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DOE OSTI2024

Optimal control of large quantum systems: assessing memory and runtime performance of GRAPE

Abstract Gradient Ascent Pulse Engineering (GRAPE) is a popular technique in quantum optimal control, and can be combined with automatic differentiation (AD) to facilitate on-the-fly evaluation of cost-function gradients. We illustrate that the convenience of AD comes at a significant memory cost due to the cumulative storage of a large number of states and propagators. For quantum systems of increasing Hilbert space size, this imposes a significant bottleneck. We revisit the strategy of hard-coding gradients in a scheme that fully avoids propagator storage and significantly reduces memory requirements. Separately, we present improvements to numerical state propagation to enhance runtime performance. We benchmark runtime and memory usage and compare this approach to AD-based implementations, with a focus on pushing towards larger Hilbert space sizes. The results confirm that the AD-free approach facilitates the application of optimal control for large quantum systems which would otherwise be difficult to tackle.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Cognitive simulation models for inertial confinement fusion: Combining simulation and experimental data

The design space for inertial confinement fusion (ICF) experiments is vast, and experiments are extremely expensive. Researchers rely heavily on computer simulations to explore the design space in search of high-performing implosions. However, ICF multiphysics codes must make simplifying assumptions, and thus deviate from experimental measurements for complex implosions. For more effective design and investigation, simulations require input from past experimental data to better predict future performance. In this work, we describe a cognitive simulation method for combining simulation and experimental data into a common, predictive model. This method leverages a machine learning technique called “transfer learning,” the process of taking a model trained to solve one task, and partially retraining it on a sparse dataset to solve a different, but related task. In the context of ICF design, neural network models are trained on large simulation databases and partially retrained on experimental data, producing models that are far more accurate than simulations alone. Here, we demonstrate improved model performance for a range of ICF experiments at the National Ignition Facility and predict the outcome of recent experiments with less than 10% error for several key observables. We discuss how the methods might be used to carry out a data-driven experimental campaign to optimize performance, illustrating the key product—models that become increasingly accurate as data are acquired.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Hydrogen Refueling Reference Station Lot Size Analysis for Urban Sites

Hydrogen Fueling Infrastructure Research and Station Technology (H2FIRST) is a project initiated by the DOE in 2015 and executed by Sandia National Laboratories and the National Renewable Energy Laboratory to address R&D barriers to the deployment of hydrogen fueling infrastructure. One key barrier to the deployment of fueling stations is the land area they require (i.e. "footprint"). Space is particularly a constraint in dense urban areas where hydrogen demand is high but space for fueling stations is limited. This work presents current fire code requirements that inform station footprint, then identifies and quantifies opportunities to reduce footprint without altering the safety profile of fueling stations. Opportunities analyzed include potential new methods of hydrogen delivery, as well as alternative placements of station technologies (i.e. rooftop/underground fuel storage). As interest in heavy-duty fueling stations and other markets for hydrogen grows, this study can inform techniques to reduce the footprint of heavy-duty stations as well. This work characterizes generic designs for stations with a capacity of 600 kg/day hydrogen dispensed and 4 dispenser hoses. Three base case designs (delivered gas, delivered liquid, and on-site electrolysis production) have been modified in 5 different ways to study the impacts of recently released fire code changes, colocation with gasoline refueling, alternate delivery assumptions, underground storage of hydrogen, and rooftop storage of hydrogen, resulting in a total of 32 different station designs. The footprints of the base case stations range from 13,000 to 21,000 ft 2 . A significant focus of this study is the NFPA 2 requirements, especially the prescribed setback distances for bulk gaseous or liquid hydrogen storage. While the prescribed distances are large in some cases, these setback distances are found to have a nuanced impact on station lot size; considerations of the delivery truck path, traffic flow, parking, and convenience store location are also important. Station designs that utilize underground and rooftop storage can reduce footprint but may not be practical or economical. For example, burying hydrogen storage tanks underground can reduce footprint, but the cost savings they enable depend on the cost of burial and the cost land. Siting and economic analysis of station lot sizes illustrate the benefit of smaller station footprints in the flexibility and cost savings they can provide. This study can be used as a reference that provides examples of the key design differences that fueling stations can incorporate, the approximate sizes of generic station lots, and considerations that might be unique to particular designs.

08 HYDROGEN↗

DOE OSTI2021

RMACXX: An Efficient High-Level C++ Interface over MPI-3 RMA

Parallel scientific applications can benefit from de- coupling communication and synchronization. One-sided pro- gramming abstractions, which separate communication from syn- chronization, have in fact served as a motivation for partitioned global address space (PGAS) models. However, the use of PGAS models in application codes in a manner that fully exploits the benefit of these programming models requires significant development effort. Meanwhile, a vast majority of scientific codes already use the Message Passing Interface (MPI) and need convenient features to support application-specific one-sided communication scenarios. MPI Remote Memory Access (RMA) can be employed for this purpose. MPI is a low-level API, however, and developing applications with MPI RMA requires programmers to be well versed in its nuances. We present RMACXX, a compact set of C++ bindings to MPI-3 RMA, to ease the use of MPI RMA. Unlike other PGAS models, which may have interoperability issues with MPI, RMACXX is written on top of MPI and uses the same runtime as MPI. The basic functionality of RMACXX adds only a relatively small number of extra instructions (about 20) to the critical communication path. Moreover, RMACXX provides an intuitive API for building a wide variety of scientific applications while enjoying performance matching handwritten MPI-3 RMA codes.

MPI-3 RMA, one-sided communication, PGAS, C++, exp↗

DOE OSTI2024

autoGEMM: Pushing the Limits of Irregular Matrix Multiplication on Arm Architectures

This paper presents an open-source library that pushes the limits of performance portability for irregular General Matrix Multiplication (GEMM) on the widely-used Arm architectures. Our library, autoGEMM, is designed to support a wide range of Arm processors: from edge devices to HPC-grade CPUs. autoGEMM generates optimized kernels for various hardware configurations by auto-combining fragments of autogenerated micro-kernels that employ hand-written optimizations to maximize computational efficiency. We optimize the kernel pipeline by tuning the register reuse and the data load/store overlapping. In addition, we use a dynamic tiling scheme to generate balanced tile shapes. Finally, we position autoGEMM on top of the TVM framework where our dynamic tiling scheme prunes the search space for TVM to identify the optimal combination of parameters for code optimization. Evaluations on five different classes of Arm chips demonstrate the advantages of autoGEMM. For small matrices, autoGEMM achieves 98% of peak and up to 2.0x speedup over state-of-the-art libraries such as LIBXSMM and LibShalom. For irregular matrices (i.e. tall skinny and long rectangles), autoGEMM is 1.3-2.0x faster than widely-used libraries such as OpenBLAS and Eigen. autoGEMM is publicly available at: https://github.com/wudu98/autoGEMM.

Wu, Du↗

DOE OSTI2023

Fierro

FIERRO is a parallel C++ code designed to simulate fluid mechanics, heat transfer, and solid mechanics in two- and three dimensional space. FIERRO is written to run on homogeneous (CPU) and heterogeneous (CPU+GPU) high performance computing machines. Fierro can aid a) modeling and design efforts that have historically relied on commercial implicit and explicit finite element codes, b) numerical methods research, c) manufacturing research, and d) computer science research. The code contains diverse numerical methods to solve the governing physics equations for both quasi-static and dynamic problems. Mathematical optimization solvers are coupled to the numerical methods to research topology and shape optimization that has application to additive manufacturing, and to create novel numerical approaches. Phase-field methods with micromechanical solvers are provided to simulate microstructure formation and evolution in manufacturing processes. The micromechanical solvers can also help research efforts create continuum-scale constitutive models for solids, as a function of the microstructure, in situ in a calculation or in a stand-alone manner. No physical data exists within the code.

Morgan, Nathaniel↗

DOE OSTI2022

Characterization of the Finite Element Computational Fluid Dynamics Capabilities in the Multiphysics Object Oriented Simulation Environment

We report the multiphysics object-oriented simulation environment (moose) is a code package that couples a variety of physics modules, allowing for highly accessible multiphysics simulations. The physics modules include a finite element Navier–Stokes (N–S) module that is designed to solve laminar fluid dynamics problems. The usage of this module in multiple recent studies coupled with the growing interest in moose for usage in nonlight water reactor safety studies by the Nuclear Regulatory Commission (NRC) prompted the authors to investigate the computational fluid dynamics capabilities of moose. A two-dimensional laminar flow past a circular cylinder scenario is simulated in the moose framework to investigate the effectiveness of the N–S module. Simulations assumed an unsteady laminar flow with a Reynolds number of 200. To verify the results from moose, similar simulations were conducted using the well-utilized simulation of turbulent flow in arbitrary regions—computational continuum mechanics C++ (star-ccm + ) finite volume code. Results from both codes are also compared to some results from literature. Velocity and pressure profiles of both transient simulations were compared. The numerical and input errors in moose are also visualized with contour plots to qualitatively understand the evolution of the errors across time and space. The comparisons between moose and star-ccm + showed nearly perfect agreement between the codes for velocity and pressure, especially after the development of the vortex street in later time-steps. The force coefficients showed excellent agreement after the development of the vortex street, but demonstrated notable discrepancies prior to the vortex street development, which is likely due to how each code simulated the approach to the vortex street in earlier time-steps.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

A Monte Carlo Laplace Transform Estimator for Radiation Transport

This work formulates and implements a Laplace transform estimator in a simple Monte Carlo radiation transport code. The estimator maps flux-based quantities of interest, like reaction rates, from a desired phase-space dimension to the complex Laplace domain. This on-the-fly Monte Carlo integration technique enables the spectral analysis of arbitrary nuclear systems via the Laplace transform. A simple code tests the estimator in neutron slowing-down problems across various infinite media, and the results compare well with Ganapol’s uninverted analytical solution of the neutron slowing-down equation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Fierro Version 2.x

FIERRO is a parallel C++ code designed to simulate fluid mechanics, heat transfer, and solid mechanics in two- and three-dimensional space. FIERRO is written to run on homogeneous (CPU) and heterogeneous (CPU+GPU) high performance computing machines. Fierro can aid a) modeling and design efforts that have historically relied on commercial implicit and explicit finite element codes, b) numerical methods research, c) manufacturing research, and d) computer science research. The code contains diverse numerical methods to solve the governing physics equations for both quasi-static and dynamic problems. Mathematical optimization solvers are coupled to the numerical methods to research topology and shape optimization that has application to additive manufacturing, and to create novel numerical approaches. Phase-field methods with micromechanical solvers are provided to simulate microstructure formation and evolution in manufacturing processes. The micromechanical solvers can also help research efforts create continuum-scale constitutive models for solids, as a function of the microstructure, in situ in a calculation or in a stand-alone manner. No physical data exists within the code.

Morgan, Nathaniel↗

DOE OSTI2022

Finite orbit width effects in large aspect ratio stellarators

New orbit-averaged equations for low collisionality neoclassical fluxes in large aspect ratio stellarators with mirror ratios close to unity are derived. The equations retain finite orbit width effects by employing the second adiabatic invariant $J$ as a velocity-space coordinate and they have been implemented in the orbit-averaged neoclassical code KNOSOS (Velasco et al. , J. Comput. Phys. , vol. 418, 2020, 109512; Velasco et al. , Nucl. Fusion , vol. 61, 2021, 116013). The equations are used to study the $1/\nu$ regime and the lower collisionality regimes. For generic large aspect ratio stellarators with mirror ratios close to unity, as the collision frequency decreases, the $1/\nu$ regime transitions directly into the $\nu$ regime, without passing through a $\sqrt {\nu }$ regime. An explicit formula for the neoclassical fluxes in the $\nu$ regime is obtained. The formula includes the effect of particles that transition between different types of wells. While these transitions produce stochastic scattering independent of the value of the collision frequency in velocity space, the diffusion in real space remains proportional to the collision frequency. The $\sqrt {\nu }$ regime is only recovered in large aspect ratio stellarators close to omnigeneity: large aspect ratio stellarators with large mirror ratios and optimized large aspect ratio stellarators with mirror ratios close to unity. Neoclassical transport in large aspect ratio stellarators with large mirror ratios can be calculated with the orbit-averaged equations derived by Calvo et al. ( Plasma Phys. Control. Fusion , vol. 59, 2017, 055014). In these stellarators, the $\sqrt {\nu }$ regime exists in the collisionality interval $(a/R) \ln (R/a) \ll \nu _{ii} R a/\rho _i v_{ti} \ll R/a$ . In optimized large aspect ratio stellarators with mirror ratios close to unity, the $\sqrt {\nu }$ regime occurs in an interval of collisionality that depends on the deviation from omnigeneity $\delta$ : $\delta ^{2} |\ln \delta | \ll \nu _{ii} R a/\rho _i v_{ti} \ll 1$ . Here, $\nu _{ii}$ is the ion–ion collision frequency, $\rho _i$ and $v_{ti}$ are the ion gyroradius and thermal speed, and $a$ and $R$ are the minor and major radii.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Fully Homomorphic Encryption

This code implements a Fully Homomorphic Encryption (FHE) system, enabling secure computation on encrypted data without requiring decryption. It supports encryption, decryption, and homomorphic operations like matrix multiplication and addition. This code is adaptable for integrating FHE into linear-time invariant (LTI) systems, including digital control and filtering. With proper configuration from subject matter expertise, encrypted system parameters and signals can be manipulated to perform tasks like state updates, output calculations, and convolution in the encrypted domain. By preserving the structure of LTI systems while ensuring privacy, the framework facilitates secure applications in areas such as autonomous systems, signal processing, and industrial automation. The code initializes the encryption system using parameters provided in the env dictionary. These parameters include the ciphertext modulus, key dimension, plaintext fixed-point scaling factor, and noise bound. During initialization, a secret key is generated, which is essential for encrypting and decrypting data securely. The modular design allows users to tailor these parameters to specific use cases or security requirements. The code implements multiple cryptographic schemes. The learning with errors (LWE) encryption method encodes cleartext message to their plaintext fixed-point representation then encrypted into ciphertext space with additive noise. This noise ensures the security of the scheme, relying on the computational hardness of the LWE problem. The code also includes the Gentry-Sahai-Waters (GSW) scheme based off the LWE problem. Homomorphic matrix multiplication is performed between the LWE and GSW to encrypted data. This is achieved using a decomposition function on the LWE ciphertext during the multiplication operation. For higher-dimensional data, the code includes a method to encrypt entire matrices (GSWMat) using GSW encryption. These encrypted matrices can then be used for homomorphic matrix multiplications (MatMult). The decryption function uses the secret key to recover the original plaintext, removing the added noise and scaling that was originally applied during encryption.

Lois, Roberts [Idaho National Laboratory (INL), Id↗

DOE OSTI2022

Preconditioned least‐squares Petrov–Galerkin reduced order models

Abstract In this article, we introduce a methodology for improving the accuracy and efficiency of reduced order models (ROMs) constructed using the least‐squares Petrov–Galerkin (LSPG) projection method through the introduction of preconditioning. Unlike prior related work, which focuses on preconditioning the linear systems arising within the ROM numerical solution procedure to improve linear solver performance, our approach leverages a preconditioning matrix directly within the minimization problem underlying the LSPG formulation. Applying preconditioning in this way has the potential to improve ROM accuracy for several reasons. First, preconditioning the LSPG formulation changes the norm defining the residual minimization, which can improve the residual‐based stability constant bounding the ROM solution's error. The incorporation of a preconditioner into the LSPG formulation can have the additional effect of scaling the components of the residual being minimized to make them roughly of the same magnitude, which can be beneficial when applying the LSPG method to problems with disparate scales (e.g., dimensional equations, multi‐physics problems). Importantly, we demonstrate that an “ideal preconditioned” LSPG ROM (a ROM in which the preconditioner is the inverse of the Jacobian of its corresponding full order model) emulates projection of the full order model solution increment onto the reduced basis. This quantity defines a lower bound on the error of a ROM solution for a given reduced basis. By designing preconditioners that approximate the Jacobian inverse—as is common in designing preconditioners for solving linear systems—it is possible to obtain a ROM whose error approaches this lower bound. The proposed approach is evaluated on several mechanical and thermo‐mechanical problems implemented within the Albany HPC code and run in the predictive regime, with prediction across material parameter space. We demonstrate numerically that the introduction of simple Jacobi, Gauss‐Seidel, and ILU preconditioners into the proper orthogonal decomposition/LSPG formulation reduces significantly the ROM solution error, the reduced Jacobian condition number, the number of nonlinear iterations required to reach convergence, and the wall time (thereby improving efficiency). Moreover, our numerical results reveal that the introduction of preconditioning can deliver a robust and accurate solution for test cases in which the unpreconditioned LSPG method fails to converge.

Lindsay, Payton↗

DOE OSTI2021

Development of a reduced model for energetic particle transport by sawteeth in tokamaks

We report that the sawtooth instability is known for inducing transport and loss of energetic particles (EPs), and for generating seed magnetic islands that can trigger tearing modes. Both effects degrade the overall plasma performance. Several theories and numerical models have been previously developed to quantify the expected EP transport caused by sawteeth, with various degrees of sophistication to differentiate the response of EPs at different energies and on different orbits (e.g. passing vs. trapped), although the analysis is frequently limited to a single time slice during a tokamak discharge. This work describes the development and initial benchmark of a framework that enables a reduced model for EP transport by sawteeth retaining the full EP phase-space information. The model, implemented in the ORBIT hamiltonian particle-following code, can be used either as a standalone post-processor taking input data from codes such as TRANSP, or as a pre-processor to compute transport coefficients that can be fed back to TRANSP for time-dependent simulations including the effects of sawteeth on EPs. The advantage of the latter approach is that the evolution of the EP distribution can be simulated quantitatively for sawtoothing discharges, thus enabling a more accurate modeling of sources, sinks and overall transport properties of EP and thermal plasma species for comprehensive physics studies that require detailed information of the fast-ion distribution function and its evolution over time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Neural architecture codesign for fast physics applications

We develop a pipeline to streamline neural architecture codesign for physics applications to reduce the need for ML expertise when designing models for novel tasks. Our method employs neural architecture search and network compression in a two-stage approach to discover hardware efficient models. This approach consists of a global search stage that explores a wide range of architectures while considering hardware constraints, followed by a local search stage that fine-tunes and compresses the most promising candidates. We exceed performance on various tasks and show further speedup through model compression techniques such as quantization-aware-training and neural network pruning. We synthesize the optimal models to high level synthesis code for FPGA deployment with the hls4ml library. Additionally, our hierarchical search space provides greater flexibility in optimization, which can easily extend to other tasks and domains. We demonstrate this with two case studies: Bragg peak finding in materials science and jet classification in high energy physics, achieving models with improved accuracy, smaller latencies, or reduced resource utilization relative to the baseline models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Time-dependent variational principle for mixed matrix product states in the thermodynamic limit

Here, we describe a time evolution algorithm for quantum spin chains whose Hamiltonians are composed of an infinite uniform left and right bulk part, and an arbitrary finite region in between. The left and right bulk parts are allowed to be different from each other. The algorithm is based on the time-dependent variational principle (TDVP) of matrix product states. It is inversion-free and very simple to adapt from an existing TDVP code for finite systems. The importance of working in the projective Hilbert space is highlighted. We study the quantum Ising model as a benchmark and an illustrative example. The spread of information after a local quench is studied in both the ballistic and the diffusive case. We also offer a derivation of TDVP directly from symplectic geometry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Orthogonal spatial coding with stimulated parametric down-conversion

Orthogonal optical coding is widely used in classical multi-user communication networks. Using the phase conjugation property of stimulated parametric down-conversion, we extend the current time-domain orthogonal optical coding scheme to the spatial domain to encode and decode image information. In this process, the idler beam inherits the complex conjugate of the field information encoded in the seed beam. An encoding phase mask introduced onto the input seed beam blurs the image transferred to the idler. The original image is restored by passing the coded transferred image through a corrective phase mask placed in the momentum space of the idler beam. We expect that this scheme can also inspire new techniques in secure image transmission, aberration cancellation, and frequency conversion imaging.

Xu, Yang↗

DOE OSTI2021

Simulation Studies on the Interactions of Electron Beam with Wastewater

The manufactured chemical pollutants, like 1,4 dioxane and PFAS (per- and polyfluroralkyl substances), found in the underground water and/or drinking water are challenging to be removed or biodegraded. Energetic electrons are capable of mediating and removing them. This paper utilizes FLUKA code to evaluate the beam-wastewater interaction effects with different energy, space and divergence distributions of the electron beam. With 8 MeV average energy, the electron beam exits from a 0.0127 cm thick titanium window, travels through a 4.3 cm distance air and a second 0.0127 cm thick stainless water container window with 2.43 cm radius, and finally is injected into the water area, where the volume of water is around 75 cubic cm. The distribution parameters of the electron beam are from the GPT (General Particle Tracer) simulations for UITF (Upgraded Injector Test Facility) in Jefferson lab. By varying the distributions, several measurements including the dose (or energy deposition) distribution, electron fluence, photon fluence are scored and compared. Taking the comparisons into consideration, this paper is aiming to find better electron beams for the wastewater irradiation.

Li, X.↗

DOE OSTI2021

Simulation Studies on the Interactions of Electron Beam with Wastewater

Li, X.↗