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At least 919 records · Page 51

CV4Quantum: Reducing the Sampling Overhead in Probabilistic Error Cancellation Using Control Variates

Quasiprobabilistic decompositions (QPDs) play a key role in maximizing the utility of near-term quantum hardware. For example, Probabilistic Error Cancellation (PEC) (an error mitigation technique) and circuit cutting (which enables large quantum computations to be performed on quantum hardware with a limited number of qubits) both involve QPDs. Computations based on QPDs typically incur large sampling overheads that grow exponentially with the number of error-terms mitigated or number of circuit-cuts employed, limiting their practical feasibility. In this work, we adapt the control variates variance reduction technique from the statistics literature in order to reduce the sampling overhead in QPD-based computations. We demonstrate our method using simulation experiments that mimic a realistic PEC scenario. In our experiments, we observed a more than 50% reduction in the number of samples needed to achieve a given precision, in more than 50% of the PEC-based estimations performed in the study when using our approach. We discuss how future research on constructing good control variates can lead to even stronger sampling overhead reduction.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Geometry-complete perceptron networks for 3D molecular graphs

Abstract Motivation The field of geometric deep learning has recently had a profound impact on several scientific domains such as protein structure prediction and design, leading to methodological advancements within and outside of the realm of traditional machine learning. Within this spirit, in this work, we introduce GCPNet, a new chirality-aware SE(3)-equivariant graph neural network designed for representation learning of 3D biomolecular graphs. We show that GCPNet, unlike previous representation learning methods for 3D biomolecules, is widely applicable to a variety of invariant or equivariant node-level, edge-level, and graph-level tasks on biomolecular structures while being able to (1) learn important chiral properties of 3D molecules and (2) detect external force fields. Results Across four distinct molecular-geometric tasks, we demonstrate that GCPNet’s predictions (1) for protein–ligand binding affinity achieve a statistically significant correlation of 0.608, more than 5%, greater than current state-of-the-art methods; (2) for protein structure ranking achieve statistically significant target-local and dataset-global correlations of 0.616 and 0.871, respectively; (3) for Newtownian many-body systems modeling achieve a task-averaged mean squared error less than 0.01, more than 15% better than current methods; and (4) for molecular chirality recognition achieve a state-of-the-art prediction accuracy of 98.7%, better than any other machine learning method to date. Availability and implementation The source code, data, and instructions to train new models or reproduce our results are freely available at https://github.com/BioinfoMachineLearning/GCPNet.

59 BASIC BIOLOGICAL SCIENCES↗

AI for Science: Report on the Department of Energy (DOE) Town Halls on Artificial Intelligence (AI) for Science

The report documents the DOE Town Halls held during 2019 at Argonne National Laboratory, Oak Ridge National Laboratory, Lawrence Berkeley National Laboratory, and in Washington, DC. From July to October 2019, the Argonne, Oak Ridge, and Berkeley National Laboratories hosted a series of four town hall meetings attended by more than 1,000 U.S. scientists and engineers. The goal of the town hall series was to examine scientific opportunities in the areas of artificial intelligence (AI), Big Data, and high-performance computing (HPC) in the next decade, and to capture the big ideas, grand challenges, and next steps to realizing these opportunities. In this report and in the Department of Energy (DOE) laboratory community, we use the term “AI for Science” to broadly represent the next generation of methods and scientific opportunities in computing, including the development and application of AI methods (e.g., machine learning, deep learning, statistical methods, data analytics, automated control, and related areas) to build models from data and to use these models alone or in conjunction with simulation and scalable computing to advance scientific research. The AI for Science town hall discussions focused on capturing the transformational uses of AI that employ HPC and/or data analysis, leveraging data sets from HPC simulations or instruments and user facilities, and addressing scientific challenges unique to DOE user facilities and the agency’s wide-ranging fundamental and applied science enterprise.

36 MATERIALS SCIENCE↗

Benchmark Data Set of Crystalline Organic Semiconductors

This work reports a Benchmark Data set of Crystalline Organic Semiconductors to test calculations of the structural and electronic properties of these materials in the solid state. The data set contains 67 crystals consisting of mostly rigid molecules with a single dominant conformer, covering the majority of known structural types. The experimental crystal structure is available for the entire data set, whereas zero-temperature unit cell volume can be reliably estimated for a subset of 28 crystals. Using this subset, we benchmark r 2 SCAN-D3 and PBE-D3 density functionals. Then, for the entire data set, we benchmark approximate density functional theory (DFT) methods, including GFN1-xTB and DFTB3(3ob-3-1), with various dispersion corrections against r 2 SCAN-D3. Our results show that r 2 SCAN-D3 geometries are accurate within a few percent, which is comparable to the statistical uncertainty of experimental data at a fixed temperature, but the unit cell volume is systematically underestimated by 2% on average. The several times faster PBE-D3 provides an unbiased estimate of the volume for all systems except for molecules with highly polar bonds, for which the volume is substantially overestimated in correlation with the underestimation of atomic charges. Considered approximate DFT methods are orders of magnitude faster and provide qualitatively correct but overcompressed crystal structures unless the dispersion corrections are fitted by unit cell volume.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of void positioning on the detonation sensitivity of a heterogeneous energetic material

We show although it is well-established that voids profoundly influence the initiation and reaction behaviors of heterogeneous energetic materials such as polymer-bonded explosives (PBX) and propellants, there has been little study of how void location in different constituents in the microstructures of such materials affect the macroscale behavior. Here, we use three-dimensional (3D) mesoscale simulations to study how void placement within the reactive grains versus the polymer binder influences the shock-to-detonation transition (SDT) in a polymer-bonded explosive. The material studied here has a microstructure comprised of 75% PETN (pentaerythritol tetranitrate) grains and 25% HTPB (hydroxyl-terminated polybutadiene) polymer binder by volume. Porosities up to 10% in the form of spherical voids distributed in both the grains and polymer are considered. An Arrhenius reactive burn relation is used to model the chemical kinetics of the PETN grains under shock loading, thereby resolving the heterogeneous detonation behavior of the PBX. The influence of void location on the shock initiation sensitivity of the material is quantitatively ranked by comparing the predicted run distance to detonation (RDD) for each sample. The analysis includes inherent quantification of uncertainties arising from the stochastic variations in the microstructure morphologies and void distributions by using statistically equivalent microstructure sample sets (SEMSS), leading to probabilistic formulations for the RDD as a function of shock pressure. The calculations reveal that the location of voids in the composite microstructure significantly affects the RDD. Specifically, voids exclusively within the grains cause the PBX to be more sensitive (having shorter RDD) than voids in the polymer binder. Unique probabilistic relationships are derived to map the probability of observing RDD for each void location material case, allowing for prediction of initiation behavior anywhere in the shock pressure – RDD space. These findings agree with trends reported in the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Calibrating Bayesian generative machine learning for Bayesiamplification

Recently, combinations of generative and Bayesian deep learning have been introduced in particle physics for both fast detector simulation and inference tasks. These neural networks aim to quantify the uncertainty on the generated distribution originating from limited training statistics. The interpretation of a distribution-wide uncertainty however remains ill-defined. We show a clear scheme for quantifying the calibration of Bayesian generative machine learning models. For a Continuous Normalizing Flow applied to a low-dimensional toy example, we evaluate the calibration of Bayesian uncertainties from either a mean-field Gaussian weight posterior, or Monte Carlo sampling network weights, to gauge their behaviour on unsteady distribution edges. Well calibrated uncertainties can then be used to roughly estimate the number of uncorrelated truth samples that are equivalent to the generated sample and clearly indicate data amplification for smooth features of the distribution.

97 MATHEMATICS AND COMPUTING↗

MFNets: Multifidelity data-driven networks for Bayesian learning and prediction

This paper presents a multifidelity uncertainty quantification framework called MFNets. We seek to address three existing challenges that arise when experimental and simulation data from different sources are used to enhance statistical estimation and prediction with quantified uncertainty. Specifically, we demonstrate that MFNets can (1) fuse heterogeneous data sources arising from simulations with different parameterizations, e.g simulation models with different uncertain parameters or data sets collected under different environmental conditions; (2) encode known relationships among data sources to reduce data requirements; and (3) improve the robustness of existing multi-fidelity approaches to corrupted data. MFNets construct a network of latent variables (LVs) to facilitate the fusion of data from an ensemble of sources of varying credibility and cost. These LVs are posited as explanatory variables that provide the source of correlation in the observed data. Furthermore, MFNets provide a way to encode prior physical knowledge to enable efficient estimation of statistics and/or construction of surrogates via conditional independence relations on the LVs. We highlight the utility of our framework with a number of theoretical results which assess the quality of the posterior mean as a frequentist estimator and compare it to standard sampling approaches that use single fidelity, multilevel, and control variate Monte Carlo estimators. We also use the proposed framework to derive the Monte Carlo-based control variate estimator entirely from the use of Bayes rule and linear-Gaussian models -- to our knowledge the first such derivation. Finally, we demonstrate the ability to work with different uncertain parameters across different models.

97 MATHEMATICS AND COMPUTING↗

Analysis of leading edge protection application on wind turbine performance through energy and power decomposition approaches

Abstract Wind power production is driven by, and varies with, the stochastic yet uncontrollable wind and environmental inputs. To compare a wind turbine's performance, a direct comparison on power outputs is always confounded by the stochastic effect of weather inputs. It is therefore crucial to control for the weather and environmental influence. Toward that objective, our study proposes an energy decomposition approach. We start with comparing the change in the total energy production and refer to the change in total energy as delta energy. On this delta energy, we apply our decomposition method, which is to separate the portion of energy change due to weather effects from that due to the turbine itself. We derive a set of mathematical relationships allowing us to perform this decomposition and examine the credibility and robustness of the proposed decomposition approach through extensive cross‐validation and case studies. We then apply the decomposition approach to Supervisory Control and Data Acquisition data associated with several wind turbines to which leading‐edge protection was carried out. Our study shows that the leading‐edge protection applied on blades may cause a small decline to the power production efficiency in the short term, although we expect the leading‐edge protection to benefit the blade's reliability in the long term.

17 WIND ENERGY↗

Estimating Electron Temperature and Density Using Van Allen Probe Data: Typical Behavior of Energetic Electrons in the Inner Magnetosphere

Abstract The Earth's inner magnetosphere contains multiple electron populations influenced by different factors. The cold electrons of the plasmasphere, warm plasma that contributes to the ring current, and the relativistic plasma of the radiation belts often seem to behave independently. Using omni‐directional flux and energy measurements from the HOPE and Magnetic Electron Ion Spectrometer instruments aboard the Van Allen Probes, we provide a detailed density and temperature description of the inner magnetosphere, offering a comprehensive statistical analysis of the entire Van Allen Probe era. While number density and temperature data at geosynchronous orbit are available, this study focuses on the warm plasma in the inner magnetosphere . Values of density and temperature are extracted by fitting energy and phase space density to obtain the distribution function. The fitted distributions are related to the zeroth and second moments to estimate the number density and temperature. Analysis has indicated that a two Maxwellian fit is sufficient over a wide range of and that there are two independent plasma populations. The more energetic population has a median number density of approximately and a temperature of around 130 keV, with a temperature peak observed between L * = 4 and L * = 4.5. This population is relatively uniform in magnetic local time (MLT). In contrast, the less energetic warm electron population has a median number density of about and a temperature of 7.4 keV. Strong statistical trends in density and temperature across both L * and MLT are presented, along with potential sources driving these variations.

58 GEOSCIENCES↗

Error statistics and scalability of quantum error mitigation formulas

Quantum computing promises advantages over classical computing in many problems. Nevertheless, noise in quantum devices prevents most quantum algorithms from achieving the quantum advantage. Quantum error mitigation provides a variety of protocols to handle such noise using minimal qubit resources. While some of those protocols have been implemented in experiments for a few qubits, it remains unclear whether error mitigation will be effective in quantum circuits with tens to hundreds of qubits. In this paper, we apply statistics principles to quantum error mitigation and analyse the scaling behaviour of its intrinsic error. We find that the error increases linearly O(ϵN) with the gate number N before mitigation and sublinearly O(ϵ'N γ ) after mitigation, where γ ≈ 0.5, ϵ is the error rate of a quantum gate, and ϵ' is a protocol-dependent factor. The $\sqrt{N}$ scaling is a consequence of the law of large numbers, and it indicates that error mitigation can suppress the error by a larger factor in larger circuits. We propose the importance Clifford sampling as a key technique for error mitigation in large circuits to obtain this result.

97 MATHEMATICS AND COMPUTING↗

Information content of higher order galaxy correlation functions

The shapes of galaxy N-point correlation functions can be used as standard rulers to constrain the distance–redshift relationship. The cosmological density fields traced by late-time galaxy formation are initially nearly Gaussian, and hence, all the cosmological information can be extracted from their two-point correlation function. Subsequent non-linear evolution under gravity, as well as halo and then galaxy formation, generates higher order correlation functions. Since the mapping of the initial to the final density field is, on large scales, invertible, it is often claimed that the information content of the initial field’s power spectrum is equal to that of all the higher order functions of the final, non-linear field. This claim implies that reconstruction of the initial density field from the non-linear field renders analysis of higher order correlation functions of the latter superfluous. We show that this claim is false when the N-point functions are used as standard rulers. Constraints available from joint analysis of the two and three-point correlation functions can, in some cases, exceed those offered by the initial power spectrum. We provide a mathematical justification for this claim and demonstrate it using a large suite of N-body simulations. In particular, we show that for the z = 0 real-space matter field in the limit of vanishing shot-noise, taking modes up to k max = 0.2 h Mpc −1 , using the bispectrum alone offers a factor of 2 reduction in the variance on the cosmic distance scale relative to that available from the linear power spectrum.

79 ASTRONOMY AND ASTROPHYSICS↗

Methods for Explainable Artificial Intelligence

We explored ways of quantifying information in a neural network. This can be used to determine the right size of a network or to infer the way in which a network is processing information. The first year and a half was somewhat exploratory while the last half of the project focused on approaches that seemed to show the most promise. The introduce a new way of computing explainable artificial intelligence (XAI) saliency maps that is several orders of magnitude faster than methods with similar fidelity We call it FastCAM. The method works be combining a Class Activation Map (CAM) method such as GradCAM with a forward activation map computed with a statistic we call SMOE Scale. The addition of the forward activation maps to CAM methods seems to always improve their fidelity. At the same time, computational overhead is not increased by very much. While Gradients with SmoothGrad scores better on some fidelity measures, it is overall not as good and requires more than 1500 times to compute. We demonstrate two completed applications of FastCAM on tasks outside of the LDRD at LLNL. The source code for FastCAM is currently being implanted into Captum, the official XAI toolkit for the popular deep learning toolkit PyTorch. The LDRD currently has 13 publications released to the public. 10 of them are journal length.

97 MATHEMATICS AND COMPUTING↗

Ground state energy and magnetization curve of a frustrated magnetic system from real-time evolution on a digital quantum processor

Models of interacting many-body quantum systems that may realize new exotic phases of matter, notably quantum spin liquids, are challenging to study using even state-of-the-art classical methods such as tensor network simulations. Quantum computing provides a promising route for overcoming these difficulties to find ground states, dynamics, and more. In this paper, we argue that recently developed hybrid quantum-classical algorithms based on real-time evolution are promising methods for solving a particularly important model in the search for spin liquids, the antiferromagnetic Heisenberg model on the two-dimensional kagome lattice. We show how to construct efficient quantum circuits to implement time evolution for the model and to evaluate key observables on the quantum computer, and we argue that the method has favorable scaling with increasing system size. We then restrict to a 12-spin star plaquette from the kagome lattice and a related 8-spin system, and we give an empirical demonstration on these small systems that the hybrid algorithms can efficiently find the ground state energy and the magnetization curve. For these demonstrations, we use four levels of approximation: exact state vectors, exact state vectors with statistical noise from sampling, noisy classical emulators, and (for the 8-spin system only) real quantum hardware, specifically the Quantinuum H1-1 processor; for the noisy simulations and hardware demonstration, we also employ error mitigation strategies based on the symmetries of the Hamiltonian. Our results strongly suggest that these hybrid algorithms present a promising direction for studying quantum spin liquids and more generally for resolving important unsolved problems in condensed matter theory and beyond.

97 MATHEMATICS AND COMPUTING↗

Micro Baselines for Operational Technology Environments

Critical infrastructure stakeholders need to baseline their networks to understand expected communications. Top-down approaches to baselining rely on observables that are generally available but lack properties upon which traditional statistical tools depend. We propose to construct micro-baselines: signatures within operational networks based on observables associated with specific events. Such observables are informed by precursor analysis reports of historical cyber attacks on operational environments developed by Cybersecurity for Operational Technology Environments (CyOTE). Baseline measurements depend upon context beyond the cyber domain. An energy plant's baseline running in the summer may statistically differ from a similar facility in a colder region. Domain knowledge must be integrated to apply general micro-baselining algorithms to a facility-specific context. Therefore, we propose to explore the feasibility of transferring micro baselining algorithms across different facilities. Facilities that implement the same processes in different geographic locations will be compared relative to observable measurements used in micro-baselining for comparable events. One evaluation approach would condition or augment dynamic observables measured within a facility network testbed with additional observables derived from geographic context or infrastructure dependencies such as those provided by the All-Hazards Analysis tool.

97 MATHEMATICS AND COMPUTING↗

Identifying and tracking bubbles and drops in simulations: A toolbox for obtaining sizes, lineages, and breakup and coalescence statistics

Knowledge of bubble and drop size distributions in two-phase flows is important for characterizing a wide range of phenomena, including combustor ignition, sonar communication, and cloud formation. The physical mechanisms driving the background flow also drive the time evolution of these distributions. Accurate and robust identification and tracking algorithms for the dispersed phase are necessary to reliably measure this evolution and thereby quantify the underlying mechanisms in interface-resolving flow simulations. The identification of individual bubbles and drops traditionally relies on an algorithm used to identify connected regions. This traditional algorithm can be sensitive to the presence of spurious structures. A cost-effective refinement is proposed to maximize volume accuracy while minimizing the identification of spurious bubbles and drops. An accurate identification scheme is crucial for distinguishing bubble and drop pairs with large size ratios. The identified bubbles and drops need to be tracked in time to obtain breakup and coalescence statistics that characterize the evolution of the size distribution, including breakup and coalescence frequencies, and the probability distributions of parent and child bubble and drop sizes. An algorithm based on mass conservation is proposed to construct bubble and drop lineages using simulation snapshots that are not necessarily from consecutive time steps. These lineages are then used to detect breakup and coalescence events, and obtain the desired statistics. Accurate identification of large-size-ratio bubble and drop pairs enables accurate detection of breakup and coalescence events over a large size range. Accurate detection of successive breakup and coalescence events requires that the snapshot interval be an order of magnitude smaller than the characteristic breakup and coalescence times to capture these successive events while minimizing the identification of repeated confounding events. Together, these algorithms serve as a toolbox for detailed analysis of two-phase simulations, and enable insights into the mechanisms behind bubble and drop formation and evolution in flows of practical importance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

How Can Probabilistic Solar Power Forecasts Be Used to Lower Costs and Improve Reliability in Power Spot Markets? A Review and Application to Flexiramp Requirements

Net load uncertainty in electricity spot markets is rapidly growing. There are five general approaches by which system operators and market participants can use probabilistic forecasts of wind, solar, and load to help manage this uncertainty. These include operator situation awareness, resource risk hedging, reserves procurement, definition of contingencies, and explicit stochastic optimization. We review these approaches, and then provide a case study in which a method for using probabilistic solar forecasts to define needs for reserves is developed and evaluated. The case study has three parts. First, we describe building blocks for enhancing the Watt-Sun solar forecasting system to produce probabilistic irradiance and power forecasts. Second, relationships between Watt-Sun forecasts for multiple sites in California and the system's need for flexible ramp capability (flexiramp) are defined by machine learning and statistical methods. Third, the performance of present methods to defining flexiramp requirements, which are not conditioned on weather and renewables forecasts, is compared with that of probabilistic solar forecast-based requirements, using a multi-timescale production costing model with an 1820-bus representation of the WECC power system. Significant potential savings in fuel and flexiramp procurement costs from using solar-informed reserve requirements are found.

14 SOLAR ENERGY↗

Adaptive Uncertainty Quantification for Stochastic Hyperbolic Conservation Laws

Here, we propose a predictor-corrector adaptive method for the study of hyperbolic partial differential equations (PDEs) under uncertainty. Constructed around the framework of stochastic finite volume (SFV) methods, our approach circumvents sampling schemes or simulation ensembles while also preserving fundamental properties, in particular hyperbolicity of the resulting systems and conservation of the discrete solutions. Furthermore, we augment the existing SFV theory with a priori convergence results for statistical quantities, in particular push-forward densities, which we demonstrate through numerical experiments. By linking refinement indicators to regions of the physical and stochastic spaces, we drive anisotropic refinements of the discretizations, introducing new degrees of freedom where deemed profitable. To illustrate our proposed method, we consider a series of numerical examples for nonlinear hyperbolic PDEs based on Burgers’ and Euler’s equations.

97 MATHEMATICS AND COMPUTING↗

Pycheron: A Python-Based Seismic Waveform Data Quality Control Software Package

Supplementing an existing high-quality seismic monitoring network with openly available station data could improve coverage and decrease magnitudes of completeness; however, this can present challenges when varying levels of data quality exist. Without discerning the quality of openly available data, using it poses significant data management, analysis, and interpretation issues. Incorporating additional stations without properly identifying and mitigating data quality problems can degrade overall monitoring capability. If openly available stations are to be used routinely, a robust, automated data quality assessment for a wide range of quality control (QC) issues is essential. To meet this need, we developed Pycheron, a Python-based library for QC of seismic waveform data. Pycheron was initially based on the Incorporated Research Institutions for Seismology’s Modular Utility for STAtistical kNowledge Gathering but has been expanded to include more functionality. Pycheron can be implemented at the beginning of a data processing pipeline or can process stand-alone data sets. Its objectives are to (1) identify specific QC issues; (2) automatically assess data quality and instrumentation health; (3) serve as a basic service that all data processing builds on by alerting downstream processing algorithms to any quality degradation; and (4) improve our ability to process orders of magnitudes more data through performance optimizations. This article provides an overview of Pycheron, its features, basic workflow, and an example application using a synthetic QC data set.

58 GEOSCIENCES↗