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At least 253 records · Page 14

Scattering of radio frequency waves by randomly modulated density interfaces in the edge of fusion plasmas

In the scrape-off layer and the edge region of a tokamak, the plasma is strongly turbulent and scatters the radio frequency (RF) electromagnetic waves that propagate through this region. It is important to know, whether used for diagnostics or for heating and current drive, the spectral properties of these scattered RF waves. The spectral changes influences the interpretation of the diagnostic-data obtained and the current and heating profiles. A full-wave, 3D electromagnetic code ScaRF (see Papadopoulos et al. 2019) has been developed for studying the RF wave propagation through turbulent plasma. ScaRF is a finite-difference frequency-domain (FDFD) method for solving Maxwell's equations. The magnetized plasma is defined through the cold plasma, anisotropic permittivity tensor. As a result, ScaRF can be used to study the scattering of any cold plasma RF wave. It can be for the study of scattering of electron cyclotron waves in ITER-type and medium-sized tokamaks such as TCV, ASDEX-U, DIII-D. For the case of medium-sized tokamaks, there's experimental evidence that drift waves and rippling modes are present in the edge region (see Ritz et al. 1984). Hence, we study the scattering of RF waves by periodic density interfaces (plasma gratings) in the form of a superposition of spatial modes with varying periodicity and random amplitudes (see Papadopoulos et al. 2019). The power reflection coefficient (a random variable) is calculated for different realizations of the density interface. In this work, the uncertainty of the power reflection coefficient is rigorously quantified by use of the Polynomial Chaos Expansion (see Xiu & Karniadakis 2002) method in conjunction with the Smolyak sparse grid integration (see Papadopoulos et al. 2018) (PCE-SG). The PCE-SG method is proven accurate and much more efficient (roughly 2-orders of magnitude shorter execution time) compared to alternative methods such as the Monte Carlo (MC) approach.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Quantum random number generators

Random number generators include a thermal optical source and detector configured to produce random numbers based on quantum-optical intensity fluctuations. An optical flux is detected, and signals proportional to optical intensity and a delayed optical intensity are combined. The combined signals can be electrical signals or optical signals, and the optical source is selected so as to have low coherence over a predetermined range of delay times. Balanced optical detectors can be used to reduce common mode noise, and in some examples, the optical flux is directed to only one of a pair of balanced detectors.

97 MATHEMATICS AND COMPUTING↗

Quantum random number generator

A system and method are provided to yield a QRNG based on homodyne detection of quantum noise (e.g., vacuum noise measured as shot noise) generated from a local oscillator, such as an LED. In one embodiment, a QRNG may be provided that is adjustable based on a control input to produce a random output that can be translated to one or more random data bits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Machine Learning Methods for Connection RTT and Loss Rate Estimation Using MPI Measurements Under Random Losses

Scientific computations are expected to be increasingly distributed across wide-area networks, and Message Passing Interface (MPI) has been shown to scale to support their communications over long distances. Application-level measurements of MPI operations reflect the connection Round-Trip Time (RTT) and loss rate, and machine learningmethods have been previously developed to estimate them under deterministic periodic losses. In this paper, we consider more complex, random losses with uniform, Poisson and Gaussian distributions. We study five disparate machine leaning methods, with linear and non-linear, and smooth and non-smooth properties, to estimate RTT and loss rate over 10 Gbps connections with 0–366 ms RTT. The diversity and complexity of these estimators combined with the randomness of losses and TCP’s non-linear response together rule out the selection of a single best among them; instead, we fuse them to retain their design diversity. Overall, the results show that accurate estimates can be generated at low loss ratesbut become inaccurate at loss rates 10% and higher, thereby illustrating both their strengths and limitations.

Rao, Nageswara S.↗

Random filters for enriching the discriminatory power of topological representations

Topological representations of data are inherently coarse summaries which endows them with certain desirable properties like stability but also potentially inhibits their discriminatory power relative to fine-scale learned features. In this work we present a novel framework for enriching the discriminatory power of topological representations based on random filters and capturing ``interference topology'' rather than direct topology. We show that our random filters outperform previously explored structured image filters while requiring orders of magnitude less computational time. The approach is demonstrated on the MNIST dataset but is broadly applicable across data sets and modalities. This work is concluded with a discussion of the mathematical intuition underlying the approach and identification of future directions to enable deeper understanding and theoretical results.

Jorgenson, Grayson S.↗

Random Filters for Enriching the Discriminatory Power of Topological Representations

Topological representations of data are inherently coarse summaries which endows them with certain desirable properties like stability but also potentially inhibits their discriminatory power relative to fine-scale learned features. In this work we present a novel framework for enriching the discriminatory power of topological representations based on random filters and capturing "interference topology'' rather than direct topology. We show that our random filters outperform previously explored structured image filters while requiring orders of magnitude less computational time. The approach is demonstrated on the MNIST dataset but is broadly applicable across data sets and modalities. This work is concluded with a discussion of the mathematical intuition underlying the approach and identification of future directions to enable deeper understanding and theoretical results.

Jorgenson, Grayson S.↗

Arbiter with random tie breaking

Candidates for selection in a weighted arbitration system are assigned priority weights and random weights. The winning candidate is determined using a tree of selectors such as a comparators. At each stage of the tree, the candidate having the greatest priority weight is selected to pass to the next stage. If multiple candidates are tied for the greatest priority weight, the candidate having the greatest random weight is selected to pass to the next stage.

Lesartre, Gregg B.↗

The influence of random packed column parameters on the liquid holdup and interfacial area

Abstract Carbon dioxide capture via solvent absorption in packed columns has emerged as a potential technology to mitigate coal‐fired power plant CO 2 emissions. Parameters, including packing types, solvent properties, and operating conditions, could potentially affect the packed column CO 2 capture efficiency. To understand the importance of those parameters and help packed column optimization, a design of experiments (DoEs) method was proposed to generate input parameter matrix. Combined with multiphase computational fluid dynamics (CFD), the random packed column parameter influence on the liquid holdup and interfacial area can be efficiently investigated. Surrogate‐based sensitivity analysis shows that the solvent flow rate and contact angle are key factors dictating liquid holdup and interfacial area. On the other hand, solvent viscosity has a marginal impact on the interfacial area. The sensitivity scores were calculated for each input parameter to guide the selection of dimensionless numbers for the liquid holdup and interfacial area correlation development.

42 ENGINEERING↗

Modeling household-level party composition behavior for multiparty activities: a random parameter nested logit modeling approach

This study presents findings of a household-level party composition model for multiparty activities. It exploits data from a comprehensive Household Travel Survey conducted by Chicago Metropolitan Agency of Planning. The study estimates a random parameter nested logit model to capture households’ unobserved preference heterogeneity and non-proportional substitution patterns in terms of activity party composition for multiparty activities. A wide variety of household demographics, activity attributes and residential neighborhood characteristics are examined in this paper. The magnitude of the impacts of the determinants are tested in this study by analyzing the elasticity of the variables, which suggests that household demographics and attributes of the multiparty activities have significant effects on the household-level activity party composition. Residential neighborhood characteristics, although somewhat less impactful, still play a meaningful role. This model will be implemented within the POLARIS transportation systems simulator to improve the activity generation modeling workflow, and the prediction accuracy of various activity-travel components.

activity party composition↗

Seed classification with random forest models

Premise: To improve forest conservation monitoring, we developed a protocol to automatically count and identify the seeds of plant species with minimal resource requirements, making the process more efficient and less dependent on human operators. Methods and Results: Seeds from six North American conifer tree species were separated from leaf litter and imaged on a flatbed scanner. In the most successful species-classification approach, an ImageJ macro automatically extracted measurements for random forest classification in the software R. The method allows for good classification accuracy, and the same process can be used to train the model on other species. Conclusions: This protocol is an adaptable tool for efficient and consistent identification of seed species or potentially other objects. Automated seed classification is efficient and inexpensive, making it a practical solution that enhances the feasibility of large-scale monitoring projects in conservation biology.

59 BASIC BIOLOGICAL SCIENCES↗

A GPU Accelerated Mixed‐Precision Finite Difference Informed Random Walker (FDiRW) Solver for Strongly Inhomogeneous Diffusion Problems

In nature, many complex multi‐physics coupling problems exhibit significant diffusivity inhomogeneity, where one process occurs several orders of magnitude faster than others temporally. Simulating rapid diffusion alongside slower processes demands intensive computational resources due to the necessity for small time steps. To address these computational challenges, we have developed an efficient numerical solver named Finite Difference informed Random Walker (FDiRW). In this study, we propose a GPU‐accelerated, mixed‐precision configuration for the FDiRW solver to maximize efficiency through GPU multi‐threaded parallel computation and lower precision computation. Numerical evaluation results reveal that the proposed GPU‐accelerated mixed‐precision FDiRW solver can achieve a 117× speedup over the CPU baseline, while an additional 1.75× speedup is achieved by employing lower precision GPU computation. Notably, for large model sizes, the GPU‐accelerated mixed‐precision FDiRW solver demonstrates strong scaling with the number of nodes used in simulation. When simulating radionuclide absorption processes by porous wasteform particles with a medium‐sized model of 192 × 192 × 192, this approach reduces the total computational time to 10 min, enabling the simulation of larger systems with strongly inhomogeneous diffusivity.

97 MATHEMATICS AND COMPUTING↗

Effects of random forest modeling decisions on biogeochemical time series predictions

Abstract Random forests (RF) are an increasingly popular machine learning approach used to model biogeochemical processes in the Earth system. While RF models are robust to many assumptions that complicate deterministic models, there are several important parameterization decisions for appropriate use and optimal model fit. We explored the role that parameter decisions, including training/testing data splitting strategies, variable selection, and hyperparameters play on RF goodness‐of‐fit by constructing models using 1296 unique parameter combinations to predict concentrations of nitrate, a key nutrient for biogeochemical cycling in aquatic ecosystems. Models were built on long‐term, publicly available water quality and meteorology time series collected by the National Estuarine Research Reserve monitoring network for two contrasting ecosystems representing freshwater and brackish estuaries. We found that accounting for temporal dependence when splitting data into training and testing subsets was key for avoiding over‐estimation of model predictive power. In addition, variable selection, the ratio of training to testing data, and to a lesser degree, variables per split and number of trees, were significant parameters for optimizing RF goodness‐of‐fit. We also explored how model parameter decisions influenced interpretation of the relative importance of predictors to the model, and model predictor‐dependent variable relationships, with results suggesting that both data structure and model parameterization influence these factors. Because much of the current RF literature is written for the computational and statistical science communities, the primary goal of this study is to provide guidelines for aquatic scientists new to machine learning to apply RF techniques appropriately to aquatic biogeochemical datasets.

54 ENVIRONMENTAL SCIENCES↗

A mathematical assessment of the isolation random forest method for anomaly detection in big data

We present the mathematical analysis of the Isolation Random Forest Method (IRF Method) for anomaly detection, proposed by Liu F.T., Ting K.M. and Zhou Z. H. in their seminal work as a heuristic method for anomaly detection in Big Data. We prove that the IRF space can be endowed with a probability induced by the Isolation Tree algorithm (iTree). In this setting, the convergence of the IRF method is proved, using the Law of Large Numbers. Here, a couple of counterexamples are presented to show that the method is inconclusive and no certificate of quality can be given, when using it as a means to detect anomalies. Hence, an alternative version of the method is proposed whose mathematical foundation is fully justified. Furthermore, a criterion for choosing the number of sampled trees needed to guarantee confidence intervals of the numerical results is presented. Finally, numerical experiments are presented to compare the performance of the classic method with the proposed one.

97 MATHEMATICS AND COMPUTING↗

Identifying Nuclear Data Correlated Through Predicting Bias in Integral Experiments via Applying Principal Component Analysis to Random Forest

ABSTRACT Nuclear data (ND) are the input data for neutron‐transport simulations to answer questions related to nuclear technologies. Subsets of ND, here > 20,000 data points, are validated with respect to thousands of criticality experiments that represent various applications on a small scale. The aim of validation with these experiments is to find errors in ND or methods. The key challenge here is that several hundreds of ND are used to simulate one integral value. Hence, one cannot clearly identify what ND are leading to bias in criticality measurements. In fact, a mistake in one nuclear‐data observable can be compensated with an error in another, and the predicted criticality value would still be predicted in agreement with experimental data. Random forest (RF) was previously employed to predict bias in criticality measurements using sensitivities of simulated criticality experiments to ND. The SHapley Additive exPlanations (SHAP) metric was then applied to attribute the importance of each ND experiment and observable to bias prediction. This, however, did not highlight what ND were jointly related to predicting bias. This is important as it could inform us about where compensating errors in ND could hide. We tackle this shortcoming here by first decomposing the ND sensitivities to integral‐experiment simulations into principal components. Then we use principal component projections to predict bias via the RF and SHAP. The SHAP values and principal components are employed to reconstruct detailed SHAP values for each ND observable. We demonstrate that these extended SHAP bias predictions are more robust, less noisy, and more efficient. In addition, we show that this approach accounts for covariance in ND sensitivities and automates the identification of where compensating errors could hide in ND.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Randomized Preconditioned Solvers for Strong Constraint 4D-Var Data Assimilation

The Strong Constraint 4D Variational (SC-4DVAR) data assimilation method is widely used in climate and weather applications. SC-4DVAR involves solving a minimization problem to compute the maximum a posteriori estimate, which we tackle using the Gauss-Newton method. The computation of the descent direction is expensive since it involves the solution of a large-scale and potentially ill-conditioned linear system, solved using the preconditioned conjugate gradient (PCG) method. Here, to address this cost, we efficiently construct scalable preconditioners using three different randomization techniques, which all rely on a certain low-rank structure involving the Gauss-Newton Hessian. The proposed techniques come with theoretical guarantees on the condition number, and at the same time, are amenable to parallelization. We also develop an adaptive approach to estimate the sketch size and choose between the reuse or recomputation of the preconditioner. We demonstrate the performance and effectiveness of our methodology on two representative model problems—the Burgers and barotropic vorticity equation—showing a drastic reduction in both the number of PCG iterations and the number of Gauss-Newton Hessian products after including the preconditioner construction cost.

Gauss-Newton↗

Robust and optimal alignment of high-dimensional data using maximum likelihood estimation through a random sample consensus framework

Abstract Correcting spatial orientations of groups of high-dimensional data sets such that they are all in a consistent coordinate system is often a time-consuming and error-prone process. Automation of this process can be accomplished by using Generalized Procrustes Analysis to estimate the relative orientations among a population of high-dimensional data sets. A least squares Procrustes solution is applied through a maximum likelihood estimation and random sample consensus framework for robustness. The likelihood model is comprised of a mixture distribution where inliers are modeled using t -distribution and outliers from a uniform distribution. Applications will focus on a synthetic data set that emulates triaxial acceleration data and also real shock data from a population of triaxial accelerometers. Outliers represent either non-rigid body responses, environmental noise, and/or sensor and data acquisition issues. The intended application for the methodology is to robustly automate the rotation of populations of experimentally collected triaxial accelerometer data sets to a single global coordinate system.

LOSAC↗

Finite elements for Matérn-type random fields: Uncertainty in computational mechanics and design optimization

This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on prevalent applications in computational mechanics and design optimization. We leverage Matérn-type Gaussian random fields (GRFs) generated using the SPDE method to model aleatoric uncertainties, including environmental influences, variating material properties, and geometric ambiguities. Our focus lies on delivering practical GRF realizations that accurately capture imperfections and variations and understanding how they impact the predictions of computational models as well as the shape and topology of optimized designs. Here we describe a numerical algorithm based on solving a generalized SPDE to sample GRFs on arbitrary meshed domains. The algorithm leverages established techniques and integrates seamlessly with the open-source finite element library MFEM and associated scientific computing workflows, like those found in industrial and national laboratory settings. Our solver scales efficiently for large-scale problems and supports various domain types, including surfaces and embedded manifolds. We showcase its versatility through biomechanics and topology optimization applications, emphasizing the potential to influence these domains. The flexibility and efficiency of SPDE-based GRF generation empowers us to run large-scale optimization problems on 2D and 3D domains, including finding optimized designs on embedded surfaces, and to generate design features and topologies beyond the reach of conventional techniques. Moreover, these capabilities allow us to model and quantify geometric uncertainties on reconstructed submanifolds, such as the interpolated surfaces of cerebral aneurysms provided by postprocessing CT scans. In addition to offering benefits in these specific domains, the proposed techniques transcend specific applications and generalize to arbitrary forward and backward problems in uncertainty quantification involving finite elements.

97 MATHEMATICS AND COMPUTING↗

Genarris 2.0: A Random Structure Generator for Molecular Crystals

Genarris is an open source Python package for generating random molecular crystal structures with physical constraints for seeding crystal structure prediction algorithms and training machine learning models. Here we present a new version of the code, containing several major improvements. A MPI-based parallelization scheme has been implemented, which facilitates the seamless sequential execution of user-defined workflows. A new method for estimating the unit cell volume based on the single molecule structure has been developed using a machine-learned model trained on experimental structures. A new algorithm has been implemented for generating crystal structures with molecules occupying special Wyckoff positions. A new hierarchical structure check procedure has been developed to detect unphysical close contacts efficiently and accurately. New intermolecular distance settings have been implemented for strong hydrogen bonds. To demonstrate these new features, we study two specific cases: benzene and glycine. Genarris finds the experimental structures of the two polymorphs of benzene and the three polymorphs of glycine. Program summary Program Title: Genarris 2.0 Program Files doi: http://dx.doi.org/10.17632/grx6mz4pjn.1 Licensing provisions: BSD-3 Clause Programming language: Python, C External routines/libraries: Spglib, ASE, pymatgen, SciPy, mpi4py, scikit-learn, PyTorch, FHI-aims. Nature of problem: Molecular crystal structure prediction. Solution method: Genarris 2.0 generates molecular crystal structures over the 230 space groups, on general and special Wyckoff positions, using physical constraints. Down-sampling of the generated structures may be performed subsequently, based on molecular crystal packing descriptors and an unsupervised machine learning algorithm. Lastly, ab initio structure relaxation may be performed for the final pool. Depending on the user-defined workflow implemented, Genarris may be used to generate diverse molecular crystal datasets to seed evolutionary algorithms or to train machine learning algorithms or as a standalone crystal structure prediction method. Restrictions: For crystal structure generation, the molecule of interest must be semi-rigid with no bond rotational degrees of freedom. Unusual features: Genarris 2.0 is a highly distributed program, making use of MPI for Python parallelization. The user has the ability to design and implement workflows by executing a user-defined list of procedures. Genarris 2.0 offers new features including a machine learning model for estimating the molecular volume in the solid state from the single molecule structure, structure generation in special Wyckoff positions of space groups, hierarchical structure checks including rigorous treatment of non-orthogonal structures, and clustering and down-selection workflows combining first principles simulations with machine learning. (C) 2020 Elsevier B.V. All rights reserved.

Crystal structure prediction↗