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DOE OSTI2022

Learning Optimal Multigrid Smoothers via Neural Networks

Multigrid methods are one of the most efficient techniques for solving large sparse linear systems arising from partial differential equations (PDEs) and graph Laplacians from machine learning applications. One of the key components of multigrid is smoothing, which aims at reducing high-frequency errors on each grid level. However, finding optimal smoothing algorithms is problem-dependent and can impose challenges for many problems. In this paper, we propose an efficient adaptive framework for learning optimized smoothers from operator stencils in the form of convolutional neural networks (CNNs). Here, the CNNs are trained on small-scale problems from a given type of PDEs based on a supervised loss function derived from multigrid convergence theories and can be applied to large-scale problems of the same class of PDEs. Numerical results on anisotropic rotated Laplacian problems and variable coefficient diffusion problems demonstrate improved convergence rates and solution time compared with classical hand-crafted relaxation methods.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1993

Time-domain analysis of planar microstrip devices using a generalized Yee-algorithm based on unstructured grids

The generalized Yee-algorithm is presented for the temporal full-wave analysis of planar microstrip devices. This algorithm has the significant advantage over the traditional Yee-algorithm in that it is based on unstructured and irregular grids. The robustness of the generalized Yee-algorithm is that structures that contain curved conductors or complex three-dimensional geometries can be more accurately, and much more conveniently modeled using standard automatic grid generation techniques. This generalized Yee-algorithm is based on the the time-marching solution of the discrete form of Maxwell's equations in their integral form. To this end, the electric and magnetic fields are discretized over a dual, irregular, and unstructured grid. The primary grid is assumed to be composed of general fitted polyhedra distributed throughout the volume. The secondary grid (or dual grid) is built up of the closed polyhedra whose edges connect the centroid's of adjacent primary cells, penetrating shared faces. Faraday's law and Ampere's law are used to update the fields normal to the primary and secondary grid faces, respectively. Subsequently, a correction scheme is introduced to project the normal fields onto the grid edges. It is shown that this scheme is stable, maintains second-order accuracy, and preserves the divergenceless nature of the flux densities. Finally, for computational efficiency the algorithm is structured as a series of sparse matrix-vector multiplications. Based on this scheme, the generalized Yee-algorithm has been implemented on vector and parallel high performance computers in a highly efficient manner.

Gedney, Stephen D.↗

DOE OSTI2022

Volumetric Rendering on Wavelet-Based Adaptive Grid

Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes.

Vezolainen, Alexei V.↗

DOE OSTI2026

Field testing and validation of a low-cost MPC for demand flexibility for grid-interactive K-12 schools

K-12 school buildings account for the highest energy consumption within the public sector. Implementing advanced HVAC controls in grid-interactive K-12 schools could bring substantial economic advantages and grid flexibility. Our previous study demonstrated that a low-cost model predictive control (MPC) solution, which coordinates multiple packaged units, can enable demand flexibility without major hardware upgrades. However, a significant gap remains between academic pilots and market-ready scalable solutions. This paper extends the previous single-site pilot to a multi-site demonstration involving three school campuses (95 total units) through a commercial technology transfer process. Addressing the challenge of verifying performance with sparse field data, we present a new statistical approach using Bayesian methods to estimate the MPC’s effect on peak demand. Unlike traditional methods, this approach robustly quantifies uncertainty in non-normal, limited datasets. The results confirm the solution’s replicability, achieving a 21.6–38.9% reduction in HVAC peak demand (10.8–22.1% at the site-level) with > 98% probability across diverse locations. Finally, we document critical barriers to scaling software-as-a-service (SaaS) solutions–such as API instability and diverse legacy systems–and offer practical strategies to accelerate the commercial adoption of grid-interactive efficient buildings.

Ham, Sang Woo↗

NASA NTRS1990

Partitioning sparse matrices with eigenvectors of graphs

The problem of computing a small vertex separator in a graph arises in the context of computing a good ordering for the parallel factorization of sparse, symmetric matrices. An algebraic approach for computing vertex separators is considered in this paper. It is shown that lower bounds on separator sizes can be obtained in terms of the eigenvalues of the Laplacian matrix associated with a graph. The Laplacian eigenvectors of grid graphs can be computed from Kronecker products involving the eigenvectors of path graphs, and these eigenvectors can be used to compute good separators in grid graphs. A heuristic algorithm is designed to compute a vertex separator in a general graph by first computing an edge separator in the graph from an eigenvector of the Laplacian matrix, and then using a maximum matching in a subgraph to compute the vertex separator. Results on the quality of the separators computed by the spectral algorithm are presented, and these are compared with separators obtained from other algorithms for computing separators. Finally, the time required to compute the Laplacian eigenvector is reported, and the accuracy with which the eigenvector must be computed to obtain good separators is considered. The spectral algorithm has the advantage that it can be implemented on a medium-size multiprocessor in a straightforward manner.

Pothen, Alex↗

DOE OSTI2024

Sparse-Stochastic Fragmented Exchange for Large-Scale Hybrid Time-Dependent Density Functional Theory Calculations

Here we extend our recently developed sparse-stochastic fragmented exchange formalism for ground-state near-gap hybrid DFT to calculate absorption spectra within linear-response time-dependent generalized Kohn-Sham DFT (LR-GKS-TDDFT) for systems consisting of thousands of valence electrons within a grid-based/plane-wave representation. A mixed deterministic/fragmented-stochastic compression of the exchange kernel, here using long-range explicit exchange functionals, provides an efficient method for accurate optical spectra. Both real-time propagation as well as frequency-resolved Casida-equation-type approaches for spectra are presented, and the method is applied to large molecular dyes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2007

Terrain Portrayal for Synthetic Vision Systems Head-Down Displays Evaluation Results

A critical component of SVS displays is the appropriate presentation of terrain to the pilot. At the time of this study, the relationship between the complexity of the terrain presentation and resulting enhancements of pilot SA and pilot performance had been largely undefined. The terrain portrayal for SVS head-down displays (TP-HDD) simulation examined the effects of two primary elements of terrain portrayal on the primary flight display (PFD): variations of digital elevation model (DEM) resolution and terrain texturing. Variations in DEM resolution ranged from sparsely spaced (30 arc-sec) to very closely spaced data (1 arc-sec). Variations in texture involved three primary methods: constant color, elevation-based generic, and photo-realistic, along with a secondary depth cue enhancer in the form of a fishnet grid overlay.

Hughes, Monica F.↗

NASA NTRS1990

Application of the TRANAIR rectangular grid approach to the aerodynamic analysis of complex configurations

A numerical method is described which uses a rectangular grid to solve the nonlinear full potential equation about complex configurations. The grid is locally refined to resolve high velocity gradients arising from leading edge expansions or shock waves. The grid penetrates the boundary (described by networks of quadrilateral panels) and is generated automatically. Discrete operators are constructed using the finite element method. The system of nonlinear discrete equations is solved iteratively using a Krylov subspace method preconditioned by an exterior Poisson solver and a direct sparse solver. The primary emphasis is to provide design engineers with an aerodynamic analysis tool (the TRANAIR code) which is accurate, reliable, economical, and flexible to use. Computational results for many interesting configurations are presented.

Johnson, Forrester T.↗

DOE OSTI2023

Evaluating 3 decades of precipitation in the Upper Colorado River basin from a high-resolution regional climate model

Abstract. Convection-permitting regional climate models (RCMs) have recently become tractable for applications at multi-decadal timescales. These types of models have tremendous utility for water resource studies, but better characterization of precipitation biases is needed, particularly for water-resource-critical mountain regions, where precipitation is highly variable in space, observations are sparse, and the societal water need is great. This study examines 34 years (1987–2020) of RCM precipitation from the Weather Research and Forecasting model (WRF; v3.8.1), using the Climate Forecast System Reanalysis (CFS; CFSv2) initial and lateral boundary conditions and a 1 km × 1 km innermost grid spacing. The RCM is centered over the Upper Colorado River basin, with a focus on the high-elevation, 750 km2 East River watershed (ERW), where a variety of high-impact scientific activities are currently ongoing. Precipitation is compared against point observations (Natural Resources Conservation Service Snow Telemetry or SNOTEL), gridded climate datasets (Newman, Livneh, and PRISM), and Bayesian reconstructions of watershed mean precipitation conditioned on streamflow and high-resolution snow remote-sensing products. We find that the cool-season precipitation percent error between WRF and 23 SNOTEL gauges has a low overall bias (x^ = 0.25 %, s = 13.63 %) and that WRF has a higher percent error during the warm season (x^ = 10.37 %, s = 12.79 %). Warm-season bias manifests as a high number of low-precipitation days, though the low-resolution or SNOTEL gauges limit some of the conclusions that can be drawn. Regional comparisons between WRF precipitation accumulation and three different gridded datasets show differences on the order of ± 20 %, particularly at the highest elevations and in keeping with findings from other studies. We find that WRF agrees slightly better with the Bayesian reconstruction of precipitation in the ERW compared to the gridded precipitation datasets, particularly when changing SNOTEL densities are taken into account. The conclusions are that the RCM reasonably captures orographic precipitation in this region and demonstrates that leveraging additional hydrologic information (streamflow and snow remote-sensing data) improves the ability to characterize biases in RCM precipitation fields. Error characteristics reported in this study are essential for leveraging the RCM model outputs for studies of past and future climates and water resource applications. The methods developed in this study can be applied to other watersheds and model configurations. Hourly 1 km × 1 km precipitation and other meteorological outputs from this dataset are publicly available and suitable for a wide variety of applications.

Geology↗

NASA NTRS2016

Spatio-Temporal Variability of Groundwater Storage in India

Groundwater level measurements from 3907 monitoring wells, distributed within 22 major river basins of India, are assessed to characterize their spatial and temporal variability. Ground water storage (GWS) anomalies (relative to the long-term mean) exhibit strong seasonality, with annual maxima observed during the monsoon season and minima during pre-monsoon season. Spatial variability of GWS anomalies increases with the extent of measurements, following the power law relationship, i.e., log-(spatial variability) is linearly dependent on log-(spatial extent).In addition, the impact of well spacing on spatial variability and the power law relationship is investigated. We found that the mean GWS anomaly sampled at a 0.25 degree grid scale closes to unweighted average over all wells. The absolute error corresponding to each basin grows with increasing scale, i.e., from 0.25 degree to 1 degree. It was observed that small changes in extent could create very large changes in spatial variability at large grid scales. Spatial variability of GWS anomaly has been found to vary with climatic conditions. To our knowledge, this is the first study of the effects of well spacing on groundwater spatial variability. The results may be useful for interpreting large scale groundwater variations from unevenly spaced or sparse groundwater well observations or for siting and prioritizing wells in a network for groundwater management. The output of this study could be used to maintain a cost effective groundwater monitoring network in the study region and the approach can also be used in other parts of the globe.

Groundwater monitoring↗

NASA NTRS2003

Terrain Portrayal for Head-Down Displays Flight Test

The Synthetic Vision Systems General Aviation (SVS-GA) element of NASA's Aviation Safety Program is developing technology to eliminate low visibility induced General Aviation (GA) accidents through the application of synthetic vision techniques. SVS displays present computer generated 3-dimensional imagery of the surrounding terrain to greatly enhance pilot's situation awareness (SA), reducing or eliminating Controlled Flight into Terrain (CFIT), as well as Low-Visibility Loss of Control (LVLOC) accidents. In addition to substantial safety benefits, SVS displays have many potential operational benefits that can lead to flight in instrument meteorological conditions (IMC) resembling those conducted in visual meteorological conditions (VMC). Potential benefits could include lower landing minimums, more approach options, reduced training time, etc. SVS conducted research will develop display concepts providing the pilot with an unobstructed view of the outside terrain, regardless of weather conditions and time of day. A critical component of SVS displays is the appropriate presentation of terrain to the pilot. The relationship between the realism of the terrain presentation and resulting enhancements of pilot SA and pilot performance has been largely undefined. Comprised of coordinated simulation and flight test efforts, the terrain portrayal for head-down displays (TP-HDD) test series examined the effects of two primary elements of terrain portrayal: variations of digital elevation model (DEM) resolution and terrain texturing. Variations in DEM resolution ranged from sparsely spaced (30 arc-sec/2,953ft) to very closely spaced data (1 arc-sec/98 ft). Variations in texture involved three primary methods: constant color, elevation-based generic, and photo-realistic, along with a secondary depth cue enhancer in the form of a fishnet grid overlay. The TP-HDD test series was designed to provide comprehensive data to enable design trades to optimize all SVS applications, as well as develop requirements and recommendations to facilitate the implementation and certification of SVS displays. The TP-HDD flight experiment utilized the NASA LaRC Cessna 206 Stationaire and evaluated eight terrain portrayal concepts in an effort to confirm and extend results from the previously conducted TP-HDD simulation experiment. A total of 15 evaluation pilots, of various qualifications, accumulated over 75 hours of dedicated research flight time at Newport News (PHF) and Roanoke (ROA), VA, airports from August through October, 2002. This report will present results from the portion of testing conducted at Roanoke, VA.

Hughes, Monica F.↗

DOE OSTI2024

Deep Reinforcement Learning for Microgrid Cost Optimization Considering Load Flexibility

This paper proposes a novel Soft-Actor-Critic (SAC) based Deep Reinforcement Learning (DRL) method for optimizing the cost of microgrid operation by leveraging load flexibility. The proposed SAC-DRL method is designed to coordinate the control of distributed energy resources (DERs) and flexible load, addressing practical energy billing formation by power distribution utilities. Key contributions include an innovative reward function to mitigate sparse reward challenges and a mixed control strategy for discrete and continuous variables, ensuring radial network topology and minimizing power loss. We evaluate the proposed method on the model of a real microgrid located in Southern California, U.S.. The SAC-DRL model is tested to demonstrate its efficacy in reducing grid dependence, optimizing resource use, and minimizing costs. The results highlight the potential of DRL in modern energy systems, offering a sustainable and economically efficient solution for energy management in microgrids.

deep reinforcement learning↗

DOE OSTI2025

A nonhydrostatic formulation for MPAS-Ocean

The Model for Prediction Across Scales-Ocean (MPAS-Ocean) is an open-source, global ocean model and is one component of a family of climate models within the MPAS framework, including atmosphere, sea-ice, and land-ice models. Here, in this work, a new formulation for the ocean model is presented that solves the nonhydrostatic, incompressible Boussinesq equations on an unstructured, staggered, z-level grid. The introduction of this nonhydrostatic capability is necessary for the resolution of internal wave dynamics and large eddy simulations. Compared to the standard, hydrostatic formulation, a nonhydrostatic pressure solver and a vertical momentum equation are added, where the PETSc (Portable Extensible Toolkit for Scientific Computation) library is used for the inversion of a large sparse system for the nonhydrostatic pressure. Numerical results on a stratified seiche, internal solitary wave, overflow and lock-exchange test cases are presented, and the parallel efficiency of the code is evaluated using up to 1024 processors.

3D Poisson equation↗

DOE OSTI2025

A nonhydrostatic formulation for MPAS-Ocean

3D Poisson equation↗

NASA NTRS2017

Development and Assessment of the SMAP Enhanced Passive Soil Moisture Product

Launched in January 2015, the National Aeronautics and Space Administration (NASA) Soil Moisture Active Passive (SMAP) observatory was designed to provide frequent global mapping of high-resolution soil moisture and freeze-thaw state every two to three days using a radar and a radiometer operating at L-band frequencies. Despite a hardware mishap that rendered the radar inoperable shortly after launch, the radiometer continues to operate nominally, returning more than two years of science data that have helped to improve existing hydrological applications and foster new ones.Beginning in late 2016 the SMAP project launched a suite of new data products with the objective of recovering some high-resolution observation capability loss resulting from the radar malfunction. Among these new data products are the SMAP Enhanced Passive Soil Moisture Product that was released in December 2016, followed by the SMAPSentinel-1 Active-Passive Soil Moisture Product in April 2017.This article covers the development and assessment of the SMAP Level 2 Enhanced Passive Soil Moisture Product (L2_SM_P_E). The product distinguishes itself from the current SMAP Level 2 Passive Soil Moisture Product (L2_SM_P) in that the soil moisture retrieval is posted on a 9 km grid instead of a 36 km grid. This is made possible by first applying the Backus-Gilbert optimal interpolation technique to the antenna temperature (TA) data in the original SMAP Level 1B Brightness Temperature Product to take advantage of the overlapped radiometer footprints on orbit. The resulting interpolated TA data then go through various correctioncalibration procedures to become the SMAP Level 1C Enhanced Brightness Temperature Product (L1C_TB_E). The L1C_TB_E product, posted on a 9 km grid, is then used as the primary input to the current operational SMAP baseline soil moisture retrieval algorithm to produce L2_SM_P_E as the final output. Images of the new product reveal enhanced visual features that are not apparent in the standard product. Based on in situ data from core validation sites and sparse networks representing different seasons and biomes all over the world, comparisons between L2_SM_P_E and in situ data were performed for the duration of April 1, 2015 October 30, 2016. It was found that the performance of the enhanced 9 km L2_SM_P_E is equivalent to that of the standard 36 km L2_SM_P, attaining a retrieval uncertainty below 0.040 m(exp 3)/m(exp 3) unbiased root-mean-square error (ubRMSE) and a correlation coefficient above 0.800. This assessment also affirmed that the Single Channel Algorithm using the V-polarized TB channel (SCA-V) delivered the best retrieval performance among the various algorithms implemented for L2_SM_P_E, a result similar to a previous assessment for L2_SM_P.

Enhanced↗

DOE OSTI2021

Cardinality-Regularized Hawkes-Granger Model

We propose a new sparse Granger-causal learning framework for temporal event data. We focus on a specific class of point processes called the Hawkes process. We begin by pointing out that most of the existing sparse causal learning algorithms for the Hawkes process suffer from a singularity in maximum likelihood estimation. As a result, their sparse solutions can appear only as numerical artifacts. In this paper, we propose a mathematically well-defined sparse causal learning framework based on a cardinality-regularized Hawkes process, which remedies the pathological issues of existing approaches. We leverage the proposed algorithm for the task of instance-wise causal event analysis, where sparsity plays a critical role. We validate the proposed framework with two real use-cases, one from the power grid and the other from the cloud data center management domain.

Ide, Tsuyoshi↗

NASA NTRS1985

Thickness of Ridged Plains Materials in Hesperia Planum, Mars

The thickness distribution of plains-forming materials in Hesperia Planum is determined by the diameter of partially buried craters. As with all Martian thickness studies, the distribution of measured thicknesses is sparse due to a low number of suitable partially buried craters. The resulting isopach of plains materials has a low level of confidence but is sufficient for generalized thickness trends. The mean of the thickness estimates is 360 + or - 120 m. The isopach of plains-forming materials exhibits an uneven thickness distribution. Average thickness, determined by grid sampling over the region, is 216 + or - 153 m. Local lenses exceed 500 m. A fifth order trend surface provides a partial match (coefficient of correlation = 0.657) to the isopach.

Dehon, R. A.↗

NASA NTRS2012

Multi-Angle Implementation of Atmospheric Correction for MODIS (MAIAC). Part 3: Atmospheric Correction

This paper describes the atmospheric correction (AC) component of the Multi-Angle Implementation of Atmospheric Correction algorithm (MAIAC) which introduces a new way to compute parameters of the Ross-Thick Li-Sparse (RTLS) Bi-directional reflectance distribution function (BRDF), spectral surface albedo and bidirectional reflectance factors (BRF) from satellite measurements obtained by the Moderate Resolution Imaging Spectroradiometer (MODIS). MAIAC uses a time series and spatial analysis for cloud detection, aerosol retrievals and atmospheric correction. It implements a moving window of up to 16 days of MODIS data gridded to 1 km resolution in a selected projection. The RTLS parameters are computed directly by fitting the cloud-free MODIS top of atmosphere (TOA) reflectance data stored in the processing queue. The RTLS retrieval is applied when the land surface is stable or changes slowly. In case of rapid or large magnitude change (as for instance caused by disturbance), MAIAC follows the MODIS operational BRDF/albedo algorithm and uses a scaling approach where the BRDF shape is assumed stable but its magnitude is adjusted based on the latest single measurement. To assess the stability of the surface, MAIAC features a change detection algorithm which analyzes relative change of reflectance in the Red and NIR bands during the accumulation period. To adjust for the reflectance variability with the sun-observer geometry and allow comparison among different days (view geometries), the BRFs are normalized to the fixed view geometry using the RTLS model. An empirical analysis of MODIS data suggests that the RTLS inversion remains robust when the relative change of geometry-normalized reflectance stays below 15%. This first of two papers introduces the algorithm, a second, companion paper illustrates its potential by analyzing MODIS data over a tropical rainforest and assessing errors and uncertainties of MAIAC compared to conventional MODIS products.

Lyapustin, A.↗