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At least 919 records · Page 51

Quantum approximate multi-objective optimization

The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, that is, the set of all Pareto-optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. Here we use a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum-cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with matrix product state numerical simulation, and show its potential to outperform classical approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Smoothed aggregation for difficult stretched mesh and coefficient variation problems

Abstract Four adaptations of the smoothed aggregation algebraic multigrid (SA‐AMG) method are proposed with an eye toward improving the convergence and robustness of the solver in situations when the discretization matrix contains many weak connections. These weak connections can cause higher than expected levels of fill‐in within the coarse discretization matrices and can also give rise to suboptimal smoothing within the prolongator smoothing phase. These smoothing drawbacks are due to the relatively small size of some diagonal entries within the filtered matrix that one obtains after dropping the weak connections. The new algorithms consider modifications to the Jacobi‐like step that defines the prolongator smoother, modifications to the filtered matrix, and also direct modifications to the resulting grid transfer operators. Numerical results are given illustrating the potential benefits of the proposed adaptations.

Hu, Jonathan J.↗

Advanced Method Optimization for Sampling and Analysis Instrumentation

This work presents a generalized approach for analytical method optimization that branches the gap between techniques historically employed and accurate modern optimization techniques suitable for various applications. The novelty of the described strategy is the utilization of multivariate, multiobjective optimization with Karush-Kuhn-Tucker conditions to bound the optimization space to solutions within the physical limitations of instrumentation. Briefly, the basic steps outlined in this paper are to (1) determine the objective(s) that should be maximized or minimized based on the goals of the analytical application, (2) conduct a screening experiment, (3) perform ANOVA to determine the parameters which have a statistically significant effect on the objective, (4) conduct an experiment (e.g., Box-Behnken design) to collect data for fitting the objective equation, and (5) determine the physical constraints of the parameters and solve the Lagrangian to determine the optimal method parameters. A broad approach to optimization target selection allows for robust method tuning to develop improved data sets amenable for chemometrics and machine learning algorithm development. Gas chromatography-mass spectrometry was selected as a use case due to its broad use across scientific fields and time-consuming method development involving numerous parameters. In conclusion, this strategy can reduce the cost of research, improve data quality, and enable the rapid development of new analytical technique.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Flame acceleration and transition to detonation in a pre-/main-chamber combustion system

Numerical simulations are performed to study the mechanism of deflagration to detonation transition (DDT) in a pre-/main-chamber combustion system with a stoichiometric ethylene–oxygen mixture. A Godunov algorithm, fifth-order in space, and third-order in time, is used to solve the fully compressible Navier–Stokes equations on a dynamically adapting mesh. A single-step, calibrated chemical diffusive model described by Arrhenius kinetics is used for energy release and conservation between the fuel and the product. The two-dimensional simulation shows that a laminar flame grows in the pre-chamber and then develops into a jet flame as it passes through the orifice. A strong shock forms immediately ahead of the flame, reflecting off the walls and interacting with the flame front. The shock–flame interactions are crucial for the development of flame instabilities, which trigger the subsequent flame development. The DDT arises due to a shock-focusing mechanism, where multiple shocks collide at the flame front. A chemical explosive mode analysis (CEMA) criterion is developed to study the DDT ignition mode. Preliminary one-dimensional computations for a laminar propagating flame, a fast flame deflagration, and a Chapman–Jouguet detonation are conducted to demonstrate the validity of CEMA on the chemical-diffusive model, as well as to determine the proper conditioning value for CEMA diagnostic. The two-dimensional analysis with CEMA indicates that the DDT initiated by the shock-focusing mechanism can form a strong thermal expansion region at the flame front that features large positive eigenvalues for the chemical explosive mode and dominance of the local autoignition mode. Thus, the CEMA criterion proposed in this study provides a robust diagnostic for identifying autoignition-supported DDT, of which the emergence of excessive local autoignition mode is found to be a precursor. The effect of grid size, initial temperature, and orifice size are then evaluated, and results show that although the close-chamber DDT is highly stochastic, the detonation initiation mechanism remains robust.

42 ENGINEERING↗

Gaussian Mixture Model Solvers for the Boltzmann Equation

This report documents our experience constructing a numerical method for the collisional Boltzmann equation that is capable of accurately capturing the collisionless through strongly collisional limits. We explore three different functional representations and present a detailed account of a numerical method based on a spatially dependent Gaussian mixture model (GMM). The Kullback-Leibler divergence is used as a closeness measure and various expectation maximization (EM) solution algorithms are implemented to find a compact representation in velocity space for distribution functions that exhibit significant non-Maxwellian character. We discuss issues that appear with this representation over a range of Knudsen numbers for a prototypical test problem and demonstrate that the strongly collisional limit recovers a solution to Euler's equations. Looking forward, this approach is broadly applicable to the non-relativistic and relativistic collisional Vlasov equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Learning Conservation Laws in Unknown Quantum Dynamics

We present a learning algorithm for discovering conservation laws given as sums of geometrically local observables in quantum dynamics. This includes conserved quantities that arise from local and global symmetries in closed and open quantum many-body systems. The algorithm combines the classical shadow formalism for estimating expectation values of observable and data analysis techniques based on singular value decompositions and robust polynomial interpolation to discover all such conservation laws in unknown quantum dynamics with rigorous performance guarantees. Our method can be directly realized in quantum experiments, which we illustrate with numerical simulations, using closed and open quantum system dynamics in a ℤ 2 gauge theory and in many-body localized spin chains.

Machine learning↗

A new field solver for modeling of relativistic particle-laser interactions using the particle-in-cell algorithm

A customized finite-difference field solver for the particle-in-cell (PIC) algorithm that provides higher fidelity for wave-particle interactions in intense electromagnetic waves is presented. In many problems of interest, particles with relativistic energies interact with intense electromagnetic fields that have phase velocities near the speed of light. Numerical errors can arise due to (1) dispersion errors in the phase velocity of the wave, (2) the staggering in time between the electric and magnetic fields and between particle velocity and position and (3) errors in the time derivative in the momentum advance. Errors of the first two kinds are analyzed in detail. It is shown that by using field solvers with different -space operators in Faraday’s and Ampere’s law, the dispersion errors and magnetic field time-staggering errors in the particle pusher can be simultaneously removed for electromagnetic waves moving primarily in a specific direction. Here, the new algorithm was implemented into Osiris by using customized higher-order finite-difference operators. Schemes using the proposed solver in combination with different particle pushers are compared through PIC simulation. It is shown that the use of the new algorithm, together with an analytic particle pusher (assuming constant fields over a time step), can lead to accurate modeling of the motion of a single electron in an intense laser field with normalized vector potentials, eA / mc 2 , exceeding for typical cell sizes and time steps.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A Multi-Function AAA Algorithm Applied to Frequency-Dependent Line Modeling: Preprint

We present a new multi-input rational approximation algorithm (MIAAA) and illustrate its advantages respect to the popular Vector Fitting (VF) algorithm using examples of approximations of admittance matrices discussed in a very recent paper and by the creators of VF. We show that not only MIAAA outperforms VF in terms of achieving better accuracy using a smaller number of poles, but also has no numerical issues to achieve convergence. In contrast to VF, MIAA is not sensitive to the location of input sample points and it does not require good estimates for the location of the desired approximation poles.

97 MATHEMATICS AND COMPUTING↗

Improving the representation of isopycnal mixing in E3SM (Final Report)

The DOE-supported Energy Exascale Earth System Model (E3SM) is a major attempt by the Department of Energy to develop a new Earth System Model using unstructured grids, which allow for the model to concentrate resolution where it is most needed and avoid numerical artifacts experienced by previous Earth System Models (ESMs) using regular grids in which the lateral resolution becomes extremely fine as the resolution shrinks at the poles. This effort required rewriting many of the algorithms previously developed for regular grids. One algorithm that was problematic in the first version of E3SM was the representation of mixing due to turbulent ocean eddies with scales smaller than the model grid. These mesoscale eddies are the primary way by which tracers are stirred along density surfaces in the ocean interior. In particular, the process of isopycnal mixing exchanges fresher, more oxygenated waters from polar regions with saltier, nutrient-rich and oxygen poor waters from tropical regions. Previous work in our group has shown that this mechanism is vitally important for bringing oxygen into poorly ventilated tropical regions (Gnanadesikan et al., 2012, 2013) and plays a significant role in determining the uptake of anthropogenic carbon dioxide (Gnanadesikan et al., 2015). However, in E3SMv1 this process was turned off, as turning it on caused the model to become unstable. Additionally, the rate of isopycnal mixing is directly proportional to a mixing coefficient $A_{Redi}$ whose value varies from less than 400 m 2 /s to 2000 m 2 /s across contemporary climate models. The main thrusts of this proposal therefore were to: 1.) Improve the numerics of isopycnal mixing in E3SM; 2.) Identify ways in which climate models are sensitive to the isopycnal mixing coefficient; and 3.) Develop better representations of the isopycnal mixing coefficient.

54 ENVIRONMENTAL SCIENCES↗

Protection Against Graph-Based False Data Injection Attacks on Power Systems

Graph signal processing (GSP) has emerged as a powerful tool for practical network applications, including power system monitoring. By representing power system voltages as smooth graph signals, recent research has focused on developing GSP-based methods for state estimation, attack detection, and topology identification. Included, efficient methods have been developed for detecting false data injection (FDI) attacks, which until now were perceived as non-smooth with respect to the graph Laplacian matrix. Consequently, these methods may not be effective against smooth FDI attacks. In this paper, we propose a graph FDI (GFDI) attack that minimizes the Laplacian-based graph total variation (TV) under practical constraints. In addition, we develop a low-complexity algorithm that solves the non-convex GDFI attack optimization problem using ell_1-norm relaxation, the projected gradient descent (PGD) algorithm, and the alternating direction method of multipliers (ADMM). We then propose a protection scheme that identifies the minimal set of measurements necessary to constrain the GFDI output to high graph TV, thereby enabling its detection by existing GSP-based detectors. Our numerical simulations on the IEEE-57 bus test case reveal the potential threat posed by well-designed GSP-based FDI attacks. Moreover, we demonstrate that integrating the proposed protection design with GSP-based detection can lead to significant hardware cost savings compared to previous designs of protection methods against FDI attacks.

Morgenstern, Gal↗

An asymptotic-preserving semi-Lagrangian algorithm for the anisotropic heat transport equation with arbitrary magnetic fields

Here, we extend the recently proposed semi-Lagrangian algorithm for the extremely anisotropic heat transport equation [Chacón et al., J. Comput. Phys ., 272 (2014)] to deal with arbitrary magnetic field topologies. The original scheme (which showed remarkable numerical properties) was valid for the so-called tokamak-ordering regime, in which the magnetic field magnitude was not allowed to vary much along field lines. The proposed extension maintains the attractive features of the original scheme (including the analytical Green's function, which is critical for tractability) with minor modifications, while allowing for completely general magnetic fields. The accuracy and generality of the approach are demonstrated by numerical experiment with an analytical manufactured solution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

GraMeR: Gra ph Me ta R einforcement learning for multi-objective influence maximization

Influence maximization (IM) is a combinatorial problem of identifying a subset of seed nodes in a network (graph), which when activated, provide a maximal spread of influence in the network for a given diffusion model and a budget for seed set size. IM has numerous applications such as viral marketing, epidemic control, sensor placement and other network-related tasks. However, its practical uses are limited due to the computational complexity of current algorithms. Recently, deep reinforcement learning has been leveraged to solve IM in order to ease the computational burden. However, there are serious limitations in current approaches, including narrow IM formulation that only consider influence via spread and ignore self-activation, low scalability to large graphs, and lack of generalizability across graph families leading to a large running time for every test network. In this work, we address these limitations through a unique approach that involves: (1) Formulating a generic IM problem as a Markov decision process that handles both intrinsic and influence activations; (2)incorporating generalizability via meta-learning across graph families. There are previous works that combine deep reinforcement learning with graph neural network, but this work solves a more realistic IM problem and incorporates generalizability across graphs via meta reinforcement learning. Extensive experiments are carried out in various standard networks to validate performance of the proposed Graph Meta Reinforcement learning (GraMeR) framework. Finally, the results indicate that GraMeR is multiple orders faster and generic than conventional approaches when applied on small to medium scale graphs.

97 MATHEMATICS AND COMPUTING↗

Effect of epitope variant co-delivery on the depth of CD8 T cell responses induced by HIV-1 conserved mosaic vaccines

To stop the HIV-1 pandemic, vaccines must induce responses capable of controlling vast HIV-1 variants circulating in the population as well as those evolved in each individual following transmission. Numerous strategies have been proposed, of which the most promising include focusing responses on the vulnerable sites of HIV-1 displaying the least entropy among global isolates and using algorithms that maximize vaccine match to circulating HIV-1 variants by vaccine cocktails of optimized complementing sequences. In this study, we investigated CD8 T cell responses induced by a bi-valent mosaic of highly conserved HIVconsvX regions delivered by a combination of simian adenovirus ChAdOx1 and poxvirus MVA. We compared partially and fully mono- and bi-valent prime-boost regimens and their ability to elicit T cells recognizing natural epitope variants using an interferon-g enzyme-linked immunospot (ELISPOT) assay. We used 11 well-defined CD8 T cell epitopes in two mouse haplotypes and, for each epitope, assessed recognition of the two vaccine forms together with the other most frequent epitope variants in the HIV-1 database. We conclude that for the magnitude and depth of epitope recognition, CD8 T cell responses benefitted in most comparisons from the combined bi-valent mosaic and envisage the main advantage of the bi-valent vaccine during its deployment to diverse populations.

59 BASIC BIOLOGICAL SCIENCES↗

Ab initio molecular dynamics on quantum computers

Ab initio molecular dynamics (AIMD) is a valuable technique for studying molecules and materials at finite temperatures where the nuclei evolve on potential energy surfaces obtained from accurate electronic structure calculations. In this work, we present an approach to running AIMD simulations on noisy intermediate-scale quantum (NISQ)-era quantum computers. The electronic energies are calculated on a quantum computer using the variational quantum eigensolver (VQE) method. Algorithms for computation of analytical gradients entirely on a quantum computer require quantum fault-tolerant hardware, which is beyond NISQ-era. Therefore, we compute the energy gradients numerically using finite differences, the Hellmann-Feynman theorem, and a correlated sampling technique. This method only requires additional classical calculations of electron integrals for each degree of freedom without any additional computations on a quantum computer beyond the initial VQE run. As a proof of concept, AIMD simulations are demonstrated for the H-2 molecule on IBM quantum devices. In addition, we demonstrate the validity of the method for larger molecules using full configuration interaction wave functions. As quantum hardware and noise mitigation techniques continue to improve, the method can be utilized for studying larger molecular systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Topanga: A kinetic ion plasma code for large-scale ionospheric simulations on magnetohydrodynamic timescales

Topanga is a kinetic ion code developed for simulating large-scale plasma phenomena in the Earth's ionosphere on magnetohydrodynamic timescales. It is a domain-decomposed parallel code that runs on high-performance computing platforms. Features of Topanga include spherical geometry for simplified boundary conditions and computational efficiency; a hybrid plasma model with inertia-less fluid electrons, kinetic ions, and an electric field specified via an Ohm's law; a Maxwell-FDTD (finite difference time domain) plasma model which retains the displacement current in Maxwell's equations and models electron currents in the ionosphere with a tensor conductivity; sponge-layer boundary conditions for absorption of electromagnetic and plasma waves incident on the domain boundaries; and a novel mixed-implicit algorithm for evolving the EM fields inside the Maxwell-FDTD region that is stable over many orders of magnitude in the electron–ion collision frequency. We verify the numerical methods used in Topanga on a pair of test problems. The first test involves modeling a three-dimensional collisionless shock using the hybrid set of equations. The second test involves modeling a spherical TEM mode in vacuum using the Maxwell-FDTD set of equations. Finally, we demonstrate how using the combined set of hybrid and Maxwell-FDTD equations to model the Starfish Prime high-altitude nuclear test recovers a “missing” EM signal on the ground that is not present when using only the hybrid set of equations. The magnitude of this signal in the simulation containing the Maxwell-FDTD region agrees well with the E3a portion of the magnetohydrodynamic electromagnetic pulse from Starfish Prime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Numerical characterization of support recovery in sparse regression with correlated design

Sparse regression is employed in diverse scientific settings as a feature selection method. A pervasive aspect of scientific data is the presence of correlations between predictive features. These correlations hamper both feature selection and estimation and jeopardize conclusions drawn from estimated models. On the other hand, theoretical results on sparsity-inducing regularized regression have largely addressed conditions for selection consistency via asymptotics, and disregard the problem of model selection, whereby regularization parameters are chosen. In this numerical study, we address these issues through exhaustive characterization of the performance of several regression estimators, coupled with a range of model selection strategies. These estimators and selection criteria were examined across correlated regression problems with varying degrees of signal to noise, distributions of non-zero model coefficients, and model sparsity. Our results reveal a fundamental tradeoff between false positive and false negative control in all regression estimators and model selection criteria examined. Additionally, we numerically explore a transition point modulated by the signal-to-noise ratio and spectral properties of the design covariance matrix at which the selection accuracy of all considered algorithms degrades. Overall, we find that SCAD coupled with BIC or empirical Bayes model selection performs the best feature selection across the regression problems considered.

97 MATHEMATICS AND COMPUTING↗

Multigrid Reduction in Time for Chaotic Dynamical Systems

As CPU clock speeds have stagnated and high performance computers continue to have ever higher core counts, increased parallelism is needed to take advantage of these new architectures. Traditional serial time-marching schemes can be a significant bottleneck, as many types of simulations require large numbers of time-steps which must be computed sequentially. Parallel-in-time schemes, such as the Multigrid Reduction in Time (MGRIT) method, remedy this by parallelizing across time-steps and have shown promising results for parabolic problems. However, chaotic problems have proved more difficult, since chaotic initial value problems (IVPs) are inherently ill-conditioned. MGRIT relies on a hierarchy of successively coarser time-grids to iteratively correct the solution on the finest time-grid, but due to the nature of chaotic systems, small inaccuracies on the coarser levels can be greatly magnified and lead to poor coarse-grid corrections. Here we introduce a modified MGRIT algorithm based on an existing quadratically converging nonlinear extension to the multigrid Full Approximation Scheme (FAS), as well as a novel time-coarsening scheme. Together, these approaches better capture long-term chaotic behavior on coarse-grids and greatly improve convergence of MGRIT for chaotic IVPs. Further, we introduce a novel low-memory variant of the algorithm for solving chaotic PDEs with MGRIT which not only solves the IVP, but also provides estimates for the unstable Lyapunov vectors of the system. Finally, we provide supporting numerical results for the Lorenz system and demonstrate parallel speedup for the chaotic Kuramoto–Sivashinsky PDE over a significantly longer time-domain than in previous works.

97 MATHEMATICS AND COMPUTING↗

Machine Learning Assisted Safety Modeling and Analysis of Advanced Reactors

With the advances in computational power and numerical methods, analysts can now rely on first-principle simulations to predict ultra-fine details in a variety of applications. Advances in machine learning (ML) have produced algorithms that can now learn high-level abstractions via hierarchical models. This project aims to leverage advances in ML techniques and the available high-resolution simulation data to develop a novel modeling and simulation (M\&S) methodology for reactor safety analysis. While application-agnostic ML techniques are available, complex physics constraints need to be incorporated into ML techniques to build ML-based closures for computationally efficient predictive simulations. This project intends to develop a physics-guided data-driven multi-scale methodology for M\&S of advanced reactors. The project focuses on thermal fluid (T/F) phenomena, which play major roles in advanced reactor safety. Specifically, we propose a data-driven coarse-mesh turbulence model based on local flow features for the transient analysis of thermal mixing and stratification in a sodium-cooled fast reactor (SFR). The model has a coarse-mesh setup to ensure computational efficiency, while it is trained by fine-mesh computational fluid dynamics (CFD) data with Reynolds-averaged Navier-Stokes (RANS) turbulence model to ensure accuracy. Three different neural networks are developed and tested for loss-of-flow transients in the hot pool of SFR, i.e. the densely connected convolutional neural network (DCNN), long-short-term-memory network based on proper orthogonal decomposition (POD-LSTM), and the DCNN informed by LSTM (DCNN-LSTM). The performances of these three neural networks are evaluated based on baseline models. The DCNN-LSTM model has been chosen for further hyperparameter optimization. Furthermore, based on a simplified two-dimensional case, uncertainty quantification (UQ) of the developed ML-based closure are investigated with three methods, i.e. Monte Carlo dropout, deep ensemble, and Bayesian neural network. The developed ML-based turbulent viscosity closure relation based on deep ensemble is then integrated into the system analysis module SAM and serves as a term in the conservation equations. Such a SAM-ML based procedure guarantees that the obtained results are consistent with the physical constraints of the thermal-fluid system. The SAM-ML simulation on the same loss-of-flow transient showed comparable accuracy with the CFD simulation but with a much coarser mesh setup. Last but not least, the ML-based closure improvement with the support of higher-fidelity data from large eddy simulation (LES) is discussed. As a first step towards this direction, a baseline LES simulation is performed to obtain comparable data with RANS results. Based on the early results, future investigation on further improving the ML-based closure is discussed. We believe the developed approach that combines scientific machine learning with nuclear system analysis code can benefit the advanced reactor community as more accurate safety analyses will better characterize reactor safety margins and reduce licensing efforts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗