large volumes of liquid inorganic waste in the 1950s, resulting in a large inventory of contaminants in the vadose zone. The objective of the ERT survey was to map plume extents resulting from the legacy discharges. The HGI interpretation of the resistivity data was performed using geometric inversion to interpolate 2D lines into a 3D image. To demonstrate a newly developed geophysical code capability (E4D), the resistivity data were re-processed to fit a full 3D model of the bulk electrical conductivity. This proof-of-concept model inversion was executed in calendar year 2011, as the large dataset was well-suited for the use of high-performance computing. The 3D re-processing of the BC Cribs and Trenches ERT data conducted in 2011 resolved the true bulk electrical conductivity. This means that all of the resistivity data were fit to a single model of the bulk electrical conductivity, with true horizontal and vertical dimensions. This differed from the HGI data interpretation approach that used geometric inversion to process 2D lines independently, which were then interpolated into a 3D image. Both the full 3D re-processing and the 2D interpolation to a 3D image demonstrated a higher electrical conductivity observed immediately beneath the trenches and cribs. The electrical conductivity is strongly correlated with nitrate concentrations, indicating the presence of nitrate and other co-located contaminants.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Equation‐Free Surrogate Modeling of Geophysical Flows at the Intersection of Machine Learning and Data Assimilation

Abstract There is a growing interest in developing data‐driven reduced‐order models for atmospheric and oceanic flows that are trained on data obtained either from high‐resolution simulations or satellite observations. The data‐driven models are non‐intrusive in nature and offer significant computational savings compared to large‐scale numerical models. These low‐dimensional models can be utilized to reduce the computational burden of generating forecasts and estimating model uncertainty without losing the key information needed for data assimilation (DA) to produce accurate state estimates. This paper aims at exploring an equation‐free surrogate modeling approach at the intersection of machine learning and DA in Earth system modeling. With this objective, we introduce an end‐to‐end non‐intrusive reduced‐order modeling (NIROM) framework equipped with contributions in modal decomposition, time series prediction, optimal sensor placement, and sequential DA. Specifically, we use proper orthogonal decomposition (POD) to identify the dominant structures of the flow, and a long short‐term memory network to model the dynamics of the POD modes. The NIROM is integrated within the deterministic ensemble Kalman filter (DEnKF) to incorporate sparse and noisy observations at optimal sensor locations obtained through QR pivoting. The feasibility and the benefit of the proposed framework are demonstrated for the NOAA Optimum Interpolation Sea Surface Temperature (SST) V2 data set. Our results indicate that the NIROM is stable for long‐term forecasting and can model dynamics of SST with a reasonable level of accuracy. Furthermore, the prediction accuracy of the NIROM gets improved by almost one order of magnitude by the DEnKF algorithm.

Pawar, Suraj↗

Non-intrusive reduced-order modeling for dynamical systems with spatially localized features

This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced and full-order non-intrusive modeling, namely Operator Inference (OpInf) and sparse Full-Order Model (sFOM) inference. We decompose the domain into two complementary subdomains that exhibit fast and slow singular value decay. The dynamics of the subdomain exhibiting slow singular value decay are learned with sFOM while the dynamics with intrinsically low dimensionality on the complementary subdomain are learned with OpInf. The resulting, coupled OpInf-sFOM formulation leverages the computational efficiency of OpInf and the high resolution of sFOM, and thus enables fast non-intrusive predictions for conditions beyond those sampled in the training data set. A novel regularization technique with a closed-form solution based on the Gershgorin disk theorem is introduced to promote stable sFOM and OpInf models. We also provide a data-driven indicator for subdomain selection and ensure solution smoothness over the interface via a post-processing interpolation step. We evaluate the efficiency of the approach in terms of offline and online speedup through a quantitative, parametric computational cost analysis. We demonstrate the coupled OpInf-sFOM formulation for two test cases: a one-dimensional Burgers’ model for which accurate predictions beyond the span of the training snapshots are presented, and a two-dimensional parametric model for the Pine Island Glacier ice thickness dynamics, for which the OpInf-sFOM model achieves an average prediction error on the order of 1% with an online speedup factor of approximately 8$\times$ compared to the numerical simulation.

42 ENGINEERING↗

Proper orthogonal decomposition based reduced-order modeling of flux-Limited gray thermal radiation

Here, in this work, a proper orthogonal decomposition (POD) based reduced-order model (ROM) is developed to solve gray, flux-limited thermal radiation diffusion. We focus on the variable opacity radiation penetration benchmark posed by Olson, Auer, and Hall. The T -3 relationship for opacity in conjunction with high-temperature radiation penetrating an initially cold material produces a strong thermal radiation shock. This class of problems is particularly challenging for standard POD-based reduced-order modeling due to the nonlinearities presented by 1) the T 4 source term, and 2) flux-limited diffusion operator. To address these challenges and develop a cost competitive ROM, we employ a “hyper-reduction” technique through discrete empirical interpolation (DEIM) and allow for adaptive reduced-order projections through principal interval decomposition (PID). Performance of the proposed methodology is quantified by comparing the cost savings and accuracy relative to a full-order computation. Reference solutions and snapshot data are obtained through a full-order calculation performed by the University of Chicago maintained astrophysics code, FLASH. For consistency and potential extensibility, the developed ROM is also implemented in FLASH. We find that in the initialization regime, where the thermal radiation wave is initially created by the warming of the material, this class of problems is highly reducible and suitable for POD-based ROMs. However, the strong convective nature of the wave propagation regime is less reducible and more challenging to create an efficient ROM.

42 ENGINEERING↗

RadSim: Particle Transport Wrapper

RadSim is being developed to provide the capability to simulate radiation source emissions, interpolate results from radiation transport tools into a common format to prepare incident flux, and model radiation detector response. This software package includes wrapper API code which is utilized in the development of the second (transport) task of the RadSim project. This software package only contains tools to interface RadSim with radiation transport tools (GEANT4 and MCNP) and does not include any part of the transport source code itself. The users will need prior access to the transport tools (GEANT4 and MCNP), and can use this software package to interface with the transport tool of their choice. This software package takes the geometry file for a radiation transport problem and converts it into an input deck for the transport tools (GEANT4 and MCNP). Additionally, it also contains filters that convert the output of the transport tools to a common flux format.

Cheung, Hoi Sing↗

Parametric dynamic mode decomposition for reduced order modeling

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by singular value decomposition of the temporal data sets. For parameter-dependent models, as found in many multi-query applications such as uncertainty quantification or design optimization, the only parametric DMD technique developed was a stacked approach, with data sets at multiple parameter values were aggregated together, increasing the computational work needed to devise low-rank dynamical reduced-order models. Here in this paper, we present two novel approach to carry out parametric DMD: one based on the interpolation of the reduced-order DMD eigen-pair and the other based on the interpolation of the reduced DMD (Koopman) operator. Numerical results are presented for diffusion-dominated nonlinear dynamical problems, including a multiphysics radiative transfer example. All three parametric DMD approaches are compared.

97 MATHEMATICS AND COMPUTING↗

Scaled Vecchia Approximation for Fast Computer-Model Emulation

Many scientific phenomena are studied using computer experiments consisting of multiple runs of a computer model while varying the input settings. Gaussian processes (GPs) are a popular tool for the analysis of computer experiments, enabling interpolation between input settings, but direct GP inference is computationally infeasible for large datasets. We adapt and extend a powerful class of GP methods from spatial statistics to enable the scalable analysis and emulation of large computer experiments. Specifically, we apply Vecchia’s ordered conditional approximation in a transformed input space, with each input scaled according to how strongly it relates to the computer-model response. The scaling is learned from the data by estimating parameters in the GP covariance function using Fisher scoring. Our methods are highly scalable, enabling estimation, joint prediction, and simulation in near-linear time in the number of model runs. In several numerical examples, our approach substantially outperformed existing methods.

97 MATHEMATICS AND COMPUTING↗

Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders

Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the reduced-basis method, and (balanced) proper orthogonal decomposition (POD). Unfortunately, restricting the state to evolve in a linear subspace imposes a fundamental limitation to the accuracy of the resulting reduced-order model (ROM). In particular, linear-subspace ROMs can be expected to produce low-dimensional models with high accuracy only if the problem admits a fast decaying Kolmogorov n -width (e.g., diffusion-dominated problems). Unfortunately, many problems of interest exhibit a slowly decaying Kolmogorov n-width (e.g., advection-dominated problems). To address this, we propose a novel framework for projecting dynamical systems onto nonlinear manifolds using minimum-residual formulations at the time-continuous and time-discrete levels; the former leads to manifold Galerkin projection, while the latter leads to manifold least-squares Petrov–Galerkin (LSPG) projection. We perform analyses that provide insight into the relationship between these proposed approaches and classical linear-subspace reduced-order models; we also derive a posteriori discrete-time error bounds for the proposed approaches. In addition, we propose a computationally practical approach for computing the nonlinear manifold, which is based on convolutional autoencoders from deep learning. Lastly, we demonstrate the ability of the method to significantly outperform even the optimal linear-subspace ROM on benchmark advection-dominated problems, thereby demonstrating the method's ability to overcome the intrinsic n -width limitations of linear subspaces.

97 MATHEMATICS AND COMPUTING↗

MPAS-Seaice (v1.0.0): sea-ice dynamics on unstructured Voronoi meshes

Abstract. We present MPAS-Seaice, a sea-ice model which uses the Model for Prediction Across Scales (MPAS) framework and spherical centroidal Voronoi tessellation (SCVT) unstructured meshes. As well as SCVT meshes, MPAS-Seaice can run on the traditional quadrilateral grids used by sea-ice models such as CICE. The MPAS-Seaice velocity solver uses the elastic–viscous–plastic (EVP) rheology and the variational discretization of the internal stress divergence operator used by CICE, but adapted for the polygonal cells of MPAS meshes, or alternatively an integral (“finite-volume”) formulation of the stress divergence operator. An incremental remapping advection scheme is used for mass and tracer transport. We validate these formulations with idealized test cases, both planar and on the sphere. The variational scheme displays lower errors than the finite-volume formulation for the strain rate operator but higher errors for the stress divergence operator. The variational stress divergence operator displays increased errors around the pentagonal cells of a quasi-uniform mesh, which is ameliorated with an alternate formulation for the operator. MPAS-Seaice shares the sophisticated column physics and biogeochemistry of CICE and when used with quadrilateral meshes can reproduce the results of CICE. We have used global simulations with realistic forcing to validate MPAS-Seaice against similar simulations with CICE and against observations. We find very similar results compared to CICE, with differences explained by minor differences in implementation such as with interpolation between the primary and dual meshes at coastlines. We have assessed the computational performance of the model, which, because it is unstructured, runs with 70 % of the throughput of CICE for a comparison quadrilateral simulation. The SCVT meshes used by MPAS-Seaice allow removal of equatorial model cells and flexibility in domain decomposition, improving model performance. MPAS-Seaice is the current sea-ice component of the Energy Exascale Earth System Model (E3SM).

58 GEOSCIENCES↗

Finite spatial-grid effects in energy-conserving particle-in-cell algorithms

Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. We also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length. Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. Finally, we also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length.

97 MATHEMATICS AND COMPUTING↗

RadSim: Math, Utility & RTK

This package includes three parts, (1) gov.llnl.math, (2)gov.llnl.utility and (3)gov.llnl.rtk, which are utilized in the development of Radiation Detector Simulator (RadSim) project. RadSim is being developed to provide the capability to: (1) simulate radiation source emissions, (2) interpolate results from radiation transport tools into a common format to prepare incident flux, and (3) model radiation detector response to rapidly produce synthetic radiation measurement templates. RadSim is targeted for open-source release, which will enable researchers and industry partners to model gamma-ray detectors response to simulated flux from the transport tool of their choice. The techniques and implementation will be entirely transparent, which will allow for improvements and boutique modifications by future researchers beyond the lifespan of this specific project. The first tool of the package, gov.llnl.math, includes classes and functions to define and perform basic math operations. Some of the example features available in the package include defining statistical distributions and performing algebra and matrix operations, all of which are already accessible on publicly available software packages such as MATLAB and ROOT. The second package gov.llnl.utility includes tools commonly used to enable optimization and readability of various data structures such as Java lists and external xml files. Lastly, the gov.llnl.rtk package includes classes and functions to implement methods commonly used in radiation physics, such as data structures to represent and characterize photon spectra and tools to apply well-defined and published methods to calibrate a given spectra.

Cheung, Hoi Sing↗

RadSim: ENSDF, Xray and N42

This package includes three parts, (1) gov.bnl.nndc.ensdf, (2) gov.nist.xray and (3) gov.nist.physics.n42, which are utilized in the development of Radiation Detector Simulator (RadSim) project. RadSim is being developed to provide the capability to: (1) simulate radiation source emissions, (2) interpolate results from radiation transport tools into a common format to prepare incident flux, and (3) model radiation detector response to rapidly produce synthetic radiation measurement templates. RadSim is targeted for open-source release, which will enable researchers and industry partners to model gamma-ray detectors response to simulated flux from the transport tool of their choice. The first tool of the package, gov.bnl.nndc.ensdf, includes functionality to parse and split publicly available decay records in ENSDF format, and pull the relevant information from ENSDF libraries. The second tool, gov.nist.xray, provides Xray information using the public NIST database. Lastly, gov.nist.physics.n42, is a tool used to convert an N42 xml file into a Java object that can be interfaced within a Java program.

Hangal, DnaushA↗