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DOE OSTI2019

GMLS-Nets: Scientific Machine Learning Methods for Unstructured Data

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and invariances. We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS). GMLS is a nonparametric technique for estimating linear bounded functionals from scattered data, and has recently been used in the literature for solving partial differential equations. By parameterizing the GMLS estimator, we obtain learning methods for operators with unstructured stencils. In GMLS-Nets the necessary calculations are local, readily parallelizable, and the estimator is supported by a rigorous approximation theory. We show how the framework may be used for unstructured physical data sets to perform functional regression to identify associated differential operators and to regress quantities of interest. The results suggest the architectures to be an attractive foundation for data-driven model development in scientific machine learning applications

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

GMLS-Nets: A Framework for Learning from Unstructured Data

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and invariances. We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS). GMLS is a non-parametric technique for estimating linear bounded functionals from scattered data, and has recently been used in the literature for solving partial differential equations. By parameterizing the GMLS estimator, we obtain learning methods for operators with unstructured stencils. In GMLS-Nets the necessary calculations are local, readily parallelizable, and the estimator is supported by a rigorous approximation theory. We show how the framework may be used for unstructured physical data sets to perform functional regression to identify associated differential operators and to regress quantities of interest. The results suggest the architectures to be an attractive foundation for data-driven model development in scientific machine learning applications

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

Mean Winds and Tides over Urbana, Illinois During November 16-22, 1981

The Urbana Meteor Radar uses a high power pulse transmitter to achieve high echo rates, and an interferometer to spatially locate the individual echoes. The irregularly spaced observations of range, radial velocity, and direction cosines are reduced to a rectangular grid, evenly spaced in time and height, of estimates of the zonal and meridional wind. This is accomplished using the method of GROVES whereby a constant horizontal wind is fitted, using least squares, to all echoes occurring within a fixed time/height interval. This interpolation region is then stepped in time and height. the size of the interpolation region is 2 hours by 5 km, the time step is approximately 11 minutes, and the height step is 2 km. The filtering of high temporal and spatial frequencies is somewhat reduced by weighting the echoes according to their distance from the center of the interpolation box.

Tetenbaum, D.↗

DOE OSTI2014

An Adaptive Memory Interface Controller for Improving Bandwidth Utilization of Hybrid and Reconfigurable Systems

Emerging applications such as data mining, bioinformatics, knowledge discovery, social network analysis are irregular. They use data structures based on pointers or linked lists, such as graphs, unbalanced trees or unstructures grids, which generates unpredictable memory accesses. These data structures usually are large, but difficult to partition. These applications mostly are memory bandwidth bounded and have high synchronization intensity. However, they also have large amounts of inherent dynamic parallelism, because they potentially perform a task for each one of the element they are exploring. Several efforts are looking at accelerating these applications on hybrid architectures, which integrate general purpose processors with reconfigurable devices. Some solutions, which demonstrated significant speedups, include custom-hand tuned accelerators or even full processor architectures on the reconfigurable logic. In this paper we present an approach for the automatic synthesis of accelerators from C, targeted at irregular applications. In contrast to typical High Level Synthesis paradigms, which construct a centralized Finite State Machine, our approach generates dynamically scheduled hardware components. While parallelism exploitation in typical HLS-generated accelerators is usually bound within a single execution flow, our solution allows concurrently running multiple execution flow, thus also exploiting the coarser grain task parallelism of irregular applications. Our approach supports multiple, multi-ported and distributed memories, and atomic memory operations. Its main objective is parallelizing as many memory operations as possible, independently from their execution time, to maximize the memory bandwidth utilization. This significantly differs from current HLS flows, which usually consider a single memory port and require precise scheduling of memory operations. A key innovation of our approach is the generation of a memory interface controller, which dynamically maps concurrent memory accesses to multiple ports. We present a case study on a typical irregular kernel, Graph Breadth First search (BFS), exploring different tradeoffs in terms of parallelism and number of memories.

BFS↗

DOE OSTI2022

Calibrating constitutive models with full‐field data via physics informed neural networks

Abstract The calibration of solid constitutive models with full‐field experimental data is a long‐standing challenge, especially in materials that undergo large deformations. In this paper, we propose a physics‐informed deep‐learning framework for the discovery of hyperelastic constitutive model parameterizations given full‐field surface displacement data and global force‐displacement data. Contrary to the majority of recent literature in this field, we work with the weak form of the governing equations rather than the strong form to impose physical constraints upon the neural network predictions. The approach presented in this paper is computationally efficient, suitable for irregular geometric domains, and readily ingests displacement data without the need for interpolation onto a computational grid. A selection of canonical hyperelastic material models suitable for different material classes is considered including the Neo–Hookean, Gent, and Blatz–Ko constitutive models as exemplars for general non‐linear elastic behaviour, elastomer behaviour with finite strain lock‐up, and compressible foam behaviour, respectively. We demonstrate that physics informed machine learning is an enabling technology and may shift the paradigm of how full‐field experimental data are utilized to calibrate constitutive models under finite deformations.

Hamel, Craig M.↗

DOE OSTI2018

Adaptive Wavelet Decomposition of Matrix Flows

Adaptive algorithms for constructing spline-wavelet decompositions of matrix flows from a linear space of matrices over a normed field are presented. The algorithms suggested provides for an a priori prescribed estimate of the deviation of the basic flow from the initial one. Comparative bounds of the volumes of data in the basic flow for various irregularity characteristics of the initial flow are obtained in the cases of pseudo-equidistant and adaptive grids. Limit characteristics of the above-mentioned volumes are given in the cases where the initial flow is generated by differentiable functions.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2001

Design of Unstructured Adaptive (UA) NAS Parallel Benchmark Featuring Irregular, Dynamic Memory Accesses

We describe the design of a new method for the measurement of the performance of modern computer systems when solving scientific problems featuring irregular, dynamic memory accesses. The method involves the solution of a stylized heat transfer problem on an unstructured, adaptive grid. A Spectral Element Method (SEM) with an adaptive, nonconforming mesh is selected to discretize the transport equation. The relatively high order of the SEM lowers the fraction of wall clock time spent on inter-processor communication, which eases the load balancing task and allows us to concentrate on the memory accesses. The benchmark is designed to be three-dimensional. Parallelization and load balance issues of a reference implementation will be described in detail in future reports.

Feng, Hui-Yu↗

NASA NTRS2011

Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow

The proposed paper reports advances in developing a method for high Reynolds number compressible viscous flow simulations using a Cartesian cut-cell method with embedded boundaries. This preliminary work focuses on accuracy of the discretization near solid wall boundaries. A model problem is used to investigate the accuracy of various difference stencils for second derivatives and to guide development of the discretization of the viscous terms in the Navier-Stokes equations. Near walls, quadratic reconstruction in the wall-normal direction is used to mitigate mesh irregularity and yields smooth skin friction distributions along the body. Multigrid performance is demonstrated using second-order coarse grid operators combined with second-order restriction and prolongation operators. Preliminary verification and validation for the method is demonstrated using flat-plate and airfoil examples at compressible Mach numbers. Simulations of flow on laminar and turbulent flat plates show skin friction and velocity profiles compared with those from boundary-layer theory. Airfoil simulations are performed at laminar and turbulent Reynolds numbers with results compared to both other simulations and experimental data

Berger, Marsha↗

NASA NTRS1990

A numerical study of hypersonic stagnation heat transfer predictions at a coordinate singularity

The problem of grid induced errors associated with a coordinate singularity on heating predictions in the stagnation region of a three-dimensional body in hypersonic flow is examined. The test problem is for Mach 10 flow over an Aeroassist Flight Experiment configuration. This configuration is composed of an elliptic nose, a raked elliptic cone, and a circular shoulder. Irregularities in the heating predictions in the vicinity of the coordinate singularity, located at the axis of the elliptic nose near the stagnation point, are examined with respect to grid refinement and grid restructuring. The algorithm is derived using a finite-volume formulation. An upwind-biased total-variation diminishing scheme is employed for the inviscid flux contribution, and central differences are used for the viscous terms.

Grasso, Francesco↗

DOE OSTI2014

Scaling Irregular Applications through Data Aggregation and Software Multithreading

Bioinformatics, data analytics, semantic databases, knowledge discovery are emerging high performance application areas that exploit dynamic, linked data structures such as graphs, unbalanced trees or unstructured grids. These data structures usually are very large, requiring significantly more memory than available on single shared memory systems. Additionally, these data structures are difficult to partition on distributed memory systems. They also present poor spatial and temporal locality, thus generating unpredictable memory and network accesses. The Partitioned Global Address Space (PGAS) programming model seems suitable for these applications, because it allows using a shared memory abstraction across distributed-memory clusters. However, current PGAS languages and libraries are built to target regular remote data accesses and block transfers. Furthermore, they usually rely on the Single Program Multiple Data (SPMD) parallel control model, which is not well suited to the fine grained, dynamic and unbalanced parallelism of irregular applications. In this paper we present {\bf GMT} (Global Memory and Threading library), a custom runtime library that enables efficient execution of irregular applications on commodity clusters. GMT integrates a PGAS data substrate with simple fork/join parallelism and provides automatic load balancing on a per node basis. It implements multi-level aggregation and lightweight multithreading to maximize memory and network bandwidth with fine-grained data accesses and tolerate long data access latencies. A key innovation in the GMT runtime is its thread specialization (workers, helpers and communication threads) that realize the overall functionality. We compare our approach with other PGAS models, such as UPC running using GASNet, and hand-optimized MPI code on a set of typical large-scale irregular applications, demonstrating speedups of an order of magnitude.

Aggregation↗

DOE OSTI2021

Concentric Spherical GNN for 3D Representation Learning

Learning 3D representations that generalize well to arbitrarily oriented inputs is a challenge of practical importance in applications varying from computer vision to physics and chemistry. We propose a novel multi-resolution convolutional architecture for learning over concentric spherical feature maps, of which the single sphere representation is a special case. Our hierarchical architecture is based on alternatively learning to incorporate both intra-sphere and inter-sphere information. We show the applicability of our method for two different types of 3D inputs, mesh objects, which can be regularly sampled, and point clouds, which are irregularly distributed. We also propose an efficient mapping of point clouds to concentric spherical images, thereby bridging spherical convolutions on grids with general point clouds. We demonstrate the effectiveness of our approach in improving state-of-the-art performance on 3D classification tasks with rotated data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Latent Neural ODE for Integrating Multi-Timescale Measurements in Smart Distribution Grids

Under a smart grid paradigm, there has been an increase in sensor installations to enhance situational awareness. The measurements from these sensors can be leveraged for real-time monitoring, control, and protection. However, these measurements are typically irregularly sampled. These measure-ments may also be intermittent due to communication bandwidth limitations. To tackle this problem, this paper proposes a novel latent neural ordinary differential equations (LODE) approach to aggregate the unevenly sampled multivariate time-series measurements. The proposed approach is flexible in performing both imputations and predictions while being computationally efficient. Simulation results on IEEE 37 bus test systems illustrate the efficiency of the proposed approach.

multi time-scale measurements↗

DOE OSTI2021

A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries

Herein, we present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an hp adaptive mesh refinement (hp-AMR) strategy that offers high-order accurate resolution of the embedded geometries. The hp-AMR strategy is based on a multi-level block-structured domain partition in which each level is represented by block-structured Cartesian grids and the embedded geometry is represented implicitly by a level set function. The intersection of the embedded geometry with the grids produces the implicitly-defined mesh that consists of a collection of regular rectangular cells plus a relatively small number of irregular curved elements in the vicinity of the embedded boundaries. High-order quadrature rules for implicitly-defined domains enable high-order accuracy resolution of the curved elements with a cell-merging strategy to address the small-cell problem. The hp-AMR algorithm treats the system with a second-order finite volume scheme at the finest level to dynamically track the evolution of solution discontinuities while using dG schemes at coarser levels to provide high-order accuracy in smooth regions of the flow. On the dG levels, the methodology supports different orders of basis functions on different levels. The space-discretized governing equations are then advanced explicitly in time using high-order Runge-Kutta algorithms. Numerical tests are presented for two-dimensional and three-dimensional problems involving an ideal gas. The results are compared with both analytical solutions and experimental observations and demonstrate that the framework provides high-order accuracy for smooth flows and accurately captures solution discontinuities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

A Grid Intensity Map-Based Source Model for Monte Carlo Modeling of IMRT Field Irradiation - Paper 5

An accurate source model is important for TPS (Treatment Planning System) dose calculation and verification, especially for IMRT (Intensity Modulated Radiotherapy) irregular and inhomogeneous fields. Monte Carlo simulation is the most accurate way to calculate dose distributions in the heterogeneous media like human bodies. A full radiotherapy modeling generally includes Linac modeling and phantom dose calculation. Full Linac modeling is very time-consuming and requires highly detailed knowledge of the accelerator composition and structure, however, which is very difficult to obtain for commercial interests. Often all relevant parameters are not known with sufficient accuracy, and thus a time-consuming tuning of e.g. the electron beam spot size and energy must be performed. A multiple source model (MSM) regards particles coming from different parts of an accelerator as if they are coming from different virtual sources. MSM uses a set of virtual sources representing the treatment beam (e.g. primary photons, head scatter, electron contamination) by a set of analytic functions or histograms with parameters derived from dosimetric measurements or a full MC simulation. Tillikainen et al built a three sub-source model by matching with measurement data using an automatic process to optimize the free model parameters for a Varian 2100 C/D accelerator. Lin et al have built a convenient five-photon-sub-source model for Varian 2300C 6 MV-X beam based on Monte Carlo simulated Linac for ARTS (Accurate Radiotherapy System). The particle generation of MSM is very fast compared to full Linac simulation, and its sampling efficiency is not limited by the size of the phase space file (PSF). However, generally MSM is generated based on regular field PSF and needs an irregular component to form the beam shape meanwhile apt to bringing error Linac modeling and MSM producing from PSF analysis actually both are multi-freedom optimization process by adjusting several parameters (e.g. electron energy and angular divergence). Linac modeling adjusts its parameters from the beginning of electron hitting target through all components to fit the simulation to the measurement. MSM tunes its PSF-derived parameters by optimizing to minimize the deviations between the simulation and the measurement. Since the full Linac modeling and the MSM model both need to fine tune their parameters to match the simulation to the measurement, and sometimes maybe offsets the real accelerator for its multi-parameter optimization process. So, why not fine tune directly all source model parameters just behind all Linac components to fit the simulation to the measurement? A grid intensity-based surface source model was suggested here, which assumed the particle emitting from the bottom surface of Linac last beam trimmer MLC (Multi Leaf Collimator). The particle emitting position is sampled on the grid intensity map optimized by TPS, and the particle weight is adjusted by its original grid intensity. This source model not only takes advantage of the Monte Carlo method in the heterogeneous media, but also avoids effectively the transportation speed shortcoming of Monte Carlo simulation through Linac components. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2014

Robust and efficient overset grid assembly for partitioned unstructured meshes

This paper presents a method to perform efficient and automated Overset Grid Assembly (OGA) on a system of overlapping unstructured meshes in a parallel computing environment where all meshes are partitioned into multiple mesh-blocks and processed on multiple cores. The main task of the overset grid assembler is to identify, in parallel, among all points in the overlapping mesh system, at which points the flow solution should be computed (field points), interpolated (receptor points), or ignored (hole points). Point containment search or donor search, an algorithm to efficiently determine the cell that contains a given point, is the core procedure necessary for accomplishing this task. Donor search is particularly challenging for partitioned unstructured meshes because of the complex irregular boundaries that are often created during partitioning. Another challenge arises because of the large variation in the type of mesh-block overlap and the resulting large load imbalance on multiple processors. Desirable traits for the grid assembly method are efficiency (requiring only a small fraction of the solver time), robustness (correct identification of all point types), and full automation (no user input required other than the mesh system). Additionally, the method should be scalable, which is an important challenge due to the inherent load imbalance. This paper describes a fully-automated grid assembly method, which can use two different donor search algorithms. One is based on the use of auxiliary grids and Exact Inverse Maps (EIM), and the other is based on the use of Alternating Digital Trees (ADT). The EIM method is demonstrated to be more efficient than the ADT method, while retaining robustness. An adaptive load re-balance algorithm is also designed and implemented, which considerably improves the scalability of the method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Combining multiple FDG-PET radiotherapy target segmentation methods to reduce the effect of variable performance of individual segmentation methods

Purpose: Many approaches have been proposed to segment high uptake objects in 18F-fluoro-deoxy-glucose positron emission tomography images but none provides consistent performance across the large variety of imaging situations. This study investigates the use of two methods of combining individual segmentation methods to reduce the impact of inconsistent performance of the individual methods: simple majority voting and probabilistic estimation. Methods: The National Electrical Manufacturers Association image quality phantom containing five glass spheres with diameters 13-37 mm and two irregularly shaped volumes (16 and 32 cc) formed by deforming high-density polyethylene bottles in a hot water bath were filled with 18-fluoro-deoxyglucose and iodine contrast agent. Repeated 5-min positron emission tomography (PET) images were acquired at 4:1 and 8:1 object-to-background contrasts for spherical objects and 4.5:1 and 9:1 for irregular objects. Five individual methods were used to segment each object: 40% thresholding, adaptive thresholding, k-means clustering, seeded region-growing, and a gradient based method. Volumes were combined using a majority vote (MJV) or Simultaneous Truth And Performance Level Estimate (STAPLE) method. Accuracy of segmentations relative to CT ground truth volumes were assessed using the Dice similarity coefficient (DSC) and the symmetric mean absolute surface distances (SMASDs). Results: MJV had median DSC values of 0.886 and 0.875; and SMASD of 0.52 and 0.71 mm for spheres and irregular shapes, respectively. STAPLE provided similar results with median DSC of 0.886 and 0.871; and median SMASD of 0.50 and 0.72 mm for spheres and irregular shapes, respectively. STAPLE had significantly higher DSC and lower SMASD values than MJV for spheres (DSC, p < 0.0001; SMASD, p= 0.0101) but MJV had significantly higher DSC and lower SMASD values compared to STAPLE for irregular shapes (DSC, p < 0.0001; SMASD, p= 0.0027). DSC was not significantly different between 128 Multiplication-Sign 128 and 256 Multiplication-Sign 256 grid sizes for either method (MJV, p= 0.0519; STAPLE, p= 0.5672) but was for SMASD values (MJV, p < 0.0001; STAPLE, p= 0.0164). The best individual method varied depending on object characteristics. However, both MJV and STAPLE provided essentially equivalent accuracy to using the best independent method in every situation, with mean differences in DSC of 0.01-0.03, and 0.05-0.12 mm for SMASD. Conclusions: Combining segmentations offers a robust approach to object segmentation in PET. Both MJV and STAPLE improved accuracy and were robust against the widely varying performance of individual segmentation methods. Differences between MJV and STAPLE are such that either offers good performance when combining volumes. Neither method requires a training dataset but MJV is simpler to interpret, easy to implement and fast.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2000

Use of a GCM to Explore Sampling Issues in Connection with Satellite Remote Sensing of the Earth Radiation Budget

Collocated in time and space, top-of-the-atmosphere measurements of the Earth radiation budget (ERB) and cloudiness from passive scanning radiometers, and lidar- and radar-in-space measurements of multilayered cloud systems, are the required combination to improve our understanding of the role of clouds and radiation in climate. Experiments to fly multiple satellites "in formation" to measure simultaneously the radiative and optical properties of overlapping cloud systems are being designed. Because satellites carrying ERB experiments and satellites carrying lidars- or radars-in space have different orbital characteristics, the number of simultaneous measurements of radiation and clouds is reduced relative to the number of measurements made by each satellite independently. Monthly averaged coincident observations of radiation and cloudiness are biased when compared against more frequently sampled observations due, in particular, to the undersampling of their diurnal cycle, Using the Colorado State University General Circulation Model (CSU GCM), the goal of this study is to measure the impact of using simultaneous observations from the Earth Observing System (EOS) platform and companion satellites flying lidars or radars on monthly averaged diagnostics of longwave radiation, cloudiness, and its cloud optical properties. To do so, the hourly varying geographical distributions of coincident locations between the afternoon EOS (EOS-PM) orbit and the orbit of the ICESAT satellite set to fly at the altitude of 600 km, and between the EOS PM orbit and the orbits of the PICASSO satellite proposed to fly at the altitudes of 485 km (PICA485) or 705 km (PICA705), are simulated in the CSU GCM for a 60-month time period starting at the idealistic July 1, 2001, launch date. Monthly averaged diagnostics of the top-of-the-atmosphere, atmospheric, and surface longwave radiation budgets and clouds accumulated over grid boxes corresponding to satellite overpasses are compared against monthly averaged diagnostics obtained from hourly samplings over the entire globe. Results show that differences between irregularly (satellite) and regularly (true) sampled diagnostics of the longwave net radiative budgets are the greatest at the surface and the smallest in the atmosphere and at the top-of-the-atmosphere, under both cloud-free and cloudy conditions. In contrast, differences between the satellite and the true diagnostics of the longwave cloud radiative forcings are the largest in the atmosphere and at the top-of-the-atmosphere, and the smallest at the surface. A poorer diurnal sampling of the surface temperature in the satellite simulations relative to the true simulation contributes a major part to sampling biases in the longwave net radiative budgets, while a poorer diurnal sampling of cloudiness and its optical properties directly affects diagnostics of the longwave cloud radiative forcings. A factor of 8 difference in the number of satellite overpasses between PICA705 and PICA485 and ICESAT leads to a systematic factor of 3 difference in the spatial standard deviations of all radiative and cloudiness diagnostics.

Fowler, Laura D.↗

NASA NTRS2010

Kriging as a Means of Improving WAAS Availability

The Wide Area Augmentation System (WAAS), an augmentation of the Global Positioning System (GPS), provides safe and reliable use of GPS signals for airline navigation over much of North America. Currently the largest source of positioning error in the system is signal delay caused by the ionosphere. To allow the user to take account of such error, WAAS computes and broadcasts ionospheric vertical delays at a set of regularly-spaced grid points. In addition, WAAS computes and broadcasts a safety-critical integrity bound at each ionospheric grid point (IGP) called the Grid Ionospheric Vertical Error (GIVE). GIVEs are constructed to be sufficiently large to protect the user against positioning error due to the presence of ionospheric irregularity. In the initial operating capability (IOC) of WAAS, the vertical delay estimate at each IGP is determined from a planar fit of neighboring slant delay measurements, projected to vertical using an obliquity factor specified by the standard thin-shell model of the ionosphere. In WAAS Follow-On (WFO) Release 3, however, the vertical delay will be estimated by an established, geo-statistical technique known as kriging. Compared to the planar fit model, the kriging model is found, in general, to match better the observed random structure of the vertical delay. This paper presents the kriging methodology that will be used to estimate the vertical delay and its uncertainty at each IGP, and it assesses the subsequent improvement in WAAS availability enabled by kriging.

GPS↗