Heat Equation Neural Simulation
This code solves a steady state heat equation problem on a wire with random walks implemented using a spiking neural algorithm. SAND2020-12194 M
Reeder, Leah↗
SEARCH · Engineering Papers
Results for “randomized algorithms”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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rBahadur: efficient simulation of structured high-dimensional genotype data with applications to assortative mating
Existing methods for generating synthetic genotype data are ill-suited for replicating the effects of assortative mating (AM). We propose rb_dplr, a novel and computationally efficient algorithm for generating high-dimensional binary random variates that effectively recapitulates AM-induced genetic architectures using the Bahadur order-2 approximation of the multivariate Bernoulli distribution. The rBahadur R library is available through the Comprehensive R Archive Network at https://CRAN.R-project.org/package=rBahadur.
59 BASIC BIOLOGICAL SCIENCES↗
A Novel Machine Learning Approach to Disentangle Multitemperature Regions in Galaxy Clusters
The hot intracluster medium (ICM) surrounding the heart of galaxy clusters is a complex medium that comprises various emitting components. Although previous studies of nearby galaxy clusters, such as the Perseus, the Coma, or the Virgo cluster, have demonstrated the need for multiple thermal components when spectroscopically fitting the ICM’s X-ray emission, no systematic methodology for calculating the number of underlying components currently exists. In turn, underestimating or overestimating the number of components can cause systematic errors in the emission parameter estimations. In this paper, we present a novel approach to determining the number of components using an amalgam of machine learning techniques. Synthetic spectra containing a various number of underlying thermal components were created using well-established tools available from the Chandra X-ray Observatory. The dimensions of the training set was initially reduced using principal component analysis and then categorized based on the number of underlying components using a random forest classifier. Our trained and tested algorithm was subsequently applied to Chandra X-ray observations of the Perseus cluster. Our results demonstrate that machine learning techniques can efficiently and reliably estimate the number of underlying thermal components in the spectra of galaxy clusters, regardless of the thermal model (MEKAL versus APEC). We also confirm that the core of the Perseus cluster contains a mix of differing underlying thermal components. We emphasize that although this methodology was trained and applied on Chandra X-ray observations, it is readily portable to other current (e.g., XMM-Newton, eROSITA) and upcoming (e.g., Athena, Lynx, XRISM) X-ray telescopes. The code is publicly available at https://github.com/XtraAstronomy/Pumpkin.
79 ASTRONOMY AND ASTROPHYSICS↗
Quantum Statistical Testing of a Quantum Random Number Generator
The unobservable elements in a quantum technology, e.g., the quantum state, complicate system verification against promised behavior. Using model-based system engineering, we present methods for verifying the opera- tion of a prototypical quantum random number generator. We begin with the algorithmic design of the QRNG followed by the synthesis of its physical design requirements. We next discuss how quantum statistical testing can be used to verify device behavior as well as detect device bias. We conclude by highlighting how system design and verification methods must influence effort to certify future quantum technologies.
quantum communication↗
Metric Ranking of Invariant Networks with Belief Propagation
The management of large-scale distributed information systems relies on the effective use and modeling of monitoring data collected at various points in the distributed information systems. A promising approach is to discover invariant relationships among the monitoring data and generate invariant networks, where a node is a monitoring data source (metric) and a link indicates an invariant relationship between two monitoring data. Such an invariant network representation can help system experts to localize and diagnose the system faults by examining those broken invariant relationships and their related metrics, because system faults usually propagate among the monitoring data and eventually lead to some broken invariant relationships. However, at one time, there are usually a lot of broken links (invariant relationships) within an invariant network. Without proper guidance, it is difficult for system experts to manually inspect this large number of broken links. Thus, a critical challenge is how to effectively and efficiently rank metrics (nodes) of invariant networks according to the anomaly levels of metrics. The ranked list of metrics will provide system experts with useful guidance for them to localize and diagnose the system faults. To this end, we propose to model the nodes and the broken links as a Markov Random Field (MRF), and develop an iteration algorithm to infer the anomaly of each node based on belief propagation (BP). Finally, we validate the proposed algorithm on both realworld and synthetic data sets to illustrate its effectiveness.
Tao, Changxia↗
ICRF wave propagation and absorption modelling via machine learning
A surrogate model of the wave absorption in the ion cyclotron range of frequencies is presented. The model is trained to capture the physics of 1D electron and ion power absorption profiles for both the high harmonic fast wave scheme in NSTX, and the minority heating scheme in WEST. The surrogate models, based on both the random forest regressor and the multilayer perceptron algorithms, reduce inference time of 1D power absorption profiles from 1-5 minutes required by TORIC to ∼50 µs with high accuracy (i.e. R2 = 0.71−0.96).
Sánchez-Villar↗
Guided basin-hopping search of small boron clusters with density functional theory
The search for the ground state structures of Boron clusters has been a difficult computational task due to the unique metalloid nature of Boron atom. Previous research works had overcome the problem in the search of the Boron ground-state structures by adding symmetry constraints prior to the process of locating the local minima in the potential energy surface (PES) of the Boron clusters. In this work, we shown that, with the deployment of a novel computational approach that incorporates density functional theory (DFT) into a guided global optimization search algorithm based on basin-hopping, it is possible to directly locate the local minima of small Boron clusters in the PES at the DFT level. The ground-state structures search algorithm as proposed in this work is initiated randomly and needs not a priori symmetry constraint artificially imposed throughout the search process. Small sized Boron clusters so obtained compare well to the results obtained by similar calculations in the literature. The electronic properties of each structures obtained are calculated within the DFT framework.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
PolyPole-1: An accurate numerical algorithm for intra-granular fission gas release
This paper describes the development of a new numerical algorithm (called PolyPole-1) to efficiently solve the equation for intra-granular fission gas release in nuclear fuel. The work was carried out in collaboration with Politecnico di Milano and Institute for Transuranium Elements. The PolyPole-1 algorithms is being implemented in INL's fuels code BISON code as part of BISON's fission gas release model. The transport of fission gas from within the fuel grains to the grain boundaries (intra-granular fission gas release) is a fundamental controlling mechanism of fission gas release and gaseous swelling in nuclear fuel. Hence, accurate numerical solution of the corresponding mathematical problem needs to be included in fission gas behaviour models used in fuel performance codes. Under the assumption of equilibrium between trapping and resolution, the process can be described mathematically by a single diffusion equation for the gas atom concentration in a grain. In this work, we propose a new numerical algorithm (PolyPole-1) to efficiently solve the fission gas diffusion equation in time-varying conditions. The PolyPole-1 algorithm is based on the analytic modal solution of the diffusion equation for constant conditions, with the addition of polynomial corrective terms that embody the information on the deviation from constant conditions. The new algorithm is verified by comparing the results to a finite difference solution over a large number of randomly generated operation histories. Furthermore, comparison to state-of-the-art algorithms used in fuel performance codes demonstrates that the accuracy of the PolyPole-1 solution is superior to other algorithms, with similar computational effort. Finally, the concept of PolyPole-1 may be extended to the solution of the general problem of intra-granular fission gas diffusion during non-equilibrium trapping and resolution, which will be the subject of future work.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
CrowdPhase: crowdsourcing the phase problem
The idea of attacking the phase problem by crowdsourcing is introduced. Using an interactive, multi-player, web-based system, participants work simultaneously to select phase sets that correspond to better electron-density maps in order to solve low-resolution phasing problems. The human mind innately excels at some complex tasks that are difficult to solve using computers alone. For complex problems amenable to parallelization, strategies can be developed to exploit human intelligence in a collective form: such approaches are sometimes referred to as ‘crowdsourcing’. Here, a first attempt at a crowdsourced approach for low-resolution ab initio phasing in macromolecular crystallography is proposed. A collaborative online game named CrowdPhase was designed, which relies on a human-powered genetic algorithm, where players control the selection mechanism during the evolutionary process. The algorithm starts from a population of ‘individuals’, each with a random genetic makeup, in this case a map prepared from a random set of phases, and tries to cause the population to evolve towards individuals with better phases based on Darwinian survival of the fittest. Players apply their pattern-recognition capabilities to evaluate the electron-density maps generated from these sets of phases and to select the fittest individuals. A user-friendly interface, a training stage and a competitive scoring system foster a network of well trained players who can guide the genetic algorithm towards better solutions from generation to generation via gameplay. CrowdPhase was applied to two synthetic low-resolution phasing puzzles and it was shown that players could successfully obtain phase sets in the 30° phase error range and corresponding molecular envelopes showing agreement with the low-resolution models. The successful preliminary studies suggest that with further development the crowdsourcing approach could fill a gap in current crystallographic methods by making it possible to extract meaningful information in cases where limited resolution might otherwise prevent initial phasing.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Benchmarking quantum logic operations relative to thresholds for fault tolerance
Contemporary methods for benchmarking noisy quantum processors typically measure average error rates or process infidelities. However, thresholds for fault-tolerant quantum error correction are given in terms of worst-case error rates—defined via the diamond norm—which can differ from average error rates by orders of magnitude. One method for resolving this discrepancy is to randomize the physical implementation of quantum gates, using techniques like randomized compiling (RC). In this work, we use gate set tomography to perform precision characterization of a set of two-qubit logic gates to study RC on a superconducting quantum processor. We find that, under RC, gate errors are accurately described by a stochastic Pauli noise model without coherent errors, and that spatially correlated coherent errors and non-Markovian errors are strongly suppressed. We further show that the average and worst-case error rates are equal for randomly compiled gates, and measure a maximum worst-case error of 0.0197(3) for our gate set. Our results show that randomized benchmarks are a viable route to both verifying that a quantum processor’s error rates are below a fault-tolerance threshold, and to bounding the failure rates of near-term algorithms, if—and only if—gates are implemented via randomization methods which tailor noise.
97 MATHEMATICS AND COMPUTING↗
A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling
Computational models are used in a variety of fields to improve our understanding of complex physical phenomena. Recently, the realism of model predictions has been greatly enhanced by transitioning from deterministic to stochastic frameworks, where the effects of the intrinsic variability in parameters, loads, constitutive properties, model geometry and other quantities can be more naturally included. A general stochastic system may be characterized by a large number of arbitrarily distributed and correlated random inputs, and a limited support response with sharp gradients or event discontinuities. This motivates continued research into novel adaptive algorithms for uncertainty propagation, particularly those handling high dimensional, arbitrarily distributed random inputs and non-smooth stochastic responses. Here, we generalize a previously proposed multi-resolution approach to uncertainty propagation to develop a method that improves computational efficiency, can handle arbitrarily distributed random inputs and non-smooth stochastic responses, and naturally facilitates adaptivity, i.e., the expansion coefficients encode information on solution refinement. Our approach relies on partitioning the stochastic space into elements that are subdivided along a single dimension, or, in other words, progressive refinements exhibiting a binary tree representation. We also show how these binary refinements are particularly effective in avoiding the exponential increase in the multi-resolution basis cardinality and significantly reduce the regression complexity for moderate to high dimensional random inputs. The performance of the approach is demonstrated through previously proposed uncertainty propagation benchmarks and stochastic multi-scale finite element simulations in cardiovascular flow.
59 BASIC BIOLOGICAL SCIENCES↗
Machine Learning for Well Log Analysis in Uranium Mining
This project explores the use of Artificial Intelligence (AI) and Machine Learning (ML) techniques to automate well log analysis for uranium mining. Geophysical log data—spontaneous potential, resistivity, and gamma ray—were used to classify lithology, correlate well logs and identify roll front zonation patterns, which are critical for locating uranium ore bodies. Supervised ML algorithms such as eXtreme Gradient Boosting (XGBoost), Categorical Boosting (CatBoost), and Random Forest were trained to classify lithology with high accuracy. Gradient Boosting Machines (GBM), XGBoost, Random Forest, and Neural Networks were also used for role front zone identification. Moreover, a Fast Dynamic Time Warping (FastDTW) algorithm was employed for well log correlation. Additionally, sample lag was addressed using dynamic programming. Results demonstrate the potential of AI and ML to streamline well log analysis and enhance uranium exploration workflows.
11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
ERRATUM: “Automated Transient Identification in the Dark Energy Survey” (2015, AJ, 150, 82)
Here, we describe an algorithm for identifying point-source transients and moving objects on reference-subtracted optical images containing artifacts of processing and instrumentation. The algorithm makes use of the supervised machine learning technique known as Random Forest. We present results from its use in the Dark Energy Survey Supernova program (DES-SN), where it was trained using a sample of 898,963 signal and background events generated by the transient detection pipeline. After reprocessing the data collected during the first DES-SN observing season (2013 September through 2014 February) using the algorithm, the number of transient candidates eligible for human scanning decreased by a factor of 13.4, while only 1.0% of the artificial Type Ia supernovae (SNe) injected into search images to monitor survey efficiency were lost, most of which were very faint events. Here we characterize the algorithm's performance in detail, and we discuss how it can inform pipeline design decisions for future time-domain imaging surveys, such as the Large Synoptic Survey Telescope and the Zwicky Transient Facility. An implementation of the algorithm and the training data used in this paper are available at at http://portal.nersc.gov/project/dessn/autoscan.
79 ASTRONOMY AND ASTROPHYSICS↗
A weighted ℓ{sub 1}-minimization approach for sparse polynomial chaos expansions
This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard ℓ{sub 1}-minimization algorithm, originally proposed in the context of compressive sampling, using a priori information about the decay of the PC coefficients, when available, and refer to the resulting algorithm as weightedℓ{sub 1}-minimization. We provide conditions under which we may guarantee recovery using this weighted scheme. Numerical tests are used to compare the weighted and non-weighted methods for the recovery of solutions to two differential equations with high-dimensional random inputs: a boundary value problem with a random elliptic operator and a 2-D thermally driven cavity flow with random boundary condition.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Constant-complexity stochastic simulation algorithm with optimal binning
At the molecular level, biochemical processes are governed by random interactions between reactant molecules, and the dynamics of such systems are inherently stochastic. When the copy numbers of reactants are large, a deterministic description is adequate, but when they are small, such systems are often modeled as continuous-time Markov jump processes that can be described by the chemical master equation. Gillespie’s Stochastic Simulation Algorithm (SSA) generates exact trajectories of these systems, but the amount of computational work required for each step of the original SSA is proportional to the number of reaction channels, leading to computational complexity that scales linearly with the problem size. The original SSA is therefore inefficient for large problems, which has prompted the development of several alternative formulations with improved scaling properties. We describe an exact SSA that uses a table data structure with event time binning to achieve constant computational complexity with respect to the number of reaction channels for weakly coupled reaction networks. We present a novel adaptive binning strategy and discuss optimal algorithm parameters. We compare the computational efficiency of the algorithm to existing methods and demonstrate excellent scaling for large problems. This method is well suited for generating exact trajectories of large weakly coupled models, including those that can be described by the reaction-diffusion master equation that arises from spatially discretized reaction-diffusion processes.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Vacuum statistics and stability in axionic landscapes
We investigate vacuum statistics and stability in random axionic landscapes. For this purpose we developed an algorithm for a quick evaluation of the tunneling action, which in most cases is accurate within 10%. We find that stability of a vacuum is strongly correlated with its energy density, with lifetime rapidly growing as the energy density is decreased. On the other hand, the probability P(B) for a vacuum to have a tunneling action B greater than a given value declines as a slow power law in B. This is in sharp contrast with the studies of random quartic potentials, which found a fast exponential decline of P(B). Our results suggest that the total number of relatively stable vacua (say, with B>100) grows exponentially with the number of fields N and can get extremely large for N∼> 100. The problem with this kind of model is that the stable vacua are concentrated near the absolute minimum of the potential, so the observed value of the cosmological constant cannot be explained without fine-tuning. To address this difficulty, we consider a modification of the model, where the axions acquire a quadratic mass term, due to their mixing with 4-form fields. This results in a larger landscape with a much broader distribution of vacuum energies. The number of relatively stable vacua in such models can still be extremely large.
79 ASTRONOMY AND ASTROPHYSICS↗
Failure prediction using machine learning in a virtualised HPC system and application
Failure is an increasingly important issue in high performance computing and cloud systems. As large-scale systems continue to grow in scale and complexity, mitigating the impact of failure and providing accurate predictions with sufficient lead time remains a challenging research problem. Traditional existing fault-tolerance strategies such as regular check-pointing and replication are not adequate because of the emerging complexities of high performance computing systems. This necessitates the importance of having an effective as well as proactive failure management approach in place aimed at minimizing the effect of failure within the system. With the advent of machine learning techniques, the ability to learn from past information to predict future pattern of behaviours makes it possible to predict potential system failure more accurately. Thus, in this paper, we explore the predictive abilities of machine learning by applying a number of algorithms to improve the accuracy of failure prediction. We have developed a failure prediction model using time series and machine learning, and performed comparison based tests on the prediction accuracy. The primary algorithms we considered are the support vector machine (SVM), random forest (RF), k-nearest neighbors (KNN), classification and regression trees (CART) and linear discriminant analysis (LDA). Experimental results indicates that the average prediction accuracy of our model using SVM when predicting failure is 90% accurate and effective compared to other algorithms. This finding implies that our method can effectively predict all possible future system and application failures within the system.
Mohammed, Bashir↗
Classical Simulation of Boson Sampling Based on Graph Structure
Boson sampling is a fundamentally and practically important task that can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In this Letter, we present classical sampling algorithms for single-photon and Gaussian input states that take advantage of a graph structure of a linear-optical circuit. The algorithms’ complexity grows as so-called treewidth, which is closely related to the connectivity of a given linear-optical circuit. Using the algorithms, we study approximated simulations for local Haar-random linear-optical circuits. For equally spaced initial sources, we show that, when the circuit depth is less than the quadratic in the lattice spacing, the efficient simulation is possible with an exponentially small error. Notably, right after this depth, photons start to interfere each other and the algorithms’ complexity becomes subexponential in the number of sources, implying that there is a sharp transition of its complexity. Finally, when a circuit is sufficiently deep enough for photons to typically propagate to all modes, the complexity becomes exponential as generic sampling algorithms. We numerically implement a likelihood test with a recent Gaussian boson sampling experiment and show that the treewidth-based algorithm with a limited treewidth renders a larger likelihood than the experimental data.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗