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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

New efforts in improving numerical aspects of atmospheric physics parameterizations

This is an invited article for GEWEX Quarterly, the newsletter of the Global Energy and Water Exchanges (GEWEX) program which is a core project of the World Climate Research Programme (https://www.gewex.org/resources/gewex-news/). The article introduces recent research results and ongoing activities being carried out in a SciDAC project funded by DOE that focuses on identifying and addressing numerical issues in physics parameterizations in global atmospheric general circulation models.

global atmospheric model↗
DOE OSTI2020

Use of Micro-Gravity Sensors for External Fluid Level Monitoring in Waste and Nuclear Related Applications - 20315

There are a number of applications in nuclear energy and hazardous waste disposal that require monitoring of fluids under extreme environments, including high levels of temperature, pressure, toxicity and radioactivity. Many of these applications will benefit from a monitoring technique that is external and non-invasive. Currently the sensors used are invasive, must reside inside the pressurized vessels and must penetrate the vessel walls, which can create a weakness in the vessel. Additionally, instruments that are used inside such containers must be exceptionally hardened to the environment. Information Systems Laboratories (ISL) has developed an external mass (gravimetric) measuring technique for monitoring nuclear coolant in Small Modular Reactors (SMRs), which will also work for measuring fluid levels in waste tanks, that avoids the problems inherent in invasive sensors. It utilizes a COTS gravitational sensor of unprecedented accuracy, leveraged via proper sensor placement geometry, to detect fluid changes of small amplitude from an outside position, obviating the need to penetrate the vessel. The technique is called Gravisense{sup TM}. ISL has proven via simulation and experiment that this concept can be usefully applied to monitoring fluid levels in both nuclear reactors and large waste tanks. Numerical simulation algorithms were developed to calculate the gravity effect of small changes in water level, which were verified by experiments at the NIST Physical Simulator facility at the Oregon State University. The measured ultralow noise levels of the superconducting gravimeter type which utilizes a Niobium sphere suspended in a magnetic field to attain its phenomenal accuracy, demonstrated that fluid levels in SMRs can be measured at least to within 3 cm. Furthermore, the method can distinguish between a contained leak (from reactor to containment vessel) from an external leak (from reactor to outside of containment). Additionally, simulations of waste canisters that hold spent fuel rods show that the fluid level measuring accuracy can potentially do better than 1 cm accuracy by measuring from below the vessel, and judicious placement of sensors on top of large waste tanks can potentially achieve a very impressive 2 mm measurement accuracy. These encouraging results prove that the Gravisense{sup TM} technique for fluid determination can be very useful in nuclear energy generation, testing, and research, as well as in waste monitoring situations that are difficult to monitor via traditional sensing technology. We believe that the next step should be to test the technique on canisters of the type that are currently storing waste in various DOE locations. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Initial exploration of a novel transient arrest system involving fuel heating

A preliminary analysis on a novel accident response system to diminish the severity of super- critical transients was conducted. The novel accident response system, called the instant shock arrest system, involves using electricity to heat the nuclear fuel at the onset of a large accidental reactivity insertion. This system is specifically designed for reactors with metallic fuel, such that the fuel is capable of conducting electricity, and being resistively heated. A reactor dynamics model of the advanced test reactor was created using the point kinetics equations and a linear reactivity feedback model to simulate how the system would effect the maximum fuel temperatures experienced during the transient. Transients with the instant shock arrest system were compared to those without it. It was found that the instant shock arrest system initially heated the fuel more than the unaffected transient but the negative reactivity inserted from such heating was enough to lower the maximum fuel temperature experienced during the transient. After simulating six different accident scenarios with reactivity insertions ranging from 0.5 to 1.3 dollar, it was found that an optimal system response could reduce peak fuel temperatures during the transient by 3.5% to 5%. Furthermore, discussion was given on how the optimal system response could be obtained using relatively simple numerical optimization algorithms due to the smoothness of the optimization problem. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

INITIAL EXPLORATION OF A NOVEL TRANSIENT ARREST SYSTEM INVOLVING FUEL HEATING (Presentation)

A preliminary analysis on a novel accident response system to diminish the severity of supercritical transients was conducted. The novel accident response system, called the instant shock arrest system, involves using electricity to heat the nuclear fuel at the onset of a large accidental reactivity insertion. This system is specifically designed for reactors with metallic fuel, such that the fuel is capable of conducting electricity, and being resistively heated. A reactor dynamics model of the advanced test reactor was created using the point kinetics equations and a linear reactivity feedback model to simulate how the system would effect the maximum fuel temperatures experienced during the transient. Transients with the instant shock arrest system were compare to those without it. It was found that the instant shock arrest system initially heated the fuel more than the unaffected transient but the negative reactivity inserted from such heating was enough to lower the maximum fuel temperature experienced during the transient. After simulating six different accident scenarios with reactivity insertions ranging from 0.5 \$ to 1.3 \$, it was found that the an optimal system response could reduce peak fuel temperatures during the transient by 3.5% to 5%. Furthermore, discussion was given on how the optimal system response could be obtained using relatively simple numerical optimization algorithms due to the smoothness of the optimization problem.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

A Model Predictive Control to Improve Grid Resilience

The following article details a model predictive control (MPC) to improve grid resilience when faced with variable generation resources. This topic is of significant interest to utility power systems where distributed intermittent energy sources will increase significantly and be relied on for electric grid ancillary services. Previous work on MPCs has focused on narrowly targeted control applications such as improving electric vehicle (EV) charging infrastructure or reducing the cost of integrating Energy Storage Systems (ESSs) into the grid. In contrast, this article develops a comprehensive treatment of the construction of an MPC tailored to electric grids and then applies it integration of intermittent energy resources. To accomplish this, the following article includes a description of a reduced order model (ROM) of an electric power grid based on a circuit model, an optimization formulation that describes the MPC, a collocation method for solving linear time-dependent differential algebraic equations (DAEs) that result from the ROM, and an overall strategy for iteratively refining the behavior of the MPC. Next, the algorithm is validated using two separate numerical experiments. First, the algorithm is compared to an existing MPC code and the results are verified by a numerically precise simulation. It is shown that this algorithm produces a control comparable to existing algorithms and the behavior of the control carefully respects the bounds specified. Second, the MPC is applied to a small nine bus system that contains a mix of turbine-spinning-machine-based and intermittent generation in order to demonstrate the algorithm’s utility for resource planning and control of intermittent resources. This study demonstrates how the MPC can be tuned to change the behavior of the control, which can then assist with the integration of intermittent resources into the grid. The emphasis throughout the paper is to provide systematic treatment of the topic and produce a novel nonlinear control compatible design framework applicable to electric grids and the control of variable resources. This differs from the more targeted application-based focus in most presentations.

microgrid↗
DOE OSTI2020

Efficient Fourier transforms for transverse momentum dependent distributions

Hadron production at low transverse momenta in semi-inclusive deep inelastic scattering can be described by transverse momentum dependent (TMD) factorization. This formalism has also been widely used to study the Drell-Yan process and back-to-back hadron pair production in $e^+e^-$ collisions. These processes are the main ones for extractions of TMD parton distribution functions and TMD fragmentation functions, which encode important information about nucleon structure and hadronization. One of the most widely used TMD factorization formalism in phenomenology formulates TMD observables in coordinate $b_\perp$-space, the conjugate space of the transverse momentum. The Fourier transform from $b_\perp$-space back into transverse momentum space is sufficiently complicated due to oscillatory integrands that it requires a careful and computationally intensive numerical treatment in order to avoid potentially large numerical errors. Within the TMD formalism, the azimuthal angular dependence is analytically integrated and the two-dimensional $b_\perp$ integration reduces to a one-dimensional integration over the magnitude $b_\perp$. In this paper we develop a fast numerical Hankel transform algorithm for such a $b_\perp$-integration that improves the numerical accuracy of TMD calculations in all standard processes. Libraries for this algorithm are implemented in Python 2.7 and 3, C++, as well as FORTRAN77. All packages are made available open source.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Quarter 4 Report: Report on Final Findings and Opportunities for Future Work in the Use of Mixed Precision in Iterative Solvers

The fourth quarter of the project was spent developing an error analysis of the s-step Lanczos and CG algorithms. Our theoretical bounds and numerical experiments show that the numerical behavior of the algorithm can be significantly improved by using extra precision in a small part of the computation related to the computation and application of the Gram matrix. We have published a technical report which includes all steps of the analysis [8]; a shortened version for journal submission is in preparation. We plan to submit this paper in the following weeks. Activities related to this also include a collaboration with Ichitaro Yamazaki on gathering performance results for these new mixed precision s-step Krylov subspace methods using single/double precision on GPUs. Namely, we would like to obtain performance results that show that the performance overhead of using double the working precision in these select computations is minimal. Other activities include attending biweekly xSDK meetings and presenting a pitch talk on this work to the group on February 25, 2021. In the remainder of the document, we summarize our findings on the potential for mixed precision in classical Krylov subspace methods and s-step Krylov subspace methods, as well as key opportunities for future work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Gauge constrained algorithm of variational discrete action theory at N = 3 for the multiorbital Hubbard model

The recently developed variational discrete action theory (VDAT) provides a systematic variational approach to the ground state of the quantum many-body problem, where the quality of the solution is controlled by an integer N, and increasing N monotonically approaches the exact solution. VDAT can be exactly evaluated in the d = ∞ multiorbital Hubbard model using the self-consistent canonical discrete action theory (SCDA), which requires a self-consistency condition for the integer time Green's functions. Previous work demonstrates that N = 3 accurately captures multiorbital Mott/Hund physics at a cost similar to the Gutzwiller approximation. Here we employ a gauge constraint to automatically satisfy the self-consistency condition of the SCDA at N = 3, yielding an even more efficient algorithm with enhanced numerical stability. We derive closed form expressions of the gauge constrained algorithm for the multiorbital Hubbard model with general density-density interactions, allowing VDAT at N = 3 to be straightforwardly applied to the seven-orbital Hubbard model. We present results and a performance analysis using N = 2 and N = 3 for the SU⁡(2⁢N orb ) Hubbard model in d = ∞ with N orb = 2–8, and compare to numerically exact dynamical mean-field theory solutions where available. Finally, the developments in this work will greatly facilitate the application of VDAT at N = 3 to strongly correlated electron materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Line curvature algorithm in laser ektacytometry of red blood cells

The iso-intensity line curvature algorithm in laser ektacytometry of red blood cells is investigated by numerical simulation. The algorithm is designed to measure the average deformability, as well as the width and asymmetry of the red blood cell deformability distribution in a blood sample under study. The accuracy and scope of the algorithm are determined. Using a bimodal ensemble as an example, the possibility of determining the fraction of weakly deformable red blood cells in a blood sample by laser ektacytometry is demonstrated. (laser medicine)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Dimensionally Aligned Signal Projection Algorithms Library

Dimensionally aligned signal projection (DASP) algorithms are used to analyze fast Fourier transforms (FFTs) and generate visualizations that help focus on the harmonics for specific signals. At a high level, these algorithms extract the FFT segments around each harmonic frequency center, and then align them in equally sized arrays ordered by increasing distance from the base frequency. This allows for a focused view of the harmonic frequencies, which, among other use cases, can enable machine learning algorithms to more easily identify salient patterns. This work seeks to provide an effective open-source implementation of the DASP algorithms proposed by Vann et al. (2018) as well as functionality to help explore and test how these algorithms work with an interactive dashboard and signal-generation tool. The DASP library is implemented in Python and contains four types of algorithms for implementing these feature engineering techniques: fixed harmonically aligned signal projection (HASP), decimating HASP, interpolating HASP, and frequency aligned signal projection (FASP). Each algorithm returns a numerical array, which can be visualized as an image. The HASP algorithms are variations of the algorithms originally presented by Vann et al. (2018). For consistency, FASP, which is the terminology used for the short-time Fourier transform (STFT), has been implemented as part of the library to provide a similar interface to the STFT of the raw signal. Additionally, the library contains an algorithm to generate artificial signals with basic customizations such as the base frequency, sample rate, duration, number of harmonics, noise, and number of signals. Finally, the library provides multiple interactive visualizations, each of which is implemented using IPyWidgets and works in a Jupyter environment. A dashboard-style visualization is provided, which contains some common signal-processing visual components (signal, FFT, spectogram) updating in unison with the HASP functions (see Figure 1 below). Separate from the dashboard, an independent visualization is provided for each of the DASP algorithms as well as for the artifical signal generator. These visualizations are included in the library to aid in developing an intuitive understanding how the algorithms are affected by different input signals and parameter selections.

harmonics↗
DOE OSTI2021

Universal Compiling and (No-)Free-Lunch Theorems for Continuous-Variable Quantum Learning

Quantum compiling, where a parameterized quantum circuit is trained to learn a target unitary, is an important primitive for quantum computing that can be used as a subroutine to obtain optimal circuits or as a tomographic tool to study the dynamics of an experimental system. While much attention has been paid to quantum compiling on discrete-variable hardware, less has been paid to compiling in the continuous-variable paradigm. Here we motivate several, closely related, short-depth continuous-variable algorithms for quantum compilation. We analyze the trainability of our proposed cost functions and numerically demonstrate our algorithms by learning arbitrary Gaussian operations and Kerr nonlinearities. We further make connections between this framework and quantum learning theory in the continuous-variable setting by deriving no-free-lunch theorems. These generalization bounds demonstrate a linear resource reduction for learning Gaussian unitaries using entangled coherent-Fock states and an exponential resource reduction for learning arbitrary unitaries using two-mode-squeezed states.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

ReMU: regional minimal updating for model-based derivative-free optimization

Derivative-free optimization (DFO) problems are optimization problems where derivative information is unavailable or extremely difficult to obtain. Model-based DFO solvers have been applied extensively in scientific computing. Powell's NEWUOA (2004) [Powell, The NEWUOA software for unconstrained optimization without derivatives, in Large-Scale Nonlinear Optimization, Nonconvex Optimization and its Applications Vol. 83, G. Di Pillo and M. Roma, eds., Springer, 2006, pp. 255–297] and Wild's POUNDerS (2014) [Wild, Solving derivative-free nonlinear least squares problems with POUNDERS, in Advances and Trends in Optimization with Engineering Applications, T. Terlaky, M.F. Anjos, and S. Ahmed, eds., SIAM, 2017, pp. 529–540] explore the numerical power of the minimal norm Hessian (MNH) model for DFO and contributed to the open discussion on building better models with fewer data to achieve faster numerical convergence. Another decade later, we propose the regional minimal updating (ReMU) models, and extend the previous models into a broader class, including the H 2 norm models [Xie and Yuan, Least H 2 norm updating of quadratic interpolation models for derivative-free trust-region algorithms, IMA J. Numer. Anal. 46 (2025), pp. 21–50]. This paper shows motivation behind ReMU models, computational details, theoretical and numerical results on particular extreme points and the barycentre of ReMU's weight coefficient region, and the associated KKT matrix error and distance. Novel metrics, such as the truncated Newton step error, are proposed to numerically understand the new models' properties. A new algorithmic strategy, based on iteratively adjusting the ReMU model type, is also proposed, and shows numerical advantages by combining and switching between the barycentric model and the classic least Frobenius norm model in an online fashion.

derivative-free trust-region methods↗
DOE OSTI2022

A nonsmooth nonconvex optimization algorithm for two-stage optimization problems

An optimization algorithm for a group of nonsmooth nonconvex problems inspired by two-stage stochastic programming problems is proposed. The main challenges for these problems include (1) the problems lack the popular lower-type properties such as prox-regularity assumed in many nonsmooth nonconvex optimization algorithms, (2) the objective can not be analytically expressed and (3) the evaluation of function values and subgradients are computationally expensive. To address these challenges, this report first examines the properties that exist in many two-stage problems, specifically upper-C 2 objectives. Then, we show that quadratic penalty method for securityconstrained alternating current optimal power flow (SCACOPF) contingency problems can make the contingency solution functions upper-C 2 . Based on these observations, a simplified bundle algorithm that bears similarity to sequential quadratic programming (SQP) method is proposed. It is more efficient in implementation and computation compared to conventional bundle methods. Global convergence analysis of the algorithm is presented under novel and reasonable assumptions. The proposed algorithm therefore fills the gap of theoretical convergence for smoothed SCACOPF problems. The inconsistency that might arise in our treatment of the constraints are addressed through a penalty algorithm whose convergence analysis is also provided. Finally, theoretical capabilities and numerical performance of the algorithm are demonstrated through numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Evaluation of KDP Estimation Algorithm Performance in Rain Using a Known-Truth Framework

Accurate estimation of specific differential phase ( K DP ) is necessary for rain rate estimation, attenuation correction, and hydrometeor classification algorithms. There are numerous published methods to process polarimetric radar observations of propagation differential phase shift (Φ DP ) and estimate K DP , but the corresponding K DP estimate uncertainty is unquantified. This study provides guidance on how commonly used K DP estimation algorithms perform in various environments. Here, we create numerous synthetic (“true”) K DP profiles, integrate over them to obtain “smoothed” Φ DP , and then add noise typical of S-band operational weather radar measurements. Each algorithm is applied to our noisy Φ DP profiles and compared to the true K DP profile such that the errors and uncertainty are quantified. The synthetic K DP profiles are Gaussian in shape, which allows systematic variations in their magnitude and width to determine how each algorithm performs in smooth, slowly changing K DP profiles, as well as steep profiles. Results demonstrate that algorithm performance is dependent on the Φ DP field received. These results are further supported by an error analysis of each algorithm for two more complicated synthetic K DP profiles. Some K DP algorithms allow users to change various tuning parameters; a subset of these tuning parameters is tested to provide guidance on how changing these parameters impacts algorithm performance. We then provide evidence that our known-truth framework provides insight into algorithm performance in observed data through two case studies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

The Potential Benefits of Handling Mixture Statistics via a Bi-Gaussian EnKF: Tests With All-Sky Satellite Infrared Radiances

The meteorological characteristics of cloudy atmospheric columns can be very different from their clear counterparts. Thus, when a forecast ensemble is uncertain about the presence/absence of clouds at a specific atmospheric column (i.e., some members are clear while others are cloudy), that column's ensemble statistics will contain a mixture of clear and cloudy statistics. Such mixtures are inconsistent with the ensemble data assimilation algorithms currently used in numerical weather prediction. Hence, ensemble data assimilation algorithms that can handle such mixtures can potentially outperform currently used algorithms. In this study, we demonstrate the potential benefits of addressing such mixtures through a bi-Gaussian extension of the ensemble Kalman filter (BGEnKF). The BGEnKF is compared against the commonly used ensemble Kalman filter (EnKF) using perfect model observing system simulated experiments (OSSEs) with a realistic weather model (the Weather Research and Forecast model). Synthetic all-sky infrared radiance observations are assimilated in this study. In these OSSEs, the BGEnKF outperforms the EnKF in terms of the horizontal wind components, temperature, specific humidity, and simulated upper tropospheric water vapor channel infrared brightness temperatures. This study is one of the first to demonstrate the potential of a Gaussian mixture model EnKF with a realistic weather model. Our results thus motivate future research toward improving numerical Earth system predictions though explicitly handling mixture statistics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Reproducibility in G 0 W 0 calculations for solids

Ab initio many-body perturbation theory within the GW approximation is a Green's function formalism widely used in the calculation of quasiparticle excitation energies of solids. In what has become an increasingly standard approach, Kohn–Sham eigenenergies, generated from a DFT calculation with a strategically-chosen exchange–correlation functional “starting point”, are used to construct G and W, and then perturbatively corrected by the resultant GW self-energy. In practice, there are several ways to construct the GW self-energy, and these can lead to variations in predicted quasiparticle energies. For example, for ZnO and TiO 2 , the GW fundamental gaps reported in the literature can vary by more than 1 eV depending on the GW code used. In this work, we calculate and analyze GW quasiparticle (QP) energies of these and other systems with three different GW codes: BERKELEYGW, ABINIT and YAMBO. Through a systematic analysis of the GW implementation of these three codes, we identify the primary origin of major discrepancies between codes reported in prior literature to be the different implementations the Coulomb divergence in the Fock exchange term and the frequency integration scheme of the GW self-energy. We then eliminate these discrepancies by using common numerical methods and algorithms, demonstrating that the same quasiparticle energies for a given material can be obtained with different codes, within numerical differences ascribable to the technical details of the underling implementations. This work will be important for users and developers in assessing the precision of future GW applications and methods.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Report on local data recovery approaches suitable for weather and climate prediction (Deliverable 1.3) (V.1.0)

Numerical weather and climate prediction rates as one of the scientific applications whose accuracy improvements greatly depend on the growth of the available computing power. As the number of cores in top computing facilities pushes into the millions, increasing average frequency of hardware and software failures forces users to review their algorithms and systems in order to protect simulations from breakdown. This report surveys approaches for fault-tolerance in numerical algorithms and system resilience in parallel simulations from the perspective of numerical weather and climate prediction systems. A selection of existing strategies is analyzed, featuring interpolation-restart and compressed checkpointing for the numerics, in-memory checkpointing, user-level failure mitigation-based and backup-based methods for the systems. Numerical examples showcase the performance of the techniques in addressing faults, with particular emphasis on iterative solvers for linear systems, a staple of atmospheric fluid flow solvers. The potential impact of these strategies is discussed in relation to current development of numerical weather prediction algorithms and systems towards the exascale. Trade-offs between performance, efficiency and effectiveness of resiliency strategies are analyzed and some recommendations outlined for future developments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Composite Qdrift-product formulas for quantum and classical simulations in real and imaginary time

Recent study has shown that it can be advantageous to implement a composite channel that partitions the Hamiltonian H for a given simulation problem into subsets A and B such that H = A + B , where the terms in A are simulated with a Trotter-Suzuki channel and the B terms are randomly sampled via the Qdrift algorithm. Here we extend Qdrift and composite product formulas to imaginary time, formulating candidate classical algorithms for quantum Monte Carlo calculations. We upper bound the induced Schatten- 1 → 1 norm on both imaginary-time Qdrift and composite channels. Another recent result demonstrated that simulations of lattice Hamiltonians containing geometrically local interactions can be improved using a Lieb-Robinson argument to decompose H into subsets that contain only terms supported on that subset of the lattice. Here, we provide a quantum algorithm by unifying this result with the composite approach into “local composite channels” and we upper bound the diamond distance. We provide exact numerical simulations of algorithmic cost by counting the number of gates of the form e − i H j t and e − H j β to meet a certain error tolerance ε . In doing so, we optimize the partitioning into sets A and B using gradient boosted tree models from machine learning. These numerical studies are important given that product formulas have been historically known to outperform analytic upper bounds. We show constant factor advantages for a variety of interesting Hamiltonians, the maximum of which is a ≈ 20 -fold speedup that occurs in the simulation of Jellium. Published by the American Physical Society 2024

Pocrnic, Matthew (ORCID:0000000203089376)↗