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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Development and Experimental Optimization of High-Temperature Modeling Tools and Methods for Concentrated Solar Power Particle - Systems

A novel, open-source radiative modeling toolset was developed to extend the functionality of particle-based modeling software (e.g. discrete element method (DEM)) to environmental conditions relevant to concentrated solar power applications. This toolset was optimized for deployment on desktop workstations instead of high-performance computing systems, to render such tools more accessible to the research community. Both particle-based modeling and radiative exchange modeling are computationally expensive and often require specialized programming expertise, making these methods cumbersome to use. Recent developments in DEM software by DCS Computing have greatly reduced these challenges, providing a graphical-user-interface based platform and modeling optimization for desktop workstations, HPCs, and cloud computing. The University of Dayton leveraged the experience of DCS Computing in developing a user-friendly, open-source radiative heat transfer expansion for DEM modeling. The University of Dayton DEM+ radiative modeling toolset was developed using a combination of fundamental experimental measurements, modeling, and simplified flow experiments over a range of temperatures and flow conditions. The toolset provides researchers with access to multiple radiative models including an accelerated Monte-Carlo Ray Tracing (application agnostic, highly computationally expensive), an expanded database of distance-based approximations (application limited, computationally light), and a weighted blending of the two methods capable of achieving over 90% reduction in computation time with equivalent accuracy compared to Monte-Carlo Ray Tracing. Through a graphical user interface, users can customize the radiative models to match their desired accuracy and available computational resources, improving access to particle based modeling for the research community. Ceramic sintered bauxite proppants were used in modeling and experimentally as a baseline. Both the radiative heat transfer and flow properties for particulate systems were investigated at elevated temperatures up to 800 °C. The major accomplishments for this work include a verified, open-source radiative modeling toolset to be distributed amongst the research community and the fabrication of three small-scale test facilities to investigate particle behavior and tune DEM flow properties for operation up to 800 °C. The findings have been shared with the research community via conference modeling workshops, deployment of the tools in DCS Computing Aspherix®, and open-source access to the developed radiative modeling tool. The development of next-generation CSP facilities and thermal energy storage systems based on ceramic particles requires providing access to computationally efficient and accurate modeling tools. Particles will experience a wide range of environments (20-800 °C) and handling conditions (dilute curtains or dense packing), requiring specially designed and optimized equipment. Optimizing solid particle physics models and establishing best-practices for particle modeling in CSP environments will assist researchers with designing optimized equipment, accelerating the deployment of more economically-competitive CSP facilities.

14 SOLAR ENERGY↗
DOE OSTI2025

Speed Optimizations for Physics Ray Trace Algorithms

Ray tracing is a process used commonly in computer graphics and in physics to track light photons and particles, respectively. Much research was found on improving execution times for the computer graphics applications; however, in the short time frame of this literary review, almost no research was found on improving the execution times for the physics applications that were relevant to this problem. Two ray trace algorithms, a STL raytrace and a conebeam raytrace, were optimized using OpenMP and CUDA.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

ACDC (Automated Campbell Diagram Code) [SWR-26-042]

This application provides a web-based graphical user interface to generating Campbell Diagrams and visualizing mode shapes for OpenFAST turbine models. Determining the aeroelastic stability and dynamic characteristics of wind turbines is a critical step in turbine design and analysis. Historically, extracting natural frequencies and mode shapes from OpenFAST—the industry-standard whole-turbine simulation code—has been a fragmented and tedious process. It required manual model configuration, command-line linearization execution, and complex post-processing via proprietary scripts to handle rotating-frame dynamics. To address these workflow bottlenecks, we present the Automated Campbell Diagram Code (ACDC), an open-source graphical software tool developed by the National Laboratory of the Rockies (NLR) under the DOE-funded Distributed Wind Aeroelastic Modeling (dWAM) project. ACDC streamlines the end-to-end linearization and stability analysis workflow into a single, intuitive cross-platform application. The software guides users through OpenFAST model configuration, definition of operating points, and the automated execution of steady-state trim and linearization simulations. Under the hood, ACDC automates the complex mathematical post-processing steps required for rotating systems, including Multi-Blade Coordinate (MBC) transformations, eigenanalysis, and advanced modal tracking utilizing the Modal Assurance Criterion (MAC) and spectral clustering. Finally, ACDC processes these results to automatically generate Campbell diagrams and features a robust 3D visualization engine to animate full-system mode shapes. By eliminating the reliance on external post-processing environments and manual data manipulation, ACDC significantly accelerates dynamic analysis and lowers the barrier to entry for wind energy researchers and engineers.

Summerville, Brent [National Laboratory of the Roc↗
DOE OSTI2025

NLR HPC Eagle GPU Node Metrics

Ganglia node metrics and iLO (Integrated Lights Out) power data captured from six representative Eagle GPU nodes The Eagle HPC operated at NLR from 2019 through 2024. Eagle was a 2,000-node, 8-petaflop system. This dataset is a representative sample of metrics for 6 of the GPU nodes. Each GPU node contained 2 CPUs and 2 GPUs. Data provided in compressed CSV format. Ganglia and iLO Power Time Series Fields ts: Timestamp dv: Device / Node - Rack and Unit - r103u17 == r(ack)103u(nit)17 mt: Metric (only present for Ganglia) vl: Value - Value in watts for iLO power (instantaneous value at sampling time) or specified Ganglia metric below Ganglia Metrics Metric name -- Metric description -- Unit cpu_aidle -- Percent of time since boot idle CPU -- Percent cpu_idle -- Percent CPU idle -- Percent cpu_nice -- Percent CPU nice -- Percent cpu_speed -- Speed in MHz of CPU -- MHz cpu_user -- Percent CPU user -- Percent cpu_wio -- The percentage of CPU Wait I/O -- Percent gpu0_bar1_memory -- Used GPU bar1 memory -- MB gpu0_decoder_util -- GPU decoder utilization -- Percent gpu0_ecc_db_error -- Total ECC error counts for the GPU -- Number gpu0_encoder_util -- GPU encoder utilization -- Percent gpu0_fan -- Fan speed -- RPM gpu0_fb_memory -- Used GPU framebuffer memory -- MB gpu0_graphics_clock_report -- Current clock speeds for the device -- MHz gpu0_mem_total -- Memory total -- MB gpu0_mem_util -- Memory utilization -- Percent gpu0_power_usage_report -- Power usage report -- Watts gpu0_temp -- GPU 1 temperature -- Celsius gpu1_bar1_memory -- Used GPU bar1 memory -- MB gpu1_decoder_util -- GPU decoder utilization -- Percent gpu1_ecc_db_error -- Total ECC error counts for the GPU -- Number gpu1_encoder_util -- GPU encoder utilization -- Percent gpu1_fan -- Fan speed -- RPM gpu1_fb_memory -- Used GPU framebuffer memory -- MB gpu1_graphics_clock_report -- Current clock speeds for the GPU -- MHz gpu1_mem_total -- Memory total -- MB gpu1_mem_util -- Memory utilization -- MB gpu1_power_usage_report -- Power usage report -- Watts gpu1_temp -- GPU 1 temperature -- Celsius ipmi_cpu1_temp -- CPU 1 temperature -- Celsius ipmi_cpu2_temp -- CPU 2 temperature -- Celsius ipmi_inlet_ambient_temp -- Temperature measured at intake -- Celsius ipmi_vr_p1_temp -- CPU 1 voltage regulator temperature -- Celsius ipmi_vr_p2_temp -- CPU 2 voltage regulator temperature -- Celsius mem_buffers -- Amount of buffered memory -- Bytes mem_cached -- Amount of cached memory -- Bytes mem_free -- Amount of available memory -- Bytes mem_shared -- Amount of shared memory -- Bytes mem_total -- Amount of available memory -- Bytes

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Leaky Buddies: Cross-Component Covert Channels on Integrated CPU-GPU Systems

Graphics Processing Units (GPUs) are ubiquitous components used across the range of today’s computing plat- forms, from phones and tablets, through personal computers, to high-end server class platforms. With the increasing importance of graphics and video workloads, recent processors are shipped with GPU devices that are integrated on the same chip. Integrated GPUs share some resources with the CPU and as a result, there is a potential for microarchitectural attacks from the GPU to the CPU or vice versa. We consider the potential for covert channel attacks that arise either from shared microarchitectural components (such as caches) or through shared contention domains (e.g., shared buses). We illustrate these two types of channels by developing two reliable covert channel attacks. The first covert channel uses the shared LLC cache in Intel’s integrated GPU architectures. The second is a contention based channel targeting the ring bus connecting the CPU and GPU to the LLC. This is the first demonstrated microarchitectural attack crossing the component boundary (GPU to CPU or vice versa). Cross-component channels introduce a number of new challenges that we had to overcome since they occur across heterogeneous components that use different computation models and are interconnected using asymmetric memory hierarchies. We also exploit GPU parallelism to increase the bandwidth of the communication, even without relying on a common clock. The LLC based channel achieves a bandwidth of 120 kbps with a low error rate of 2%, while the contention based channel delivers up to 400 kbps with a 0.8% error rate. We also demonstrate a proof- of-concept prime-and-probe side channel attack that probes the full LLC from the GPU.

Cyber secruity, high performance comptuing, Hetero↗
DOE OSTI2025

Developing Digital Twin Visualizations: A Methodology and Case Study on Chemical Separation Processing

As advances in digital engineering continue to push the technological boundaries, digital twin (DT) visualizations for diagnostics and safeguards advancement become much more feasible and practical. DTs generate large and complex data streams that require effective user interfaces to provide monitoring and diagnostic capabilities. Unfortunately, while these frameworks exist, there is not much research on the systematic documentation of human–computer interaction (HCI) for DT visualization. This work presents a dual-mode visualization methodology (two dimensional [2D] graphical user interface dashboard and 3D mixed reality) designed to support diagnostic tasks in DT systems and building on a validated framework and applying established HCI principles. The methodology is demonstrated through a case study of aqueous processing at Idaho National Laboratory, using experimental data from the chemical solvent extraction runs. Our interfaces display real-time alerts and monitoring to inform users of safeguards anomalies. The interfaces use immersive 3D mixed-reality visualization for further system and experiment investigation. This work demonstrates how the systematic application of HCI principles can inform DT visualization design for diagnostic and safeguards applications. While formal user evaluation studies remain as future work, this paper documents the systematic design methodology and demonstrates a proof-of-concept implementation.

3D visualization↗
DOE OSTI2024

The Effect of the Prior and the Experimental Design on the Inference of the Precision Matrix in Gaussian Chain Graph Models

Here, we investigate whether (and how) experimental design could aid in the estimation of the precision matrix in a Gaussian chain graph model, especially the interplay between the design, the effect of the experiment and prior knowledge about the effect. Estimation of the precision matrix is a fundamental task to infer biological graphical structures like microbial networks. We compare the marginal posterior precision of the precision matrix under four priors: flat, conjugate Normal-Wishart, Normal-MGIG and a general independent. Under the flat and conjugate priors, the Laplace-approximated posterior precision is not a function of the design matrix rendering useless any efforts to find an optimal experimental design to infer the precision matrix. In contrast, the Normal-MGIG and general independent priors do allow for the search of optimal experimental designs, yet there is a sharp upper bound on the information that can be extracted from a given experiment. We confirm our theoretical findings via a simulation study comparing (i) the KL divergence between prior and posterior and (ii) the Stein’s loss difference of MAPs between random and no experiment. Our findings provide practical advice for domain scientists conducting experiments to better infer the precision matrix as a representation of a biological network.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Mesoscopic Modeling and Rapid Simulation of Incremental Changes in Epidemic Scenarios on GPUs

In simulation-based studies and analyses of epidemics, a major challenge lies in resolving the conflict between fidelity of models and the speed of their simulation. Another related challenge arises in dealing with the large number of what–if scenarios that need to be explored. Here, we describe new computational methods that together provide an approach to dealing with both challenges. A mesoscopic modeling approach is described that strikes a middle ground between macroscopic models based on coupled differential equations and microscopic models built on fine-grained behaviors at the individual entity level. The mesoscopic approach offers the ability to incorporate complex compositions of multiple layers of dynamics even while retaining the potential for aggregate behaviors at varying levels. It also is an excellent match to the accelerator-based architectures of modern computing platforms in which graphical processing units (GPUs) can be exploited for fast simulation via the parallel execution mode of single instruction multiple thread (SIMT). The challenge of simulating a large number of scenarios is addressed via a method of sharing model state and computation across a tree of what–if scenarios that are localized, incremental changes to a large base simulation. A combination of the mesoscopic modeling approach and the incremental what–if scenario tree evaluation has been implemented in the software on modern GPUs. Synthetic simulation scenarios are presented to demonstrate the computational characteristics of our approach. Results from the experiments with large population data, including USA, UK, and India, illustrate the modeling methodology and computational performance on thousands of synthetically generated what–if scenarios. Execution of our implementation scaled to 8192 GPUs of supercomputing platforms demonstrates the ability to rapidly evaluate what–if scenarios several orders of magnitude faster than the conventional methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Scalable probabilistic estimates of electric vehicle charging given observed driver behavior

To prepare for rapid growth in global electric vehicle adoption, grid and policy planners depend on detailed forecasts of future charging demand. In this paper we propose a novel holistic, scalable, probabilistic framework to produce large-scale estimates of electric vehicle charging load for long-term planning that capture real drivers’ charging patterns. Our framework captures the uncertainty and stochasticity in charging demand by taking a graphical modeling approach. It has three core elements: driver groups, charging segment choices, and charging session time and energy requirements. The framework uses hierarchical clustering to group drivers by their charging histories, capturing their heterogeneous behaviors and preferences across different segments or types of charging. The framework uses probabilistic mixture models for each driver group’s sessions to identify the unique charging behaviors observed within each segment. We illustrate its application with a large data set from California, profiling the charging patterns and unique driver clusters it identifies. Using the model knobs representing drivers’ battery capacities, behavior, and segment access we present scenarios for California’s charging demand in 2030 with 8 million passenger electric vehicles. Peak charging demand ranged from 3.3 to 8.7 GW across scenarios. Furthermore, each was calculated in under 45 s on a laptop computer.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Thermo4PFM: Facilitating Phase-field simulations of alloys with thermodynamic driving forces

Phase-field modeling is a popular front-tracking approach used to model solidification. Its time-evolution equations are often coupled to alloy composition and/or thermal diffusion in high-resolution multiphysics approaches. Materials thermodynamic properties tabulated in CALPHAD databases can be used for phase-field modeling to parameterize bulk energies of alloys. In addition, they can be naturally integrated into models such as the Kim-Kim-Suzuki (KKS) model where driving forces depend on the differences between chemical potentials of co-existing phases. In that case, a small system of coupled nonlinear equations needs to be solved at every point in space where the phase-field order parameter is to be updated and evolved in time. Here we present Thermo4PFM, a solver for the KKS equations for binary and ternary alloys, with two or three phases, and parameterized with CALPHAD models. Thermo4PFM is open source, written in C++, and can take advantage of Graphics Processing Units (GPU) accelerators. Using OpenMP offload capabilities for C++ classes, an excellent performance is demonstrated on GPU using the LLVM compiler. CALPHAD data is read from simple JSON files using an open source parser from the boost library.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Vidyut3d: A GPU accelerated fluid solver for non-equilibrium plasmas on adaptive grids

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures, in this work. Our plasma fluid model solves the coupled conservation equations for species transport, electrostatic Poisson and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive-grid/particle management library, AMReX, and is portable over widely available vendor specific GPU architectures. We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth-order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on capacitive discharges and atmospheric pressure streamer propagation. We demonstrate the use of our solver on two 3D simulation cases: an atmospheric streamer propagation in Ar-H2 mixtures and a low pressure three-electrode radio frequency reactor. Our performance studies on three different CPU+GPU architectures indicate ~ 150-400X speed-up using AMD and NVIDIA GPUs per time step compared to a single CPU core for a 4 million cell simulation with 15 species.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Holistic energy analysis method for thermal management architectures of data centers

Modern high-performance computing (HPC) data centers (DCs), particularly those supporting energy-intensive artificial intelligence (AI) workloads, face escalating thermal management challenges that degrade performance through thermal throttling and drive up cooling power consumption and operational costs. To address this challenge, many have developed a wide variety of thermal management solutions (single-phase, two-phase, direct, indirect, hybrid, and more) which attempt to cool HPC DCs effectively while attempting to minimize overall system power consumption. However, the analysis of these solutions and methods to effectively compare one with another is lacking. Overall power usage effectiveness (PUE) and total-power usage effectiveness (TUE) provide a metric to quantify power consumption but fail to identify components in the system which require further optimization. To address this, we propose a holistic analytical framework – the waterfall diagram (WFD) – which leverages a waterfall chart methodology, offering a comprehensive visualization of both the thermal management system loop and heat flow pathways from individual server components to the outdoor ambient. Use of the WFD enables graphical estimations of power efficiency and cooling performance across each component of a DC cooling system and complements Sankey-style energy flow visualizations by additionally resolving stage-wise temperature changes and incremental TUE contributions. The framework is used in conjunction with simulation-based approaches, to conduct a detailed pressure drop and flow distribution analysis aimed at identifying the optimal coolant distribution architecture for a single-phase direct-to-chip water-cooled DC, which serves as the baseline for subsequent WFD analysis. Among the evaluated architectures, the 3 U modular coolant distribution architecture is found to demonstrate the best performance, considering minimal pressure drop and uniform flow distribution. In addition, TUE is calculated for each cooling loop component based on its associated pressure drop and corresponding pumping power, which are integrated into the WFD. This correlation between TUE and local temperature offers immediate insight into the power efficiency and thermal performance contributions of individual components, facilitating further development and optimization. Examples of WFD applications are presented under varying thermal loads and ambient conditions, demonstrating reasonable cooling strategies. Notably, the 3 U modular architecture maintains a consistent chip case temperature of 85°C, achieving a TUE of 1.016 at ambient temperature of 47°C, and a TUE of 1.026 at ambient temperature of 52°C. The WFD methodology provides an efficient, holistic, and streamlined framework for DC thermal management architecture assessment and enables design optimization which is important for addressing the thermal-fluidic energy challenges of current and next-generation DCs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Asynchronous GPU-based DEM solver embedded in commercial CFD software with polyhedral mesh support

A novel graphical processing unit-based discrete element method solver is introduced to improve stability, performance, and provide seamless integration into commercial or open-source computational fluid dynamics software. A key innovation is eliminating a need for network communication between solvers, which was previously required for cross-platform coupling. This is accomplished by a direct coupling method that employs dynamic-linked libraries. Furthermore, the solver optimizes memory usage by streamlining the particle-cell search algorithm by eliminating the cells' searching grid. This ensures the solver is compatible with a wide range of mesh types, providing high geometric flexibility. The approach simplifies the simulation process by directly incorporating computational fluid dynamics mesh information into the discrete element method solver. The performance analysis indicates about sixteen times boost in computational speed compared to benchmark central processing unit-based solvers. Finally, the solver's compatibility with polyhedral meshes, a vital advantage for complex geometries, is tested against a referenced study regarding the simulation of an immersed-tube fluidized bed.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion quantum Monte Carlo

We review recent advances in the capabilities of the open source ab initio Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus used for greater efficiency and reproducibility. The auxiliary field QMC (AFQMC) implementation has been greatly expanded to include k-point symmetries, tensor-hypercontraction, and accelerated graphical processing unit (GPU) support. These scaling and memory reductions greatly increase the number of orbitals that can practically be included in AFQMC calculations, increasing the accuracy. Advances in real space methods include techniques for accurate computation of bandgaps and for systematically improving the nodal surface of ground state wavefunctions. Results of these calculations can be used to validate application of more approximate electronic structure methods, including GW and density functional based techniques. To provide an improved foundation for these calculations, we utilize a new set of correlation-consistent effective core potentials (pseudopotentials) that are more accurate than previous sets; these can also be applied in quantum-chemical and other many-body applications, not only QMC. These advances increase the efficiency, accuracy, and range of properties that can be studied in both molecules and materials with QMC and QMCPACK.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

ddcMD: A fully GPU-accelerated molecular dynamics program for the Martini force field

We have implemented the Martini force field within Lawrence Livermore National Laboratory’s molecular dynamics program, ddcMD. The program is extended to a heterogeneous programming model so that it can exploit graphics processing unit (GPU) accelerators. In addition to the Martini force field being ported to the GPU, the entire integration step, including thermostat, barostat, and constraint solver, is ported as well, which speeds up the simulations to 278-fold using one GPU vs one central processing unit (CPU) core. A benchmark study is performed with several test cases, comparing ddcMD and GROMACS Martini simulations. The average performance of ddcMD for a protein–lipid simulation system of 136k particles achieves 1.04 µs/day on one NVIDIA V100 GPU and aggregates 6.19 µs/day on one Summit node with six GPUs. The GPU implementation in ddcMD offloads all computations to the GPU and only requires one CPU core per simulation to manage the inputs and outputs, freeing up remaining CPU resources on the compute node for alternative tasks often required in complex simulation campaigns.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

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

GPU acceleration of hybrid functional calculations in the SPARC electronic structure code

We present a Graphics Processing Unit (GPU)-accelerated version of the real-space SPARC electronic structure code for performing hybrid functional calculations in generalized Kohn–Sham density functional theory. In particular, we develop a batch variant of the recently formulated Kronecker product-based linear solver for the simultaneous solution of multiple linear systems. We then develop a modular, math kernel based implementation for hybrid functionals on NVIDIA architectures, where computationally intensive operations are offloaded to the GPUs, while the remaining workload is handled by the central processing units (CPUs). Considering bulk and slab examples, we demonstrate that GPUs enable up to 8× speedup in node-hours and 80× in core-hours compared to CPU-only execution, reducing the time to solution on V100 GPUs to around 300 s for a metallic system with over 6000 electrons, and significantly reducing the computational resources required for a given wall time.

Kohn-Sham density functional theory↗
DOE OSTI2020

Wave function analysis with a maximum flow algorithm

An efficient algorithm for computing the maximum-flow path in a network is applied to the identification of the dominant configuration state functions (CSFs) in a graphically contracted function (GCF), configuration interaction, wave function. The flow network is a space of spin-adapted CSFs represented by a Shavitt graph, wherein the nodes correspond to orbital occupations and spin quantum numbers. The graph nodes are connected by arcs, and an arc density is defined as sums of the associated squared CSF coefficients. A max-min approach determines an upper bound to the maximum possible incoming flow for each graph node. A backtracking step generates a candidate walk and is followed by a limited search of alternative branching paths for the dominant CSF. The arc density contributions are removed from the graph, and the algorithm is reapplied to the updated graph. This list of generated walks can be partitioned in order to guarantee that the dominant CSFs have been identified. All of the steps in this algorithm are computationally efficient and do not depend on the potentially large dimension of the underlying linear CSF expansion space. An analysis of low-lying valence states of C-2 illustrates the method.

74 ATOMIC AND MOLECULAR PHYSICS↗