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DOE OSTI2021

Multilevel Combinatorial Optimization across Quantum Architectures

Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore’s law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world datasets directly in the near future, leading to new challenges in utilizing these quantum processors for practical purposes. Furthermore, hybrid quantum-classical algorithms that leverage both quantum and classical types of devices are considered as one of the main strategies to apply quantum computing to large-scale problems. In this article, we advocate the use of multilevel frameworks for combinatorial optimization as a promising general paradigm for designing hybrid quantum-classical algorithms. To demonstrate this approach, we apply this method to two well-known combinatorial optimization problems, namely, the Graph Partitioning Problem, and the Community Detection Problem. We develop hybrid multilevel solvers with quantum local search on D-Wave’s quantum annealer and IBM’s gate-model based quantum processor. We carry out experiments on graphs that are orders of magnitude larger than the current quantum hardware size, and we observe results comparable to state-of-the-art solvers in terms of quality of the solution.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Scalable line and plane relaxation in a parallel structured multigrid solver

The efficient solution of sparse, linear systems that arise through the discretization of partial differential equations remains a key challenge for a range of high performance scientific simulations. One approach for reducing data movement and improving performance is by exposing and exploiting structure in a problem through the use of robust structured multilevel solvers. By choosing coarsening that preserves the structure of the problem, these methods maintain efficient structured computation and communication throughout the multigrid hierarchy. However, when coarsening is not permitted to be dependent on the operator, anisotropy must be addressed by the smoother — producing error compatible for coarse-grid correction with structured coarsening. Here, the components required in a scalable parallel structured solver are described with a focus on memory and communication efficiency of robust smoothers. While the implementation of communication and memory reduction techniques in smoothers integrated in a complete 3D solver present a significant engineering challenge, a novel approach is proposed that addresses these challenges systematically through a change to the solver’s execution model. Enabled by user-level threading paired with a set of data and communication abstractions, this approach permits seamless aggregation of communication in plane smoothers — directly reusing code for a 2D distributed multilevel cycle. Results show an effective reduction in communication costs for coarse-grid problems, and result in a speedup of 8.7x in smoothing routines shown in Fig. 12 using this approach. This produces a significant improvement to strong scalability while maintaining favorable weak scaling behavior. Finally, a parallel scaling study using a series of refined meshes is included that demonstrates the effectiveness of this approach in an application of interest.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Mechanically Robust, Ultraelastic Hierarchical Foam with Tunable Properties via 3D Printing

We present a mechanically robust, ultraelastic foam with controlled multiscale architectures and tunable mechanical/conductive performance is fabricated via 3D printing. Hierarchical porosity, including both macro- and microscaled pores, are produced by the combination of direct ink writing (DIW), acid etching, and phase inversion. The thixotropic inks in DIW are formulated by a simple one-pot process to disperse duo nanoparticles (nanoclay and silica nanoparticles) in a polyurethane suspension. The resulting lightweight foam exhibits tailorable mechanical strength, unprecedented elasticity (standing over 1000 compression cycles), and remarkable robustness (rapidly and fully recover after a load more than 20 000 times of its own weight). Surface coating of carbon nanotubes yields a conductive elastic foam that can be used as piezoresistivity sensor with high sensitivity. For the first time, this strategy achieves 3D printing of elastic foam with controlled multilevel 3D structures and mechanical/conductive properties. In conclusion, the facile ink preparation method can be utilized to fabricate foams of various materials with desirable performance via 3D printing.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Extended Summary: Performance Improvements to the 2D/1D Subplane Method in MPACT

Recent work in MPACT, the primary deterministic neutron transport solver in CASL’s VERA, has focused on significantly improving the overall performance of the calculations and many components within the code have been improved. The paper focuses on the most recent development to improve the 2D/1D subplane method in preparation for a production-level capability. The key developments presented here focus on incorporating a multilevel-in-space CMFD solver that also collapses on the subplane bases, a dynamic subplane meshing capability that better preserves accuracy during control rod movements, and overall usability improvements to make using the subplane method seamless. Compared to the current default 2D/1D solver in MPACT, substantial improvements are demonstrated on two progression problems, including a standard quarter core model, where potential savings observed at ~2× in memory and ~5-6× in core-hour requirements.

Stimpson, Shane G.↗

DOE OSTI2019

Performance Improvements to the 2D/1D Subplane Method in MPACT

Stimpson, Shane G.↗

DOE OSTI2021

Algebraic Multigrid with Optimal Interpolation and Adaptive Smoothers (Final Report)

The project team continued with work on developing new bootstrap AMG techniques for solving symmetric and non-symmetric PDE systems. The focus of this work is to derive more reliable measures of the quality of the coarse space set than the convergence rate of the standard F-relaxation form of CR and a more robust form of interpolation than the so-called ideal form. We have successfully derived a sharp variant of CR that gives the precise convergence rate of the two-grid method using this optimal interpolation and, in addition, we derived a new Generalized Bootstrap AMG setup algorithm that uses as its main tool a multilevel eigensolver for the generalized eigenvalue problem involving the system matrix and the symmetrized smoother. In addition, the approach allows for general block smoothers with overlap. We have applied the method to scalar diffusion problems, linear elasticity, and Maxwell’s and the method shows marked improvements over existing AMG methods for these problems. In addition, the team worked with CASC members on new forms of ideal AMG interpolation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions]

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switching technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. In conclusion, we also show that the strategy is efficient and scales optimally with problem size.

02 PETROLEUM↗

DOE OSTI2018

Bayesian Static Parameter Estimation for Partially Observed Diffusions via Multilevel Monte Carlo

In this article we consider static Bayesian parameter estimation for partially observed diffusions that are discretely observed. We work under the assumption that one must resort to discretizing the underlying diffusion process, for instance, using the Euler--Maruyama method. Given this assumption, we show how one can use Markov chain Monte Carlo (MCMC) and particularly particle MCMC [C. Andrieu, A. Doucet, and R. Holenstein, J. R. Stat. Soc. Ser. B Stat. Methodol., 72 (2010), 269--342] to implement a new approximation of the multilevel (ML) Monte Carlo (MC) collapsing sum identity. Our approach comprises constructing an approximate coupling of the posterior density of the joint distribution over parameter and hidden variables at two different discretization levels and then correcting by an importance sampling method. The variance of the weights are independent of the length of the observed data set. The utility of such a method is that, for a prescribed level of mean square error, the cost of this MLMC method is provably less than i.i.d. sampling from the posterior associated to the most precise discretization. However the method here comprises using only known and efficient simulation methodologies. Finally, the theoretical results are illustrated by inference of the parameters of two prototypical processes given noisy partial observations of the process: the first is an Ornstein--Uhlenbeck process and the second is a more general Langevin equation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Femtosecond Laser-Induced Nano-Joining of Volatile Tellurium Nanotube Memristor

Nanowire/nanotube memristor devices provide great potential for random-access high-density resistance storage. However, fabricating high-quality and stable memristors is still challenging. This paper reports multileveled resistance states of tellurium (Te) nanotube based on the clean-room free femtosecond laser nano-joining method. The temperature for the entire fabrication process was maintained below 190 °C. A femtosecond laser joining technique was used to form nanowire memristor units with enhanced properties. Femtosecond (fs) laser-irradiated silver-tellurium nanotube-silver structures resulted in plasmonic-enhanced optical joining with minimal local thermal effects. This produced a junction between the Te nanotube and the silver film substrate with enhanced electrical contacts. Noticeable changes in memristor behavior were observed after fs laser irradiation. Capacitor-coupled multilevel memristor behavior was observed. Compared to previous metal oxide nanowire-based memristors, the reported Te nanotube memristor system displayed a nearly two-order stronger current response. The research displays that the multileveled resistance state is rewritable with a negative bias.

42 ENGINEERING↗

DOE OSTI2024

Multilevel Cybersecurity for Photovoltaic Systems

The motivation behind this project is to protect critical infrastructure in electric power generation pertaining to solar photovoltaic (PV) systems. This growing renewable energy resource is becoming a more vital part of the nation’s energy portfolio, particularly since it has achieved grid-parity to existing generation methods in terms of cost. It is thus vital that steps be taken to ensure the cybersecurity of these assets. The project goal was to devise a multilevel cybersecurity solution to address PV security gaps at the inverter and system levels, and field test the solution under the supervision and review of a US-based solar inverter manufacturer and PV installer/operator. A two-level cyberattack defense approach was formulated whereby the first level, the solar inverter level, hardens individual devices and achieves a deeply cyber-secure inverter. The inverter level security involves a multi-layer defense-in-depth approach for securing the inverter while also providing data for the system level algorithms. The second level, the system level, addresses intrusion detection and restoration involving an ensemble of inverters and relevant systems.

14 SOLAR ENERGY↗

DOE OSTI2018

Capacitor Voltage Ripple Reduction of A 4-Level Hybrid Clamped Converter Using Switching State Redundancy for Medium-Voltage Drive

Abstract—A four-level Hybrid Clamped Converter (4LHCC) is a novel promising DC/AC multilevel converter for high-efficiency medium-voltage drives. This paper presents a new control method of the 4L-HCC using the switching state redundancy to reduce the DC-link capacitor voltage ripples at low frequencies (<=30 Hz). The new switching state selection algorithm and flying capacitor balancing method are introduced and analyzed.Both of a3.6 kV 1MW 4L-HCC simulation model and a SiC-based 4L-HCC prototype is established to verify the proposed method. Simulation and experimental result shows that the maximum DC-link capacitor ripple can be reduced effectively from over 50% to less than 5% at low frequencies with the new method. Meanwhile, load voltage and currentdistortion caused by the excessive capacitor rippleisalso mitigatedsignificantly.

hybrid clamped converter, motor drive, voltage bal↗

DOE OSTI2022

An Inrush Current Limiting Method for Grid-Connected Converters Considering Grid Voltage Disturbances

To support the electric power grid, some grid-connected converters are required to ride through abnormal grid conditions, including voltage disturbances. However, at the moment, when a grid voltage disturbance happens, a large inrush current could be induced due to the large difference between the grid and converter output pulsewidth modulation (PWM) voltages. This inrush current could be more severe in the faster switching SiC-based multilevel converter, which only needs a small filter inductance to meet its normal operation requirements, such as harmonics and peak ripple currents. In this article, a PWM mask method is used to limit the inrush current. With this method, the inrush current can be effectively limited to a preset value and can help the converter ride through grid voltage disturbances. Furthermore, the method is validated through experiments conducted on a single-phase SiC-based five-level converter considering low voltage, high voltage, and phase angle disturbances.

42 ENGINEERING↗

DOE OSTI2019

Pilot Point Optimization of Mining Boundaries for Lateritic Metal Deposits: Finding the Trade-off Between Dilution and Ore Loss

Geological contacts in lateritic metal deposits (footwall topographies) often delineate the orebody boundaries. Spatial variations seen in such contacts are frequently higher than those for the metal grades of the deposit. Therefore, borehole spacing chosen based on the grade variations cannot adequately capture the geological contact variability. Consequently, models created using such boreholes cause high volumetric uncertainties in the actual and targeted ore extraction volumes, which, in turn, lead to high unplanned dilution and ore losses. In this paper, a method to design optimum ore/mining boundaries for lateritic metal deposits is presented. The proposed approach minimizes the dilution/ore losses and comprises two main steps. First, the uncertainty on the orebody boundary is represented using a set of stochastic realizations generated with a multiple-point statistics algorithm. Then, the optimal orebody boundary is determined using an optimization technique inspired by a model calibration method called Pilot Points. The pilot points represent synthetic elevation values, and they are used to construct smooth mining boundaries using the multilevel B-spline technique. The performance of a generated surface is evaluated using the expected sum of losses in each of the stochastic realizations. The simulated annealing algorithm is used to iteratively determine the pilot point values which minimize the expected losses. The results show a significant reduction in the dilution volume as compared to those obtained from the actual mining operation.

58 GEOSCIENCES↗

DOE OSTI2018

Bottom-up estimation and top-down prediction: Solar energy prediction combining information from multiple sources

Accurately forecasting solar power using the data from multiple sources is an important but challenging problem. Our goal is to combine two different physics model forecasting outputs with real measurements from an automated monitoring network so as to better predict solar power in a timely manner. To this end, we propose a new approach of analyzing large-scale multilevel models with great computational efficiency requiring minimum monitoring and intervention. This approach features a division of the large scale data set into smaller ones with manageable sizes, based on their physical locations, and fit a local model in each area. The local model estimates are then combined sequentially from the specified multilevel models using our novel bottom-up approach for parameter estimation. The prediction, on the other hand, is implemented in a top-down matter. The proposed method is applied to the solar energy prediction problem for the U.S. Department of Energy's SunShot Initiative.

14 SOLAR ENERGY↗

DOE OSTI2019

Hydrogeological Model Selection Among Complex Spatial Priors

Hydrogeological field studies rely often on a single conceptual representation of the subsurface. This is problematic since the impact of a poorly chosen conceptual model on predictions might be significantly larger than the one caused by parameter uncertainty. Furthermore, conceptual models often need to incorporate geological concepts and patterns in order to provide meaningful uncertainty quantification and predictions. Consequently, several geologically realistic conceptual models should ideally be considered and evaluated in terms of their relative merits. Here, we propose a full Bayesian methodology based on Markov chain Monte Carlo to enable model selection among 2-D conceptual models that are sampled using training images and concepts from multiple-point statistics. More precisely, power posteriors for the different conceptual subsurface models are sampled using sequential geostatistical resampling and Graph Cuts. To demonstrate the methodology, we compare and rank five alternative conceptual geological models that have been proposed in the literature to describe aquifer heterogeneity at the MAcroDispersion Experiment site in Mississippi, USA. We consider a small-scale tracer test for which the spatial distribution of hydraulic conductivity impacts multilevel solute concentration data observed along a 2-D transect. The thermodynamic integration and the stepping-stone sampling methods were used to compute the evidence and associated Bayes factors using the computed power posteriors. We find that both methods are compatible with multiple-point statistics-based inversions and provide a consistent ranking of the competing conceptual models considered.

58 GEOSCIENCES↗

DOE OSTI2018

Multilevel Effects in a Driven Generalized Rabi Model

We study numerically the onset of higher-level excitations and resonance frequency shifts in the generalized multilevel Rabi model with dispersive coupling under strong driving. The response to a weak probe is calculated using the Floquet method, which allows us to calculate the probe spectrum and extract the resonance frequency. We test our predictions using a superconducting circuit consisting of a transmon coupled capacitively to a coplanar waveguide resonator. This system is monitored by a weak probe field and at the same time driven at various powers by a stronger microwave tone. We show that the transition from the quantum to the classical regime is accompanied by a rapid increase of the transmon occupation and consequently that the qubit approximation is valid only in the extreme quantum limit.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Spectroscopic factors, overlaps, and isospin symmetry from an R -matrix point of view

Background: Spectroscopic factors, overlaps, and isospin symmetry are often used in conjunction with single-particle wave functions for the phenomenological analysis of nuclear structure and reactions. Many differing prescriptions for connecting these quantities to physically relevant asymptotic normalization constants or widths are available in the literature, but their relationship and degree of validity are not always clear. Purpose: This paper derives relationships among the above quantities of interest using well-defined methodology and starting assumptions. Method: R -matrix theory is used as the primary tool to interoperate among the quantities of interest to this work. Particular attention is paid to effects arising from beyond the nuclear surface, where isospin symmetry is strongly violated. Results: Relationships between the quantities of interest are derived. Example applications of these methods to mirror levels in nucleon + 12 C, nucleon + 16 O, and nucleon + 26 Al are presented. A new approach to multilevel mirror symmetry is derived and applied to the first three 2 + states of 18 O and 18 Ne. Conclusions: In this work, the relationship between the quantities of interest is clarified and certain procedures are recommended. It is found that the asymptotic normalization constant of the second 2 + state in 18 Ne deduced from the mirror state in 18 O is significantly larger than found in previous work. This finding has the effect of increasing the 17 F($\textit{p,γ}$) 18 Ne reaction rate in novae.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

A Miniature Multilevel Structures for Lossless Ion Manipulations Ion Mobility Spectrometer with Wide Mobility Range Separation Capabilities

Here, ion mobility spectrometry employing structures for lossless ion manipulations (SLIM-IMS) is an attractive gas-phase separation technique due to its ability to achieve unprecedented effective ion path lengths (>1 km) and IMS resolving powers in a small footprint. The emergence of multilevel SLIM technology, where ions are transferred between vertically stacked SLIM electrode surfaces, has subsequently allowed for ultralong single pass path lengths (>40 m) to be achieved, enabling ultrahigh resolution IMS measurements to be performed over the entire mobility range in a single experiment. The implementation of multiple SLIM levels requires very little additional space for the SLIM system, and we developed a miniature SLIM module (miniSLIM) based on multilevel SLIM technology and report the performance here. The module is 11.1 cm x 6.7 cm x 1.4 cm (L x W x H) and consists of three SLIM levels totaling 1-meter path length. Ion trajectory simulations were used to optimize the SLIM board spacings and SLIM board thicknesses of the miniSLIM IMS system. Methods of efficiently transferring ions between SLIM levels were examined and a new approach using asymmetric traveling waves (TWs) was developed and implemented in the miniSLIM. We experimentally characterized the performance of the --meter multilevel miniSLIM IMS-MS relative to a drift tube IM--MS using an Agilent tuning mixture and tetraalkylammonium cations. The 1-meter miniSLIM achieved a resolving power of up to 131 (CCS/ΔCCS), ~1.5x higher than achievable with a 78 cm path length drift tube IMS, and successfully transmitted the entire ion mobility range in a single separation. We also demonstrated the miniSLIM’s performance as a standalone IMS system (i.e., without MS), showing baseline separation between Agilent tuning mixture cations with the full mobility range observed, and a standard peptide mixture with different charge states readily differentiated. Overall the miniSLIM provides a compact alternative to high performance IMS instruments possessing similar path lengths.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗