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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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At least 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

MOCUM: A two-dimensional method of characteristics code based on unstructured meshing for general geometries

A transport theory code MOCUM based on the Method of Characteristics (MOC) as the flux solver with an advanced general geometry processor is developed for two-dimensional lattice and full core neutronics modeling. The core structure is represented by Constructive Solid Geometry (CSG) that uses Boolean operations to build complex geometries from simple polygons. Arbitrary-precision arithmetic is also used in the process of building CSG objects to eliminate the round-off error from the commonly used double precision numbers. Then, the constructed core frame will be decomposed and refined into a conforming Delaunay triangulation to ensure the quality of the meshes. The MOC solver kernel is fully paralleled using OpenMP and the developed numerical code is validated by several benchmarks representing various core geometries. For the cases modeled, the maximum percentage error for multiplication factor and the pin power compared to reference values are 0.1% and 0.7% respectively. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2015

TU-G-204-05: The Effects of CT Acquisition and Reconstruction Conditions On Computed Texture Feature Values of Lung Lesions

Purpose: Texture features have been investigated as a biomarker of response and malignancy. Because these features reflect local differences in density, they may be influenced by acquisition and reconstruction parameters. The purpose of this study was to investigate the effects of radiation dose level and reconstruction method on features derived from lung lesions. Methods: With IRB approval, 33 lung tumor cases were identified from clinically indicated thoracic CT scans in which the raw projection (sinogram) data were available. Based on a previously-published technique, noise was added to the raw data to simulate reduced-dose versions of each case at 25%, 10% and 3% of the original dose. Original and simulated reduced dose projection data were reconstructed with conventional and two iterative-reconstruction settings, yielding 12 combinations of dose/recon conditions. One lesion from each case was contoured. At the reference condition (full dose, conventional recon), 17 lesions were randomly selected for repeat contouring (repeatability). For each lesion at each dose/recon condition, 151 texture measures were calculated. A paired differences approach was employed to compare feature variation from repeat contours at the reference condition to the variation observed in other dose/recon conditions (reproducibility). The ratio of standard deviation of the reproducibility to repeatability was used as the variation measure for each feature. Results: The mean variation (standard deviation) across dose levels and kernel was significantly different with a ratio of 2.24 (±5.85) across texture features (p=0.01). The mean variation (standard deviation) across dose levels with conventional recon was also significantly different with 2.30 (7.11) (p=0.025). The mean variation across reconstruction settings of original dose has a trend in showing difference with 1.35 (2.60) among all features (p=0.09). Conclusion: Texture features varied considerably with variations in dose and reconstruction condition. Care should be taken to standardize these conditions when using texture as a quantitative feature. This effort supported in part by a grant from the National Cancer Institute’s Quantitative Imaging Network (QIN): U01 CA181156; The UCLA Department of Radiology has a Master Research Agreement with Siemens Healthcare; Dr. McNitt-Gray has previously received research support from Siemens Healthcare.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Hybrid programming-model strategies for GPU offloading of electronic structure calculation kernels

To address the challenge of performance portability and facilitate the implementation of electronic structure solvers, we developed the basic matrix library (BML) and Parallel, Rapid O(N), and Graph-based Recursive Electronic Structure Solver (PROGRESS) library. The BML implements linear algebra operations necessary for electronic structure kernels using a unified user interface for various matrix formats (dense and sparse) and architectures (CPUs and GPUs). Focusing on density functional theory and tight-binding models, PROGRESS implements several solvers for computing the single-particle density matrix and relies on BML. In this paper, we describe the general strategies used for these implementations on various computer architectures, using OpenMP target functionalities on GPUs, in conjunction with third-party libraries to handle performance critical numerical kernels. In this study, we demonstrate the portability of this approach and its performance in benchmark problems.

36 MATERIALS SCIENCE↗
DOE OSTI2025

On the discretization error of the discrete generalized quantum master equation

The transfer tensor method (TTM) [Cerrillo and Cao, Phys. Rev. Lett. 112 , 110401 (2014)] can be considered a discrete-time formulation of the Nakajima–Zwanzig quantum master equation (NZ-QME) for modeling non-Markovian quantum dynamics. A recent paper [Makri, J. Chem. Theory Comput. 21 , 5037 (2025)] raised concerns regarding the consistency of the TTM discretization, particularly a spurious term at the initial time t = 0. Here, this work presents a detailed analysis of the discretization structure of the TTM, clarifying the origin of the initial-time correction and establishing a consistent relationship between the TTM discrete-time memory kernel K N and the continuous-time NZ-QME kernel $\mathscr{K}$( N Δ t ). This relationship is validated numerically using the spin-boson model, demonstrating convergence of reconstructed memory kernels and accurate dynamical evolution as Δ t → 0. While the TTM provides a consistent discretization, we note that alternative schemes are also viable, such as the midpoint derivative/midpoint integral scheme proposed in Makri’s work. The relative performance of various schemes for either computing accurate $\mathscr{K}$( N Δ t ) from exact dynamics or obtaining accurate dynamics from exact $\mathscr{K}$( N Δ t ) warrants further investigation.

Density-matrix↗
DOE OSTI2021

Accelerating Multigrid-based Hierarchical Scientific Data Refactoring on GPUs

Rapid growth in scientific data and a widening gap between computational speed and I/O bandwidth make it increasingly infeasible to store and share all data produced by scientific simulations. Instead, we need methods for reducing data volumes: ideally, methods that can scale data volumes adaptively so as to enable negotiation of performance and fidelity tradeoffs in different situations. Multigrid-based hierarchical data representations hold promise as a solution to this problem, allowing for flexible conversion between different fidelities so that, for example, data can be created at high fidelity and then transferred or stored at lower fidelity via logically simple and mathematically sound operations. However, the effective use of such representations has been hindered until now by the relatively high costs of creating, accessing, reducing, and otherwise operating on such representations. We describe here highly optimized data refactoring kernels for GPU accelerators that enable efficient creation and manipulation of data in multigrid-based hierarchical forms. We demonstrate that our optimized design can achieve up to 250 TB/s aggregated data refactoring throughput—83% of theoretical peak—on 1024 nodes of the Summit supercomputer. We showcase our optimized design by applying it to a large-scale scientific visualization workflow and the MGARD lossy compression software.

Data refactoring↗
NASA NTRS1972

Common radiation analysis model for 75,000 pound thrust NERVA engine (1137400E)

The mathematical model and sources of radiation used for the radiation analysis and shielding activities in support of the design of the 1137400E version of the 75,000 lbs thrust NERVA engine are presented. The nuclear subsystem (NSS) and non-nuclear components are discussed. The geometrical model for the NSS is two dimensional as required for the DOT discrete ordinates computer code or for an azimuthally symetrical three dimensional Point Kernel or Monte Carlo code. The geometrical model for the non-nuclear components is three dimensional in the FASTER geometry format. This geometry routine is inherent in the ANSC versions of the QAD and GGG Point Kernal programs and the COHORT Monte Carlo program. Data are included pertaining to a pressure vessel surface radiation source data tape which has been used as the basis for starting ANSC analyses with the DASH code to bridge into the COHORT Monte Carlo code using the WANL supplied DOT angular flux leakage data. In addition to the model descriptions and sources of radiation, the methods of analyses are briefly described.

Warman, E. A.↗
DOE OSTI2021

Accelerating Multigrid-based Hierarchical Scientific Data Refactoring on GPUs

Rapid growth in scientific data and a widening gap between computational speed and I/O bandwidth make it increasingly infeasible to store and share all data produced by scientific simulations. Instead, we need methods for reducing data volumes: ideally, methods that can scale data volumes adaptively so as to enable negotiation of performance and fidelity tradeoffs in different situations. Multigrid-based hierarchical data representations hold promise as a solution to this problem, allowing for flexible conversion between different fidelities so that, for example, data can be created at high fidelity and then transferred or stored at lower fidelity via logically simple and mathematically sound operations. However, the effective use of such representations has been hindered until now by the relatively high costs of creating, accessing, reducing, and otherwise operating on such representations. We describe here highly optimized data refactoring kernels for GPU accelerators that enable efficient creation and manipulation of data in multigrid-based hierarchical forms. We demonstrate that our optimized design can achieve up to 250 TB/s aggregated data refactoring throughput—83% of theoretical peak—on 1024 nodes of the Summit supercomputer. We showcase our optimized design by applying it to a large-scale scientific visualization workflow and the MGARD lossy compression software.

Chen, Jieyang↗
DOE OSTI2019

Improving Precipitation Estimation Using Convolutional Neural Network

Precipitation process is generally considered to be poorly represented in numerical weather/climate models. Statistical downscaling (SD) methods, which relate precipitation with model resolved dynamics, often provide more accurate precipitation estimates compared to model's raw precipitation products. Herein we introduce the convolutional neural network model to foster this aspect of SD for daily precipitation prediction. Specifically, we restrict the predictors to the variables that are directly resolved by discretizing the atmospheric dynamics equations. In this sense, our model works as an alternative to the existing precipitation-related parameterization schemes for numerical precipitation estimation. We train the model to learn precipitation-related dynamical features from the surrounding dynamical fields by optimizing a hierarchical set of spatial convolution kernels. We test the model at 14 geogrid points across the contiguous United States. Results show that provided with enough data, precipitation estimates from the convolutional neural network model outperform the reanalysis precipitation products, as well as SD products using linear regression, nearest neighbor, random forest, or fully connected deep neural network. Evaluation for the test set suggests that the improvements can be seamlessly transferred to numerical weather modeling for improving precipitation prediction. Based on the default network, we examine the impact of the network architectures on model performance. Also, we offer simple visualization and analyzing approaches to interpret the models and their results. Our study contributes to the following two aspects: First, we offer a novel approach to enhance numerical precipitation estimation; second, the proposed model provides important implications for improving precipitation-related parameterization schemes using a data-driven approach.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

WE-FG-207B-10: Dual-Energy CT Monochromatic Image Consistency Across Vendors and Platforms

Purpose: Although dual-energy CT provides improved sensitivity of HU for certain tissue types at lower simulated energy levels, if these values vary by scanner type they may impact clinical patient management decisions. Each manufacturer has selected a specific dual-energy CT approach (or in one case, three different approaches); understanding HU variability among low monochromatic images may be required when more than one dual-energy CT scanner type is available for use. Methods: A large elliptical dualenergy quality control phantom (Gammex Inc.; Middleton, WI) containing several standard tissue type materials was scanned at least three times on each of the following systems: GE HD750, prototype GE Revolution CT with GSI, Siemens Flash, Siemens Edge, Siemens AS 128, and Philips IQon. Images were generated at 50, 70, and 140 keV. Soft tissue and Iodine HU were measured on a single central 5mm-thick image; NIST constants were used to calculate the ideal HU for each material. Scan acquisitions were approximately dose-matched (∼25mGy CTDIvol) and image parameters were held as consistent as possible (thickness, kernel, no noise reduction). Results: Measured soft tissue (29 HU at 120 kVp) varied from 28 HU to 44 HU at 50 keV (excluding one outlier), from 21 HU to 31 HU at 70 keV, and from 19 HU to 32 HU at 140 keV. Measured iodine (5mg/ml, 106 HU at 120 kVp) varied from 246 HU to 280 HU at 50 keV, from 123 HU to 129 HU at 70 keV, and from 22 HU to 32 HU at 140 keV. Conclusion: Measured HU in standard rods across 3 dual-energy CT manufacturers and 6 scanner models varied directly with monochromatic level, with the most variability was observed at 50 keV and least variability at 70keV. Future work will include additional scanner platforms and how measurement variability impacts radiologists. This research has been supported by funds from Dr. William Murphy, Jr., the John S. Dunn, Sr. Distinguished Chair in Diagnostic Imaging at MD Anderson Cancer Center.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Accelerating Random Forest Classification on GPU and FPGA

Random Forests (RFs) are a commonly used machine learning method for classification and regression tasks spanning a variety of application domains, including bioinformatics, business analytics, and software optimization. While prior work has focused primarily on improving performance of the training of RFs, many applications, such as malware identification, cancer prediction, and banking fraud detection, require fast RF classification. In this work, we accelerate RF classification on GPU and FPGA. In order to provide efficient support for large datasets, we propose a hierarchical memory layout suitable to the GPU/FPGA memory hierarchy. We design three RF classification code variants based on that layout, and we investigate GPU- and FPGA-specific considerations for these kernels. Our experimental evaluation, performed on an Nvidia Xp GPU and on a Xilinx Alveo U250 FPGA accelerator card using publicly available datasets on the scale of millions of samples and tens of features, covers various aspects. First, we evaluate the performance benefits of our hierarchical data structure over the standard compressed sparse row (CSR) format. Second, we compare our GPU implementation with cuML, a machine learning library targeting Nvidia GPUs. Third, we explore the performance/accuracy tradeoff resulting from the use of different tree depths in the RF. Finally, we perform a comparative performance analysis of our GPU and FPGA implementations. Our evaluation shows that for high accuracy targets, our GPU implementation yields 5-9x speedup over CSR, and up to a 2x speedup over cuML.

FPGA, Xilinx FPGA, GPU, Random Forest classificati↗
NASA NTRS1990

Domain decomposition methods in aerodynamics

Compressible Euler equations are solved for two-dimensional problems by a preconditioned conjugate gradient-like technique. An approximate Riemann solver is used to compute the numerical fluxes to second order accuracy in space. Two ways to achieve parallelism are tested, one which makes use of parallelism inherent in triangular solves and the other which employs domain decomposition techniques. The vectorization/parallelism in triangular solves is realized by the use of a recording technique called wavefront ordering. This process involves the interpretation of the triangular matrix as a directed graph and the analysis of the data dependencies. It is noted that the factorization can also be done in parallel with the wave front ordering. The performances of two ways of partitioning the domain, strips and slabs, are compared. Results on Cray YMP are reported for an inviscid transonic test case. The performances of linear algebra kernels are also reported.

Venkatakrishnan, V.↗
DOE OSTI2023

Exploring temporal community evolution: algorithmic approaches and parallel optimization for dynamic community detection

Abstract Dynamic (temporal) graphs are a convenient mathematical abstraction for many practical complex systems including social contacts, business transactions, and computer communications. Community discovery is an extensively used graph analysis kernel with rich literature for static graphs. However, community discovery in a dynamic setting is challenging for two specific reasons. Firstly, the notion of temporal community lacks a widely accepted formalization, and only limited work exists on understanding how communities emerge over time. Secondly, the added temporal dimension along with the sheer size of modern graph data necessitates new scalable algorithms. In this paper, we investigate how communities evolve over time based on several graph metrics under a temporal formalization. We compare six different algorithmic approaches for dynamic community detection for their quality and runtime. We identify that a vertex-centric (local) optimization method works as efficiently as the classical modularity-based methods. To its advantage, such local computation allows for the efficient design of parallel algorithms without incurring a significant parallel overhead. Based on this insight, we design a shared-memory parallel algorithm DyComPar , which demonstrates between 4 and 18 fold speed-up on a multi-core machine with 20 threads, for several real-world and synthetic graphs from different domains.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

FD-TD modeling of 2-D dielectric waveguides for propagation and scattering of femtosecond optical solitons

Experimentalists have produced all-optical switches capable of 100-fs responses. To adequately model such switches, nonlinear effects in optical materials (both instantaneous and dispersive) must be included. In principle, the behavior of electromagnetic fields in nonlinear dielectrics can be determined by solving Maxwell's equations subject to the assumption that the electric polarization has a nonlinear relation to the electric field. However, until our previous work, the resulting nonlinear Maxwell's equations have not been solved directly. Rather, approximations have been made that result in a class of generalized nonlinear Schrodinger equations (GNLSE) that solve only for the envelope of the optical pulses. In this paper, we present first-time calculations from the vector nonlinear Maxwell's equations of femtosecond soliton propagation and scattering, including carrier waves, in two-dimensional systems of dielectric waveguides exhibiting the Kerr and Raman quantum effects. We use the finite-difference time-domain (FD-TD) method in an extension of our 1-D work. There, in a fundamental innovation, we treated the linear and nonlinear convolutions for the electric polarization as new dependent variables. By differentiating these convolutions in the time domain, we derived an equivalent system of coupled, nonlinear second-order ODE's. These equations together with Maxwell's equations form the system that is solved to determine the electromagnetic fields in inhomogeneous nonlinear dispersive media. Backstorage in time is limited to only that needed by the time-integration algorithm for the ODE's, rather than that needed to store the time-history of the kernel functions of the convolutions (1000-10,000 time steps). Thus, a 2-D nonlinear optics model from Maxwell's equations is now feasible.

Joseph, Rose↗
NASA NTRS2019

IKOS: Sound Static Program Analysis

IKOS (Inference Kernel for Open Static Analyzers) is a static analyzer for C/C++ based on the theory of Abstract Interpretation. It can detect or prove the absence of runtime errors (e.g, buffer overflows, integer overflows, null pointer dereferences, etc.) in the source code. IKOS uses Abstract Interpretation techniques to compute an over-approximation of all the reachable states of the program, thus it cannot miss a bug. In this talk, I will give an overview of the tool, then show how to apply it to a large software. I will present ikos-view, a web interface to examine the analysis results. I will discuss about methods to improve the analysis, such as adding code annotations, modeling library functions, and avoiding specific code patterns.

Arthaud, Maxime↗
DOE OSTI2016

WE-FG-207B-08: Dual-Energy CT Iodine Accuracy Across Vendors and Platforms

Purpose: Although a major benefit of dual-energy CT is its quantitative capabilities, it is critical to understand how results vary by scanner manufacturer and/or model before making clinical patient management decisions. Each manufacturer utilizes a specific dual-energy CT approach; cross-calibration may be required for facilities with more than one dual-energy CT scanner type. Methods: A solid dual-energy quality control phantom (Gammex, Inc.; Appleton, WI) representing a large body cross-section containing three Iodine inserts (2mg/ml, 5mg/ml, 15 mg/ml) was scanned on these CT systems: GE HD-750 (80/140kVp), prototype GE Revolution CT with GSI (80/140kVp), Siemens Flash (80/140kVp and 100/140kVp), and Philips IQon (120kVp and 140kVp). Iodine content was measured in units of concentration (mg/ml) from a single 5mm-thick central image. Three to five acquisitions were performed on each scanner platform in order to compute standard deviation. Scan acquisitions were approximately dose-matched (∼25mGy CTDIvol) and image parameters were as consistent as possible (thickness, kernel, no noise reduction applied). Results: Iodine measurement error ranges were −0.24-0.16 mg/ml for the 2mg/ml insert (−12.0 − 8.0%), −0.28–0.26 mg/ml for the 5mg/ml insert (−5.6 − 5.2%), and −1.16−0.99 mg/ml for the 15mg/ml insert (−7.7 − 6.6%). Standard deviations ranged from 0 to 0.19 mg/ml for the repeated acquisitions from each scanner. The average iodine measurement error and standard deviation across all systems and inserts was −0.21 ± 0.48 mg/ml (−1.5 ± 6.48%). The largest absolute measurement error was found in the 15mg/ml iodine insert. Conclusion: There was generally good agreement in Iodine quantification across 3 dual-energy CT manufacturers and 4 scanner models. This was unexpected given the widely different underlying dual-energy CT mechanisms employed. Future work will include additional scanner platforms, independent verification of the Iodine insert standard concentrations (especially the 15 mg/ml insert), and how much measurement variability can be clinically tolerated. This research has been supported by funds from Dr. William Murphy, Jr., the John S. Dunn, Sr. Distinguished Chair in Diagnostic Imaging at MD Anderson Cancer Center.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

An actuarial approach to retrofit savings in buildings

An actuarial method has been developed for determining energy savings from retrofits from energy use data for a number of buildings. This method should be contrasted with the traditional method of using pre- and post-retrofit data on the same building. This method supports the U.S. Department of Energy Building Performance Database of real building performance data and related tools that enable engineering and financial practitioners to evaluate retrofits. The actuarial approach derives, from the database, probability density functions (PDFs) for energy savings from retrofits by creating peer groups for the user’s pre post buildings. From the energy use distribution of the two groups, the savings PDF is derived. This provides the basis for engineering analysis as well as financial risk analysis leading to investment decisions. Several technical issues are addressed: The savings PDF is obtained from the pre- and post-PDF through a convolution. Smoothing using kernel density estimation is applied to make the PDF more realistic. The low data density problem can be mitigated through a neighborhood methodology. Correlations between pre and post buildings are addressed to improve the savings PDF. Sample size effects are addressed through the Kolmogorov--Smirnov tests and quantile-quantile plots.

Subbarao, Krishnappa↗
DOE OSTI2014

Adaptive nonlocal means filtering based on local noise level for CT denoising

Purpose: To develop and evaluate an image-domain noise reduction method based on a modified nonlocal means (NLM) algorithm that is adaptive to local noise level of CT images and to implement this method in a time frame consistent with clinical workflow. Methods: A computationally efficient technique for local noise estimation directly from CT images was developed. A forward projection, based on a 2D fan-beam approximation, was used to generate the projection data, with a noise model incorporating the effects of the bowtie filter and automatic exposure control. The noise propagation from projection data to images was analytically derived. The analytical noise map was validated using repeated scans of a phantom. A 3D NLM denoising algorithm was modified to adapt its denoising strength locally based on this noise map. The performance of this adaptive NLM filter was evaluated in phantom studies in terms of in-plane and cross-plane high-contrast spatial resolution, noise power spectrum (NPS), subjective low-contrast spatial resolution using the American College of Radiology (ACR) accreditation phantom, and objective low-contrast spatial resolution using a channelized Hotelling model observer (CHO). Graphical processing units (GPU) implementation of this noise map calculation and the adaptive NLM filtering were developed to meet demands of clinical workflow. Adaptive NLM was piloted on lower dose scans in clinical practice. Results: The local noise level estimation matches the noise distribution determined from multiple repetitive scans of a phantom, demonstrated by small variations in the ratio map between the analytical noise map and the one calculated from repeated scans. The phantom studies demonstrated that the adaptive NLM filter can reduce noise substantially without degrading the high-contrast spatial resolution, as illustrated by modulation transfer function and slice sensitivity profile results. The NPS results show that adaptive NLM denoising preserves the shape and peak frequency of the noise power spectrum better than commercial smoothing kernels, and indicate that the spatial resolution at low contrast levels is not significantly degraded. Both the subjective evaluation using the ACR phantom and the objective evaluation on a low-contrast detection task using a CHO model observer demonstrate an improvement on low-contrast performance. The GPU implementation can process and transfer 300 slice images within 5 min. On patient data, the adaptive NLM algorithm provides more effective denoising of CT data throughout a volume than standard NLM, and may allow significant lowering of radiation dose. After a two week pilot study of lower dose CT urography and CT enterography exams, both GI and GU radiology groups elected to proceed with permanent implementation of adaptive NLM in their GI and GU CT practices. Conclusions: This work describes and validates a computationally efficient technique for noise map estimation directly from CT images, and an adaptive NLM filtering based on this noise map, on phantom and patient data. Both the noise map calculation and the adaptive NLM filtering can be performed in times that allow integration with clinical workflow. The adaptive NLM algorithm provides effective denoising of CT data throughout a volume, and may allow significant lowering of radiation dose.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2014

A probabilistic graphical model based stochastic input model construction

Model reduction techniques have been widely used in modeling of high-dimensional stochastic input in uncertainty quantification tasks. However, the probabilistic modeling of random variables projected into reduced-order spaces presents a number of computational challenges. Due to the curse of dimensionality, the underlying dependence relationships between these random variables are difficult to capture. In this work, a probabilistic graphical model based approach is employed to learn the dependence by running a number of conditional independence tests using observation data. Thus a probabilistic model of the joint PDF is obtained and the PDF is factorized into a set of conditional distributions based on the dependence structure of the variables. The estimation of the joint PDF from data is then transformed to estimating conditional distributions under reduced dimensions. To improve the computational efficiency, a polynomial chaos expansion is further applied to represent the random field in terms of a set of standard random variables. This technique is combined with both linear and nonlinear model reduction methods. Numerical examples are presented to demonstrate the accuracy and efficiency of the probabilistic graphical model based stochastic input models. - Highlights: • Data-driven stochastic input models without the assumption of independence of the reduced random variables. • The problem is transformed to a Bayesian network structure learning problem. • Examples are given in flows in random media.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗