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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Optimizing deep learning hyper-parameters through an evolutionary algorithm. In: MLHPC '15 Proceedings of the Workshop on Machine Learning in High-Performance Computing Environments, Article No. 4

There has been a recent surge of success in utilizing Deep Learning (DL) in imaging and speech applications for its relatively automatic feature generation and, in particular for convolutional neural networks (CNNs), high accuracy classification abilities. While these models learn their parameters through data-driven methods, model selection (as architecture construction) through hyper-parameter choices remains a tedious and highly intuition driven task. To address this, Multi-node Evolutionary Neural Networks for Deep Learning (MENNDL) is proposed as a method for automating network selection on computational clusters through hyper-parameter optimization performed via genetic algorithms.

Young, Steven R.↗
DOE OSTI2018

Interior Decoration of Stable Metal–Organic Frameworks

Metal–organic frameworks (MOFs) are a diverse class of hybrid organic/inorganic crystalline materials composed of metal-containing nodes held in place by organic linkers. Through a discerning selection of these components, many properties such as the internal surface area, cavity size and shape, catalytic properties, thermal properties, and mechanical properties may be manipulated. Because of this high level of tunability, MOFs have been heralded as ideal platforms for various applications including gas storage, separation, catalysis, and chemical sensing.(1-8) Regrettably, these theoretical possibilities are limited by the reality of constraining conditions for solvothermal synthesis, which typically include high temperatures (usually over 100 °C), the use of specific solvents, and necessary exposure to acidic or basic conditions. In order to incorporate more delicate functionalities, postsynthesis decoration methods were developed. This feature article focuses on developed interior decoration methods for stable MOFs and the dynamic relationship between such methods and MOF stability. In particular, methods to transform organic, inorganic, and organometallic MOF parts as well as combination techniques, the generation of defects, and the inclusion of enzymes are addressed.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A Reconfigurable Neural Network ASIC for Detector Front-End Data Compression at the HL-LHC

Despite advances in the programmable logic capabilities of modern trigger systems, a significant bottleneck remains in the amount of data to be transported from the detector to off-detector logic where trigger decisions are made. We demonstrate that a neural network (NN) autoencoder model can be implemented in a radiation-tolerant application-specific integrated circuit (ASIC) to perform lossy data compression alleviating the data transmission problem while preserving critical information of the detector energy profile. For our application, we consider the high-granularity calorimeter from the Compact Muon Solenoid (CMS) experiment at the CERN Large Hadron Collider. The advantage of the machine learning approach is in the flexibility and configurability of the algorithm. By changing the NN weights, a unique data compression algorithm can be deployed for each sensor in different detector regions and changing detector or collider conditions. To meet area, performance, and power constraints, we perform quantization-aware training to create an optimized NN hardware implementation. The design is achieved through the use of high-level synthesis tools and the hls4ml framework and was processed through synthesis and physical layout flows based on a low-power (LP)-CMOS 65-nm technology node. The flow anticipates 200 Mrad of ionizing radiation to select gates and reports a total area of 3.6 mm 2 and consumes 95 mW of power. The simulated energy consumption per inference is 2.4 nJ. Furthermore, this is the first radiation-tolerant on-detector ASIC implementation of an NN that has been designed for particle physics applications.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

SU-F-T-173: One-Scan Protocol: Verifying the Delivery of Spot-Scanning Proton Beam

Purpose: Radiochromic film for spot-scanning QA provides high spatial resolution and efficiency gains from one-shot irradiation for multiple depths. However, calibration can be a tedious procedure which may limit widespread use. Moreover, since there may be an energy dependence, which manifests as a depth dependence, this may require additional measurements for each patient. We present a one-scan protocol to simplify the procedure. Methods: We performed the calibration using an EBT3 film at depths of 18, 20, 24cm of Plastic Water exposed by a 6-level step-wedge plan on a Proteus Plus proton system (IBA, Belgium). The calibration doses ranged 65–250 cGy(RBE) for proton energies of 170–200MeV. A clinical prostate+nodes plan was used for validation. The planar doses at selected depths were measured with EBT3 films and analyzed using one-scan protocol (one-scan digitization of QA film and at least one film exposed to known dose). The Gamma passing rates, dose-difference maps, and profiles of 2D planar doses measured with EBT3 film, IBA MatriXX PT, versus TPS calculations were analyzed and compared. Results: The EBT3 film measurement results matched well with the TPS calculation data with an average passing rate of ∼95% for 2%/2mm and slightly lower passing rates were obtained from an ion chamber array detector. We were able to demonstrate that the use of a proton step-wedge provided clinically acceptable results and minimized variations between film-scanner orientation, inter-scan, and scanning conditions. Furthermore, it could be derived from no more than two films exposed to known doses (one could be zero) for rescaling the master calibration curve at each depth. Conclusion: The use of a proton step-wedge for calibration of EBT3 film increases efficiency. The sensitivity of the calibration to depth variations has been explored. One-scan protocol results appear to be comparable to that of the ion chamber array detector. One author has a research grant from Ashland Inc., the manufacturer of the GafChromic film.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

Left-sided breast cancer irradiation using rotational and fixed-field radiotherapy

The 3-dimensional conformal radiotherapy (3DCRT) technique is the standard for breast cancer radiotherapy. During treatment planning, not only the coverage of the planning target volume (PTV) but also the minimization of the dose to critical structures, such as the lung, heart, and contralateral breast tissue, need to be considered. Because of the complexity and variations of patient anatomy, more advanced radiotherapy techniques are sometimes desired to better meet the planning goals. In this study, we evaluated external-beam radiation treatment techniques for left breast cancer using various delivery platforms: fixed-field including TomoDirect (TD), static intensity-modulated radiotherapy (sIMRT), and rotational radiotherapy including Elekta volumetric-modulated arc therapy (VMAT) and tomotherapy helical (TH). A total of 10 patients with left-sided breast cancer who did or did not have positive lymph nodes and were previously treated with 3DCRT/sIMRT to the entire breast were selected, their treatment was planned with Monaco VMAT, TD, and TH. Dosimetric parameters including PTV coverage, organ-at-risk (OAR) sparing, dose-volume histograms, and target minimum/maximum/mean doses were evaluated. It is found that for plans providing comparable PTV coverage, the Elekta VMAT plans were generally more inhomogeneous than the TH and TD plans. For the cases with regional node involvement, the average mean doses administered to the heart were 9.2 (± 5.2) and 8.8 (± 3.0) Gy in the VMAT and TH plans compared with 11.9 (± 6.4) and 11.8 (± 9.2) Gy for the 3DCRT and TD plans, respectively, with slightly higher doses given to the contralateral lung or breast or both. On average, the total monitor units for VMAT plans are 11.6% of those TH plans. Our studies have shown that VMAT and TH plans offer certain dosimetric advantages over fixed-field IMRT plans for advanced breast cancer requiring regional nodal treatment. However, for early-stage breast cancer fixed-field radiotherapy is potentially more beneficial in terms of OAR sparing.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2017

Bridging Zirconia Nodes within a Metal–Organic Framework via Catalytic Ni-Hydroxo Clusters to Form Heterobimetallic Nanowires

Metal-organic frameworks (MOFs), with their well-ordered pore networks and tunable surface chemistries, offer a versatile platform for preparing well-defined nanostructures wherein functionality such as catalysis can be incorporated. We resolved the atomic structure of Ni-oxo species deposited in the MOF NU-1000 through atomic layer deposition using local and long-range structure probes, including X-ray absorption spectroscopy, pair distribution function analysis and difference envelope density analysis, with electron microscopy imaging and computational modeling.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2022

Quantification of electron correlation for approximate quantum calculations

State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable computational cost to solve the many-body Schrödinger equation. By far, the most common property used to assess accuracy has been the total energy; however, total energies do not give a complete picture of electron correlation. In this work, we assess the von Neumann entropy of the one-particle reduced density matrix (1-RDM) to compare selected configuration interaction (CI), coupled cluster, variational Monte Carlo, and fixed-node diffusion Monte Carlo for benchmark hydrogen chains. A new algorithm, the circle reject method, is presented, which improves the efficiency of evaluating the von Neumann entropy using quantum Monte Carlo by several orders of magnitude. The von Neumann entropy of the 1-RDM and the eigenvalues of the 1-RDM are shown to distinguish between the dynamic correlation introduced by the Jastrow and the static correlation introduced by determinants with large weights, confirming some of the lore in the field concerning the difference between the selected CI and Slater–Jastrow wave functions.

Chemistry↗
DOE OSTI2020

Exploring the Effects of Node Topology, Connectivity, and Metal Identity on the Binding of Nerve Agents and Their Hydrolysis Products in Metal–Organic Frameworks

Recent studies have shown that metal–organic frameworks (MOFs) built from hexanuclear M(IV) oxide cluster nodes are effective catalysts for nerve agent hydrolysis, where the properties of the active sites on the nodes can strongly influence the reaction energetics. The connectivity and metal identity of these M6 nodes can be easily tuned, offering extensive opportunities for computational screening to predict promising new materials. Thus, we used density functional theory (DFT) to examine the effects of node topology, connectivity, and metal identity on the binding energies of multiple nerve agents and their corresponding hydrolysis products. By computing an optimization metric based on the relative binding strengths of key hydrolysis reaction species (water, agent, and bidentate-bound products), we predicted optimal M6 nodes for hydrolyzing specific nerve agent and simulant molecules, where our results are in qualitative agreement with observed experimental trends. This analysis highlighted the notion that no single metal or node topology is optimal for all possible organophosphates, suggesting that MOFs should be selected based on the agent of interest. Using the large amount of data generated from our DFT calculations, we then derived quantitative structure–activity relationship (QSAR) models to help explain the complex trends observed in the binding energies. Through linear regression, we identified the most important descriptors for describing the binding of nerve agents and their hydrolysis products to M6 nodes. These results suggested that both molecular and node properties, including both structural and chemical features, collectively contribute to the binding energetics. By performing a thorough statistical analysis, we showed that our QSAR models are capable of making quantitatively accurate binding energy predictions for nerve agents and their hydrolysis products in a wide variety of M(IV)-MOFs. In conclusion, the insights gained herein can be used to guide future experiments for the synthesis of MOFs with enhanced catalytic activity for organophosphate hydrolysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Interplay effects between dose distribution quality and positioning accuracy in total marrow irradiation with volumetric modulated arc therapy

Purpose: To evaluate the dosimetric consequences of inaccurate isocenter positioning during treatment of total marrow (lymph-node) irradiation (TMI-TMLI) using volumetric modulated arc therapy (VMAT).Methods: Four patients treated with TMI and TMLI were randomly selected from the internal database. Plans were optimized with VMAT technique. Planning target volume (PTV) included all the body bones; for TMLI, lymph nodes and spleen were considered into the target, too. Dose prescription to PTV was 12 Gy in six fractions, two times per day for TMI, and 2 Gy in single fraction for TMLI. Ten arcs on five isocenters (two arcs for isocenter) were used to cover the upper part of PTV (i.e., from cranium to middle femurs). For each plan, three series of random shifts with values between −3 and +3 mm and three between −5 and +5 mm were applied to the five isocenters simulating involuntary patient motion during treatment. The shifts were applied separately in the three directions: left–right (L-R), anterior–posterior (A-P), and cranial–caudal (C-C). The worst case scenario with simultaneous random shifts in all directions simultaneously was considered too. Doses were recalculated for the 96 shifted plans (24 for each patient).Results: For all shifts, differences <0.5% were found for mean doses to PTV, body, and organs at risk with volumes >100 cm{sup 3}. Maximum doses increased up to 15% for C-C shifted plans. PTV covered by the 95% isodose decreased of 2%–8% revealing target underdosage with the highest values in C-C direction.Conclusions: The correct isocenter repositioning of TMI-TMLI patients is fundamental, in particular in C-C direction, in order to avoid over- and underdosages especially in the overlap regions. For this reason, a dedicated immobilization system was developed in the authors' center to best immobilize the patient.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2022

Metal-organic framework supported single-site nickel catalysts for butene dimerization

Homotopic sites in a well-controlled environment are not only ideal systems for mechanistic studies, but also allow optimal control of catalytic transformations. Sites having only a single metal cation and sites consisting of metal oxo complexes with few nickel (Ni) cations supported on the nodes of UiO-66 metal-organic framework (Ni-UiO-66) are studied for 1-butene dimerization. Monomeric Ni sites, which bind to the Zr 6 node via two Zr-OH(µ3) linkages, are active and selective for the dimerization of 1-butene to linear and mono-branched C 8 isomers. Ni oxo complexes with few Ni cations show lower activity and promote the oligomerization of transiently formed C 8 isomers. In conclusion, Kohn-Sham density function theory calculations combined with spectroscopic measurements and kinetic analyses indicate that dimerization follows a Cossee-Arlman reaction mechanism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Achieving strength-ductility synergy in hierarchical aluminum metal matrix composites via friction extrusion

We report the fabrication of aluminum metal matrix composites (Al-MMCs) with hierarchical architectures via friction extrusion (FE), a scalable, single-step, solid-phase processing technique. Precursor pucks containing 0–15 vol% Al₂O₃ particles were extruded into fully dense AA6061-based composite rods. The FE induced a tree-ring-like architecture of concentric particle-rich and particle-lean bands, yielding refined grains in particle-rich regions and coarser grains elsewhere. At the nanoscale, magnesium in AA6061 selectively reacted with Al₂O₃ particles to form virus-like nodes, improving particle–matrix bonding. This multi-scale design strategy, combining mesoscale architecture, microscale grain refinement, and nanoscale interface engineering overcome the conventional strength–ductility trade-off. Tensile testing showed substantial increases in yield and ultimate tensile strengths while retaining high ductility ( > 20%). Enhanced strain hardening, driven by the accumulation of geometrically necessary dislocations at interfaces, contributed to the performance. The hierarchical microstructure produced by FE demonstrates a promising pathway for scalable fabrication of lightweight MMCs for structural applications requiring a combined high strength and ductility.

Kalsar, Rajib [Pacific Northwest National Laborato↗
DOE OSTI2016

SU-F-T-387: A Novel Optimization Technique for Field in Field (FIF) Chestwall Radiation Therapy Using a Single Plan to Improve Delivery Safety and Treatment Planning Efficiency

Purpose: A novel optimization technique was developed for field-in-field (FIF) chestwall radiotherapy using bolus every other day. The dosimetry was compared to currently used optimization. Methods: The prior five patients treated at our clinic to the chestwall and supraclavicular nodes with a mono-isocentric four-field arrangement were selected for this study. The prescription was 5040 cGy in 28 fractions, 5 mm bolus every other day on the tangent fields, 6 and/or 10 MV x-rays, and multileaf collimation.Novelly, tangents FIF segments were forward planned optimized based on the composite bolus and non-bolus dose distribution simultaneously. The prescription was spilt into 14 fractions for both bolus and non-bolus tangents. The same segments and monitor units were used for the bolus and non-bolus treatment. The plan was optimized until the desired coverage was achieved, minimized 105% hotspots, and a maximum dose of less than 108%. Each tangential field had less than 5 segments.Comparison plans were generated using FIF optimization with the same dosimetric goals, but using only the non-bolus calculation for FIF optimization. The non-bolus fields were then copied and bolus was applied. The same segments and monitor units were used for the bolus and non-bolus segments. Results: The prescription coverage of the chestwall, as defined by RTOG guidelines, was on average 51.8% for the plans that optimized bolus and non-bolus treatments simultaneous (SB) and 43.8% for the plans optimized to the non-bolus treatments (NB). Chestwall coverage of 90% prescription averaged to 80.4% for SB and 79.6% for NB plans. The volume receiving 105% of the prescription was 1.9% for SB and 0.8% for NB plans on average. Conclusion: Simultaneously optimizing for bolus and non-bolus treatments noticeably improves prescription coverage of the chestwall while maintaining similar hotspots and 90% prescription coverage in comparison to optimizing only to non-bolus treatments.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Emulator-Based Bayesian Calibration of the CISNET Colorectal Cancer Models

Purpose To calibrate Cancer Intervention and Surveillance Modeling Network (CISNET)'s SimCRC, MISCAN-Colon, and CRC-SPIN simulation models of the natural history colorectal cancer (CRC) with an emulator-based Bayesian algorithm and internally validate the model-predicted outcomes to calibration targets.Methods We used Latin hypercube sampling to sample up to 50,000 parameter sets for each CISNET-CRC model and generated the corresponding outputs. We trained multilayer perceptron artificial neural networks (ANNs) as emulators using the input and output samples for each CISNET-CRC model. We selected ANN structures with corresponding hyperparameters (i.e., number of hidden layers, nodes, activation functions, epochs, and optimizer) that minimize the predicted mean square error on the validation sample. We implemented the ANN emulators in a probabilistic programming language and calibrated the input parameters with Hamiltonian Monte Carlo-based algorithms to obtain the joint posterior distributions of the CISNET-CRC models' parameters. We internally validated each calibrated emulator by comparing the model-predicted posterior outputs against the calibration targets.Results The optimal ANN for SimCRC had 4 hidden layers and 360 hidden nodes, MISCAN-Colon had 4 hidden layers and 114 hidden nodes, and CRC-SPIN had 1 hidden layer and 140 hidden nodes. The total time for training and calibrating the emulators was 7.3, 4.0, and 0.66 h for SimCRC, MISCAN-Colon, and CRC-SPIN, respectively. The mean of the model-predicted outputs fell within the 95% confidence intervals of the calibration targets in 98 of 110 for SimCRC, 65 of 93 for MISCAN, and 31 of 41 targets for CRC-SPIN.Conclusions Using ANN emulators is a practical solution to reduce the computational burden and complexity for Bayesian calibration of individual-level simulation models used for policy analysis, such as the CISNET CRC models. In this work, we present a step-by-step guide to constructing emulators for calibrating 3 realistic CRC individual-level models using a Bayesian approach.

artificial neural networks↗
DOE OSTI2021

Stochastic parametric skeletal dosimetry model for humans: General approach and application to active marrow exposure from bone-seeking beta-particle emitters

The objective of this study is to develop a skeleton model for assessing active marrow dose from bone-seeking beta-emitting radionuclides. This article explains the modeling methodology which accounts for individual variability of the macro- and microstructure of bone tissue. Bone sites with active hematopoiesis are assessed by dividing them into small segments described by simple geometric shapes. Spongiosa, which fills the segments, is modeled as an isotropic three-dimensional grid (framework) of rod-like trabeculae that “run through” the bone marrow. Randomized multiple framework deformations are simulated by changing the positions of the grid nodes and the thickness of the rods. Model grid parameters are selected in accordance with the parameters of spongiosa microstructures taken from the published papers. Stochastic modeling of radiation transport in heterogeneous media simulating the distribution of bone tissue and marrow in each of the segments is performed by Monte Carlo methods. Model output for the human femur at different ages is provided as an example. The uncertainty of dosimetric characteristics associated with individual variability of bone structure was evaluated. An advantage of this methodology for the calculation of doses absorbed in the marrow from bone-seeking radionuclides is that it does not require additional studies of autopsy material. The biokinetic model results will be used in the future to calculate individual doses to members of a cohort exposed to 89,90 Sr from liquid radioactive waste discharged to the Techa River by the Mayak Production Association in 1949–1956. Further study of these unique cohorts provides an opportunity to gain more in-depth knowledge about the effects of chronic radiation on the hematopoietic system. In addition, the proposed model can be used to assess the doses to active marrow under any other scenarios of 90 Sr and 89 Sr intake to humans.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Classification of Nuclear Reactor Operations Using Spatial Importance and Multisensor Networks

Distributed multisensor networks record multiple data streams that can be used as inputs to machine learning models designed to classify operations relevant to proliferation at nuclear reactors. The goal of this work is to demonstrate methods to assess the importance of each node (a single multisensor) and region (a group of proximate multisensors) to machine learning model performance in a reactor monitoring scenario. This, in turn, provides insight into model behavior, a critical requirement of data-driven applications in nuclear security. Using data collected at the High Flux Isotope Reactor at Oak Ridge National Laboratory via a network of Merlyn multisensors, two different models were trained to classify the reactor’s operational state: a hidden Markov model (HMM), which is simpler and more transparent, and a feed-forward neural network, which is less inherently interpretable. Traditional wrapper methods for feature importance were extended to identify nodes and regions in the multisensor network with strong positive and negative impacts on the classification problem. These spatial-importance algorithms were evaluated on the two different classifiers. The classification accuracy was then improved relative to baseline models via feature selection from 0.583 to 0.839 and from 0.811 ± 0.005 to 0.884 ± 0.004 for the HMM and feed-forward neural network, respectively. While some differences in node and region importance were observed when using different classifiers and wrapper methods, the nodes near the facility’s cooling tower were consistently identified as important—a conclusion further supported by studies on feature importance in decision trees. Node and region importance methods are model-agnostic, inform feature selection for improved model performance, and can provide insight into opaque classification models in the nuclear security domain.

Tibbetts, Jake↗
DOE OSTI2022

Modulating Chemical Environments of Metal–Organic Framework-Supported Molybdenum(VI) Catalysts for Insights into the Structure–Activity Relationship in Cyclohexene Epoxidation

Solid supports are crucial in heterogeneous catalysis due to their profound effects on catalytic activity and selectivity. However, elucidating the specific effects arising from such supports remains challenging. We selected a series of metal–organic frameworks (MOFs) with 8-connected Zr 6 nodes as supports to deposit molybdenum(VI) onto to study the effects of pore environment and topology on the resulting Mo-supported catalysts. As characterized by X-ray absorption spectroscopy (XAS) and single-crystal X-ray diffraction (SCXRD), we modulated the chemical environments of the deposited Mo species. For Mo-NU-1000, the Mo species monodentately bound to the Zr 6 nodes were anchored in the microporous c-pore, but for Mo-NU-1008 they were bound in the mesopore of Mo-NU-1008. Both monodentate and bidentate modes were found in the mesopore of Mo-NU-1200. Cyclohexene epoxidation with H 2 O 2 was probed to evaluate the support effect on catalytic activity and to unveil the resulting structure–activity relationships. SCXRD and XAS studies demonstrated the atomically precise structural differences of the Mo binding motifs over the course of cyclohexene epoxidation. No apparent structural change was observed for Mo-NU-1000, whereas the monodentate mode of Mo species in Mo-NU-1008 and the monodentate and bidentate Mo species in Mo-NU-1200 evolved to a new bidentate mode bound between two adjacent oxygen atoms from the Zr 6 node. This work demonstrates the great advantage of using MOF supports for constructing heterogeneous catalysts with modulated chemical environments of an active species and elucidating structure–activity relationships in the resulting reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Extending SEER for Extreme Heterogeneity

Heterogeneous and multi-device nodes are increasingly common in high-performance computing and data centers, yet existing programming models often lack simple, transparent, and portable support for these diverse architectures. The main contribution of this work is the development of novel SEER capabilities to address this challenge by providing a descriptive programming model that allows applications to seamlessly leverage heterogeneous nodes across various device types. SEER uses efficient memory management and can select the proper device[s] depending on the computational cost of the applications. This is completely transparent to the programmer, thereby providing a highly productive programming environment. Integrating extreme heterogeneity into the SEER library as shown with the use of NVIDIA and AMD GPUs simultaneously allows it to expand and exploit the performance possibilities. Our analysis based on the well-known Conjugate Gradient algorithm reports accelerations above 1.5 × on computationally demanding steps of such an algorithm by using both architectures simultaneously.

Teranishi, Keita [ORNL] (ORCID:0000000166472690)↗
DOE OSTI2023

Execution of computation graphs

A computation graph is accessed. In the computation graph, operations to be performed are represented as interior nodes, inputs to the operations are represented as leaf nodes, and a result of the operations is represented as a root. Selected sets of the operations are combined to form respective kernels of operations. Code is generated execute the kernels of operations. The code is executed to determine the result.

Ravishankar, Mahesh↗