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DOE OSTI2022

Graph Partitioning and Sparse Matrix Ordering using Reinforcement Learning and Graph Neural Networks

We present a novel method for graph partitioning, based on reinforcement learning and graph convolutional neural networks. Our approach is to recursively partition coarser representations of a given graph. The neural network is implemented using SAGE graph convolution layers, and trained using an advantage actor critic (A2C) agent. We present two variants, one for finding an edge separator that minimizes the normalized cut or quotient cut, and one that finds a small vertex separator. The vertex separators are then used to construct a nested dissection ordering to permute a sparse matrix so that its triangular factorization will incur less fill-in. The partitioning quality is compared with partitions obtained using METIS and SCOTCH, and the nested dissection ordering is evaluated in the sparse solver SuperLU. Our results show that the proposed method achieves similar partitioning quality as METIS and SCOTCH. Furthermore, the method generalizes across different classes of graphs, and works well on a variety of graphs from the SuiteSparse sparse matrix collection.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Registration of the sorghum carbon–partitioning nested association mapping (CP–NAM) population

The sorghum [ Sorghum bicolor (L.) Moench] carbon-partitioning nested association mapping (CP_NAM) (Reg. no. MP-4, NSL 542189 MAP) population was developed at Clemson University, SC, using 11 diverse, male founder accessions, each crossed with a recurrent female parent ‘Grassl’. The male parents represent all five major botanical races and the four major agronomic types: cellulosic (5), sweet (3), grain (2) and forage (1). A set of 11 recombinant inbred line (RIL) families CP_NAM01 to CP_NAM011 were maintained, which consisted of 2,484 (F 6 ) individuals. Each RIL family contained a minimum of 193 individuals (CP_NAM01) and a maximum of 287 individuals (CP_NAM06). For the development of this population, the founder lines were judiciously selected from the sorghum Bioenergy Association Panel based on carbon-partitioning phenotypes that make this population an ideal genetic resource for dissecting a wide range of agronomic and compositional traits for basic and applied research. The founder accessions of the CP_NAM were phenotypically characterized for various traits, including agronomic, biomass and related components, and additional compositional components. Each of the 11 F 6 RIL families of the CP_NAM were genotyped using genotyping-by-sequencing analysis, and 144,087 single nucleotide polymorphisms were generated for each individual. Genotypic information along with phenotypic data were used for the characterization of this population and to explore the range of phenotypes that permits the understanding of carbon-partitioning dynamics. This population is a unique resource for researchers to study a wide range of contrasting carbon-partitioning characteristics in sorghum to understand the genetic architecture underlying whole-plant carbon partitioning and allocation.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

A Semi‐Mechanistic Model for Partitioning Evapotranspiration Reveals Transpiration Dominates the Water Flux in Drylands

Abstract Popular evapotranspiration (ET) partitioning methods make assumptions that might not be well‐suited to dryland ecosystems, such as high sensitivity of plant water‐use efficiency (WUE) to vapor pressure deficit (VPD). Our objectives were to (a) create an ET partitioning model that can produce fine‐scale estimates of transpiration (T) in drylands, and (b) use this approach to evaluate how climate controls T and WUE across ecosystem types and timescales along a dryland aridity gradient. We developed a novel, semi‐mechanistic ET partitioning method using a Bayesian approach that constrains abiotic evaporation using process‐based models, and loosely constrains time‐varying WUE within an autoregressive framework. We used this method to estimate daily T and weekly WUE across seven dryland ecosystem types and found that T dominates ET across the aridity gradient. Then, we applied cross‐wavelet coherence analysis to evaluate the temporal coherence between focal response variables (WUE and T/ET) and environmental variables. At yearly scales, we found that WUE at less arid, higher elevation sites was primarily limited by atmospheric moisture demand, and WUE at more arid, lower elevation sites was primarily limited by moisture supply. At sub‐yearly timescales, WUE and VPD were sporadically correlated. Hence, ecosystem‐scale dryland WUE is not always sensitive to changes in VPD at short timescales, despite this being a common assumption in many ET partitioning models. This new ET partitioning method can be used in dryland ecosystems to better understand how climate influences physically and biologically driven water fluxes.

Environmental Sciences & Ecology↗

DOE OSTI2023

Spectral-partitioned Kohn-Sham density functional theory

Here we introduce a general, variational scheme for systematic approximation of a given Kohn-Sham free-energy functional by partitioning the density matrix into distinct spectral domains, each of which may be spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact (unpartitioned) Kohn-Sham free energy, attaining this limit as the representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multiprojector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Efficient Hierarchical State Vector Simulation of Quantum Circuits via Acyclic Graph Partitioning

Early but promising results in quantum computing have been enabled by the concurrent development of quantum algorithms, devices, and materials. Classical simulation of quantum programs has enabled the design and analysis of algorithms and implementation strategies targeting current and anticipated quantum device architectures. In this paper, we present a graph-based approach to achieve efficient quantum circuit simulation. Our approach involves partitioning the graph representation of a given quantum circuit into sub-graphs/circuits that exhibit better data locality. Simulation of each sub-circuit is organized hierarchically, with the iterative construction and simulation of smaller state vectors, improving overall performance. Also, this partitioning reduces the number of passes through data, improving the total computation time. We present three partitioning strategies and observe that acyclic graph partitioning typically results in the best time-to-solution. In contrast, other strategies reduce the partitioning time at the expense of potentially increased simulation times. Experimental evaluation demonstrates the effectiveness of our approach.

Fang, Bo↗

DOE OSTI2023

TDAG: Tree-based Directed Acyclic Graph Partitioning for Quantum Circuits

We propose the Tree-based Directed Acyclic Graph (TDAG) partitioning for quantum circuits, a novel quantum circuit partitioning method which partitions circuits by viewing them as a series of binary trees and selecting the tree containing the most gates. TDAG produces results of comparable quality (number of partitions) to an existing method called ScanPartitioner (an exhaustive search algorithm) with an 95% average reduction in execution time. Furthermore, TDAG improves compared to a faster partitioning method called QuickPartitioner by 38% in terms of quality of the results with minimal overhead in execution time.

Clark, Joseph↗

DOE OSTI2023

Eu speciation in apatite at 1 bar: An experimental study of valence-state partitioning by XANES, lattice strain, and Eu/Eu* in basaltic systems

Abstract Partition coefficients for rare earth elements (REEs) between apatite and basaltic melt were determined as a function of oxygen fugacity (fO2; iron-wüstite to hematite-magnetite buffers) at 1 bar and between 1110 and 1175 °C. Apatite-melt partitioning data for REE3+ (La, Sm, Gd, Lu) show near constant values at all experimental conditions, while bulk Eu becomes more incompatible (with an increasing negative anomaly) with decreasing fO2. Experiments define three apatite calibrations that can theoretically be used as redox sensors. The first, a XANES calibration that directly measures Eu valence in apatite, requires saturation at similar temperature-composition conditions to experiments and is defined by: ( E u 3 + ∑ E u ) Apatite = 1 1 + 10 - 0.10 ± 0.01 × l o g ⁡ ( f o 2 ) - 1.63 ± 0.16 . The second technique involves analysis of Sm, Eu, and Gd in both apatite and coexisting basaltic melt (glass), and is defined by: ( Eu E u * ) D Sm × Gd = 1 1 + 10 - 0.15 ± 0.03 × l o g ⁡ ( f o 2 ) - 2.46 ± 0.41 . The third technique is based on the lattice strain model and also requires analysis of REE in both apatite and basalt. This calibration is defined by ( Eu E u * ) D lattice strain = 1 1 + 10 - 0.20 ± 0.03 × l o g ⁡ ( f o 2 ) - 3.03 ± 0.42 . The Eu valence-state partitioning techniques based on (Sm×Gd) and lattice strain are virtually indistinguishable, such that either methodology is valid. Application of any of these calibrations is best carried out in systems where both apatite and coexisting glass are present and in direct contact with one another. In holocrystalline rocks, whole rock analyses can be used as a guide to melt composition, but considerations and corrections must be made to either the lattice strain or Sm×Gd techniques to ensure that the effect of plagioclase crystallization either prior to or during apatite growth can be removed. Similarly, if the melt source has an inherited either a positive or negative Eu anomaly, appropriate corrections must also be made to lattice strain or Sm×Gd techniques that are based on whole rock analyses. This being the case, if apatite is primary and saturates from the parent melt early during the crystallization sequence, these corrections may be minimal. The partition coefficients for the REE between apatite and melt range from a maximum DEu3+ = 1.67 ± 0.25 (as determined by lattice strain) to DLu3+ = 0.69 ± 0.10. The REE partition coefficient pattern, as observed in the Onuma diagram, is in a fortuitous situation where the most compatible REE (Eu3+) is also the polyvalent element used to monitor fO2. These experiments provide a quantitative means of assessing Eu anomalies in apatite and how they be used to constrain the oxygen fugacity of silicate melts.

Geochemistry & Geophysics↗

NASA NTRS1978

Ductility normalized-strain-range partitioning life relations for creep-fatigue life predictions

Techniques utilizing strainrange partitioning may be used to estimate the effects of the environment on the high-temperature, low-cycle, creep-fatigue resistance of alloys. Three levels of ductility-normalized strainrange-partitioning life relations are discussed: (1) strainrange partitioning relations from ductility data, (2) strainrange partitioning relations scaled by ductility ratios, and (3) strainrange partitioning life relations with measured PP lines. The procedures have demonstrated good agreement with available creep-fatigue data.

Halford, G. R.↗

NASA NTRS1979

Dominant partition method

By use of the L'Huillier, Redish, and Tandy (LRT) wave function formalism, a partially connected method, the dominant partition method (DPM) is developed for obtaining few body reductions of the many body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. The DPM maps the many body problem to a fewer body one by using the criterion that the truncated formalism must be such that consistency with the full Schroedinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, which is introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition, which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few body reaction mechanism prevails.

Dixon, R. M.↗

NASA NTRS1980

Crystal/liquid partitioning in augite - Effects of cooling rate

The partitioning of major and minor elements between augite and melt was determined as a function of cooling rate for two high-titanium basalt compositions. The results of this study of lunar rock systems 10017 and 75055 were compared with the results of other kinetic studies of augite-liquid partitioning in other rock systems. It was found that the partitioning of major elements (i.e., Ca, Fe, Mg) is essentially rate independent and is insensitive to bulk rock composition and to the nature and order of appearance of coexisting phases for cooling rates of less than 100 C/hr. The partitioning behavior of minor elements (i.e., Al, Cr, Ti) for the same range of cooling rates is complex, being dependent on cooling rate and bulk rock composition. Consideration of these factors is important when augite chemistry and/or partitioning behavior are used in modeling certain magmatic processes or in estimating the thermal history of basaltic rocks.

Gamble, R. P.↗

NASA NTRS1983

Experimental investigation of the partitioning of phosphorus between metal and silicate phases - Implications for the earth, moon and eucrite parent body

An experimental study is reported of the partitioning of Phosphorus between solid metal and basaltic silicate liquid as a function of temperature and oxygen fugacity and of the implications for the earth, moon and eucrite parent body (EPB). The relationship established between the partition coefficient and the fugacity is given at 1190 C by log D(P) = -1.12 log fO2 - 15.95 and by log D(P) = -1.53 log fO2 17.73 at 1300 C. The partition coefficient D(P) was determined, and it is found to be consistent with a valence state of 5 for P in the molten silicate. Using the determined coefficient the low P/La ratios of the earth, moon, and eucrites relative to C1 chondrites can be explained. The lowering of the P/La ratio in the eucrites relative to Cl chondrite by a factor of 40 can be explained by partitioning P into 20-25 wt% sulfur-bearing metallic liquid corresponding to 5-25% of the total metal plus silicate system. The low P/La and W/La ratios in the moon may be explained by the partitioning of P and W into metal during formation of a small core by separation of liquid metal from silicate at low degrees of partial melting of the silicates. These observations are consistent with independent formation of the moon and the earth.

Newsom, H. E.↗

NASA NTRS1984

Problems with the process partitioning theory of stratocumulus entrainment

Three different approaches to partitioning were proposed. Ball (1960), Lilly (1968), and Deardorff et al. (1969, 1974) considered the sign of the net buoyancy flux at each level. If the net flux is positive, it is counted as TKE producing; otherwise, it is counted as TKE consuming. This approach can be called Eulerian partitioning. The second approach can be called process partitioning. It is assumed that the various processes acting in concert each produce and consume the same energy as if they acted independently (Manins and Turner, 1978). The total rates of TKE production and consumption are obtained by summing the effects of all the forcing processes. The third approach is Lagrangian partitioning. Each air parcel is considered as either producing or consuming TKE, according to the sign of the product of its density and vertical velocity anomalies. Stage and Businger (1981a,b) have applied process partitioning to the cloud topped mixed layer. One of the most important processes influencing entrainment into such a layer is cloud top radiative cooling. The production and consumption due to entrainment and radiative cooling are thus closely related. Model results are sensitive to the choice of formulation.

Randall, D. A.↗

NASA NTRS1984

Purification of biomaterials by phase partitioning

A technique which is particularly suited to microgravity environments and which is potentially more powerful than electrophoresis is phase partitioning. Phase partitioning is purification by partitioning between the two immiscible aqueous layers formed by solution of the polymers poly(ethylene glycol) and dextran in water. This technique proved to be very useful for separations in one-g but is limited for cells because the cells are more dense than the phase solutions thus tend to sediment to the bottom of the container before reaching equilibrium with the preferred phase. There are three phases to work in this area: synthesis of new polymers for affinity phase partitioning; development of automated apparatus for ground-based separations; and design of apparatus for performing simple phase partitioning space experiments, including examination of mechanisms for separating phases in the absence of gravity.

Harris, J. M.↗

NASA NTRS1992

Automatic data partitioning on distributed memory multicomputers

Distributed-memory parallel computers are increasingly being used to provide high levels of performance for scientific applications. Unfortunately, such machines are not very easy to program. A number of research efforts seek to alleviate this problem by developing compilers that take over the task of generating communication. The communication overheads and the extent of parallelism exploited in the resulting target program are determined largely by the manner in which data is partitioned across different processors of the machine. Most of the compilers provide no assistance to the programmer in the crucial task of determining a good data partitioning scheme. A novel approach is presented, the constraints-based approach, to the problem of automatic data partitioning for numeric programs. In this approach, the compiler identifies some desirable requirements on the distribution of various arrays being referenced in each statement, based on performance considerations. These desirable requirements are referred to as constraints. For each constraint, the compiler determines a quality measure that captures its importance with respect to the performance of the program. The quality measure is obtained through static performance estimation, without actually generating the target data-parallel program with explicit communication. Each data distribution decision is taken by combining all the relevant constraints. The compiler attempts to resolve any conflicts between constraints such that the overall execution time of the parallel program is minimized. This approach has been implemented as part of a compiler called Paradigm, that accepts Fortran 77 programs, and specifies the partitioning scheme to be used for each array in the program. We have obtained results on some programs taken from the Linpack and Eispack libraries, and the Perfect Benchmarks. These results are quite promising, and demonstrate the feasibility of automatic data partitioning for a significant class of scientific application programs with regular computations.

Gupta, Manish↗

NASA NTRS1993

A modified approach to controller partitioning

The idea of computing a decentralized control law for the integrated flight/propulsion control of an aircraft by partitioning a given centralized controller is investigated. An existing controller partitioning methodology is described, and a modified approach is proposed with the objective of simplifying the associated controller approximation problem. Under the existing approach, the decentralized control structure is a variable in the partitioning process; by contrast, the modified approach assumes that the structure is fixed a priori. Hence, the centralized controller design may take the decentralized control structure into account. Specifically, the centralized controller may be designed to include all the same inputs and outputs as the decentralized controller; then, the two controllers may be compared directly, simplifying the partitioning process considerably. Following the modified approach, a centralized controller is designed for an example aircraft mode. The design includes all the inputs and outputs to be used in a specified decentralized control structure. However, it is shown that the resulting centralized controller is not well suited for approximation by a decentralized controller of the given structure. The results indicate that it is not practical in general to cast the controller partitioning problem as a direct controller approximation problem.

Garg, Sanjay↗

NASA NTRS1993

Application of controller partitioning optimization procedure to integrated flight/propulsion control design for a STOVL aircraft

A parameter optimization framework has earlier been developed to solve the problem of partitioning a centralized controller into a decentralized, hierarchical structure suitable for integrated flight/propulsion control implementation. This paper presents results from the application of the controller partitioning optimization procedure to IFPC design for a Short Take-Off and Vertical Landing (STOVL) aircraft in transition flight. The controller partitioning problem and the parameter optimization algorithm are briefly described. Insight is provided into choosing various 'user' selected parameters in the optimization cost function such that the resulting optimized subcontrollers will meet the characteristics of the centralized controller that are crucial to achieving the desired closed-loop performance and robustness, while maintaining the desired subcontroller structure constraints that are crucial for IFPC implementation. The optimization procedure is shown to improve upon the initial partitioned subcontrollers and lead to performance comparable to that achieved with the centralized controller. This application also provides insight into the issues that should be addressed at the centralized control design level in order to obtain implementable partitioned subcontrollers.

Garg, Sanjay↗

NASA NTRS1993

Application of controller partitioning optimization procedure to integrated flight/propulsion control design for a STOVL aircraft

Garg, Sanjay↗

NASA NTRS1993

Partitioning of Nb, Mo, Ba, Ce, Pb, Th and U between immiscible carbonate and silicate liquids: Evaluating the effects of P2O5,F, and carbonate composition

Previously we have reported carbonate liq./silicate liq. partition coefficients (D) for a standard suite of trace elements (Nb, Mo, Ba, Ce, Pb, Th, and U) and Ra and Pa as well. In brief, we have found that immiscible liquid partitioning is a strong function of temperature. As the critical temperature of the carbonate-silicate solvus is approached, all partition coefficients approach unity. Additionally, for the overwhelming majority of the partitioning elements, InD is a linear function of 'ionic field strength,' z/r, where z is the charge of the partitioned cation and r is its ionic radius.

Jones, J. H.↗