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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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Extending the Roofline Model for Asynchronous Many-Task Runtimes

New architectural trends and extreme scale parallelism challenge the efficient mapping of applications to large scale and emerging systems. Fine-grained Asynchronous Manytask Runtimes (AMR) offer a unique flexibility to hide the varying latencies of contentious operations, and facilitate the effective exploitation of abundant resources. By decomposing work into smaller asynchronous chunks, the impact of unpredictable operations can be mitigated through a tighter overlapping of tasks. Unfortunately, the cost of this decomposition comes at a potentially steep price in the form of runtime overhead which can at times rival the cost of the computation itself. This leads to the question, how large should a task be? A common practice for application developers is to experimentally determine the granularity of a task after a code has been parallelized. Instead, we propose a new methodology based on an extended Roofline model to provide practical upper bounds on the throughput performance of an application. First, we extend the Roofline model to support not only latency hiding analysis, but also a multidimensional amortized analysis. By combining this new methodology with a serial application and an AMR implementation, we can predict the worst case runtime overhead attribution of individual runtime features prior to the development of parallel code. Thus, this runtimecentric methodology can provide a vehicle for application/runtime codesign by providing a comprehensive bottleneck analysis based on existing runtime features.

Suetterlein, Joshua D.↗
DOE OSTI2022

Elastic Resource Management for Deep Learning Applications in a Container Cluster

The increasing demand for learning from massive datasets is restructuring our economy. Effective learning, however, involves nontrivial computing resources. Most businesses utilize commercial infrastructure providers (e.g., AWS) to host their computing clusters in the cloud, where various jobs compete for available resources. While cloud resource management is a fruitful research field that has made many advances in production, such as Kubernetes and YARN, few efforts have been invested to further optimize the system performance, especially for deep learning (DL) training jobs in a container cluster. This work introduces FlowCon, a system that is able to monitor the individual evaluation functions of DL jobs at runtime, and thus to make placement decisions on resource allocations elastically. Here, we present a detailed design and implementation of FlowCon and conduct intensive experiments over various DL models. The results demonstrate that FlowCon significantly improves DL job completion time and resource utilization efficiency, compared to default systems. According to the results, FlowCon is able to improve the completion time by up to 68.8% and meanwhile, reduce the makespan by 18.0%, in the presence of various DL job workloads.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Full-Stack Exploration of Language-Based Parallelism in Fortran 2023

This poster explores native parallel features in Fortran 2023 through the lens of supporting applications with libraries, compilers, and parallel runtimes. The language revision informally named Fortran 2008 introduced parallelism in the form of Single Program Multiple Data (SPMD) execution with two broad feature sets: (1) loop-level parallelism via do concurrent and (2) a Partitioned Global Address Space (PGAS) comprised of distributed “coarray” data structures. Fortran’s native parallelism has demonstrated high performance [1] and reduced the burden of inserting what sometimes amounts to more directives than code. Several compilers support both feature sets, typically by translating do concurrent into serial do loops annotated by parallel directives and by translating SPMD/PGAS features into direct calls to a communication library. Our research focuses primarily on two questions: (1) can the compiler’s parallel runtime library be developed in the language being compiled (Fortran) and (2) can we define an interface to the runtime that liberates compilers from being hardwired to one runtime and vice versa. We are answering these questions by developing the Parallel Runtime Interface for Fortran (PRIF) [2] and the Co-Array Fortran Framework of Efficient Interfaces to Network Environments (Caffeine) [3]. Caffeine is initially targeting adoption by LLVM Flang, a new open-source Fortran compiler developed by a broad community in industry, academia, and government labs. We are also exploring the use of these features in Inference-Engine, a deep learning library designed to facilitate neural network training and inference for high-performance computing applications written in modern Fortran.

Rasmussen, Katherine↗
DOE OSTI2024

Designing and prototyping extensions to the Message Passing Interface in MPICH

As HPC system architectures and the applications running on them continue to evolve, the MPI standard itself must evolve. The trend in current and future HPC systems toward powerful nodes with multiple CPU cores and multiple GPU accelerators makes efficient support for hybrid programming critical for applications to achieve high performance. However, the support for hybrid programming in the MPI standard has not kept up with recent trends. The MPICH implementation of MPI provides a platform for implementing and experimenting with new proposals and extensions to fill this gap and to gain valuable experience and feedback before the MPI Forum can consider them for standardization. Here, in this work, we detail six extensions implemented in MPICH to increase MPI interoperability with other runtimes, with a specific focus on heterogeneous architectures. First, the extension to MPI generalized requests lets applications integrate asynchronous tasks into MPI’s progress engine. Second, the iovec extension to datatypes lets applications use MPI datatypes as a general-purpose data layout API beyond just MPI communications. Third, a new MPI object, MPIX_Stream, can be used by applications to identify execution contexts beyond MPI processes, including threads and GPU streams. MPIX stream communicators can be created to make existing MPI functions thread-aware and GPU-aware, thus providing applications with explicit ways to achieve higher performance. Fourth, MPIX Streams are extended to support the enqueue semantics for offloading MPI communications onto a GPU stream context. Fifth, thread communicators allow MPI communicators to be constructed with individual threads, thus providing a new level of interoperability between MPI and on-node runtimes such as OpenMP. Lastly, we present an extension to invoke MPI progress, which lets users spawn progress threads with fine-grained control to adapt the communication performance to their application designs. We describe the design and implementation of these extensions, provide usage examples, and highlight their expected benefits with performance results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Static and Dynamic Frequency Scaling on Multicore CPUs

Dynamic voltage and frequency scaling (DVFS) adapts CPU power consumption by modifying a processor’s operating frequency (and the associated voltage). Typical approaches employing DVFS involve default strategies such as running at the lowest or the highest frequency, or observing the CPU’s runtime behavior and dynamically adapting the voltage/frequency configuration based on CPU usage. In this paper, we argue that many previous approaches suffer from inherent limitations, such as not account- ing for processor-specific impact of frequency changes on energy for different workload types. We first propose a lightweight runtime-based approach to automatically adapt the frequency based on the CPU workload, that is agnostic of the processor characteristics. We then show that further improvements can be achieved for affine kernels in the application, using a compile-time characterization instead of run-time monitoring to select the frequency and number of CPU cores to use. Our framework relies on a one-time energy characterization of CPU-specific DVFS profiles followed by a compile-time categorization of loop-based code segments in the application. These are combined to determine a priori of the frequency and the number of cores to use to execute the application so as to optimize energy or energy-delay product, outperforming runtime approach. Extensive evaluation on 60 benchmarks and five multi-core CPUs show that our approach systematically outperforms the powersave Linux governor, while improving overall performance.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Design, Analysis, and Operations Toolkit (DAO-Tk)

The Design, Analysis, and Operations Toolkit (DAO-Tk) is a software package that allows users to explore design optimization, operations decision, and performance characterization of concentrating solar power tower plants. Users interface with the tool through a scripting language, and results are reported in time series tables, plots, runtime logs, and design outputs. Users choose from a list of variables such as tower height, solar multiple, design-point irradiance, thermal storage size, etc., and specify information about the system using a list of parameters. The software can then optimize the specified variables to reduce the cost of energy produced by the system while meeting certain production requirements, accounting for uncertain weather and electricity price forecasts, and correcting for equipment failures or repair time. The DAO-Tk software is the first comprehensive design tool of it's kind to incorporate all of these aspects while being deployed as open source.

Martinek, Janna↗
DOE OSTI2018

ASC CSSE Level 2 Milestone #6362: Resilient Asynchronous Many Task Programming Model

This report is an outcome of the ASC CSSE Level 2 Milestone 6362: Analysis of Re- silient Asynchronous Many-Task (AMT) Programming Model. It comprises a summary and in-depth analysis of resilience schemes adapted to the AMT programming model. Herein, performance trade-offs of a resilient-AMT prograrnming model are assessed through two ap- proaches: (1) an analytical model realized by discrete event simulations and (2) empirical evaluation of benchmark programs representing regular and irregular workloads of explicit partial differential equation solvers. As part of this effort, an AMT execution simulator and a prototype resilient-AMT programming framework have been developed. The former permits us to hypothesize the performance behavior of a resilient-AMT model, and has undergone a verification and validation (V&V) process. The latter allows empirical evaluation of the perfor- mance of resilience schemes under emulated program failures and enabled the aforementioned V&V process. The outcome indicates that (1) resilience techniques implemented within an AMT framework allow efficient and scalable recovery under frequent failures, that (2) the abstraction of task and data instances in the AMT programming model enables readily us- able Application Program Interfaces (APIs) for resilience, and that (3) this abstraction enables predicting the performance of resilient-AMT applications with a simple simulation infrastruc- ture. This outcome will provide guidance for the design of the AMT programming model and runtime systems, user-level resilience support, and application development for ASC's next generation platforms (NGPs).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Concurrent Optimization of Capital Cost and Expected O&M

Concentrating solar power (CSP) technologies can utilize heat from concentrated sunlight from a field of tracking mirrors to generate electricity, reform fuel, provide process heat, or augment fossil plant heat sources. Electricity-generating power tower systems focus light from thousands of independent heliostats onto a thermal receiver, which uses the focused light to warm a heat transfer fluid (HTF), typically, a molten nitrate salt. The HTF is then sent to a power generation cycle or diverted into thermal energy storage (TES) for later use. Thermal storage is – in principle – a straightforward proposition. However, optimal utilization of a TES resource is complex and multi-faceted: thermal energy may be dispatched to produce electricity immediately upon first availability, or thermal energy may be reserved for next-day peak periods at risk of filling storage and dumping energy, or a portion of the thermal energy can be reserved to maintain equipment temperatures, reducing power cycle startup time, etc. Many possible dispatch permutations variously emphasize producing peak power, operating through transients, expediting daily startup, etc. The best operation strategy can change day-to-day throughout the year, depending on the weather and market pricing forecasts. The project we describe in this report develops a software package that allows users to explore design optimization, operations decisions, and performance characterization of concentrating solar power tower plants. Users interface with the tool through a scripting language, and results are reported in time series tables, plots, runtime logs, and design outputs. Users choose from a list of variables such as tower height, solar multiple, design-point irradiance, thermal storage size, etc., and specify information about the system using a list of parameters. The software can then optimize the specified variables to reduce the cost of energy produced by the system while meeting certain production requirements, accounting for uncertain weather and electricity price forecasts, and correcting for equipment failures or repair time. The software we develop is the first comprehensive design tool of its kind to incorporate all of these aspects while being deployed as open source.

14 SOLAR ENERGY↗
DOE OSTI2015

Scalable Out-of-Core Solvers on Xeon Phi Cluster

This paper documents the implementation of a distributive out-of-core (OOC) solver for performing LU and Cholesky factorizations of a large dense matrix on clusters of many-core programmable co-processors. The out-of- core algorithm combines both the left-looking and right-looking schemes aimed to minimize the movement of data between the CPU host and the co-processor, optimizing data locality as well as computing throughput. The OOC solver is built to align with the format of the ScaLAPACK software library, making it readily portable to any existing codes using ScaLAPACK. A runtime analysis conducted on Beacon (an Intel Xeon plus Intel Xeon Phi cluster which composed of 48 nodes of multi-core CPU and MIC) at the Na- tional Institute for Computational Sciences is presented. Comparison of the performance on the Intel Xeon Phi and GPU clusters are also provided.

D'Azevedo, Ed F↗
DOE OSTI2019

Accelerating the Global Arrays ComEx Runtime using Multiple Progress Ranks

Partitioned Global Address Space (PGAS) models are part of system software that are being designed to support communication runtime for exascale applications. Suitability of using MPI as a scalable PGAS communication subsystem has been shown as a viable option due to its standardization and higher performance. We used MPI two-sided semantics with a combination of automatic and user defined splitting of MPI communicators to achieve asynchronous progress. Our implementation can make use of multiple asynchronous progress ranks (PR) per node that can be mapped to the computing architecture of a node in a distributed cluster. We are able to show significant speed up of over 2.0X and scaling of communication bound computational chemistry application over 1024 nodes of state- of-the-art HPC clusters. Our results show that while running a communication bound application workload on a certain number of cluster nodes, a use of optimum number of ranks dedicated for communication may be used to achieve asynchronous communication progress and obtain highest performance.

PGAS, global-arrays, NWCHEM, NWChemEx, HPC, GPGPU↗
DOE OSTI2025

A Scalable Multi-Modal Framework for High-Fidelity Distributed Human Mobility Simulations

The development of data-driven models for human mobility in urban settings requires access to substantial and diverse real-world data. However, existing historical data often presents challenges such as limited volume, variety, and veracity, as well as missing data and privacy preservation concerns. Also, urban mobility modeling is inherently time-variant, complex, and multi-modal, encompassing everything from individual walking and running to private road travel and large-scale public transportation. These challenges call for innovative solutions to overcome data limitations and compute needs to model mobility behaviors accurately. To address these challenges, we propose a distributed, co-simulation-based architecture DURMOSim that integrates real-world data with scalable, high-fidelity simulations, demonstrating distributed co-simulation feasibility with existing mobility models. DURMOSim underpins a modular integration that would enable using any available mobility simulators for greater extensibility and scalability in performing various urban scenarios. In this paper, we present the design, implementation, and performance evaluation of DURMOSim, highlighting its capability to model population-scale mobility patterns. Our initial results show its ability to dynamically synchronize multiple simulation models at runtime with negligible computational overhead. We believe DURMOSim could be a robust tool for advancing urban mobility research and intelligent transportation systems.

Yoginath, Srikanth [ORNL] (ORCID:0000000184236050)↗
DOE OSTI2014

Thrifty: An Exascale Architecture for Energy Proportional Computing

The objective of this project is to design different aspects of a novel exascale architecture called Thrifty. Our goal is to focus on the challenges of power/energy efficiency, performance, and resiliency in exascale systems. The project includes work on computer architecture (Josep Torrellas from University of Illinois), compilation (Daniel Quinlan from Lawrence Livermore National Laboratory), runtime and applications (Laura Carrington from University of California San Diego), and circuits (Wilfred Pinfold from Intel Corporation). In this report, we focus on the progress at the University of Illinois during the last year of the grant (September 1, 2013 to August 31, 2014). We also point to the progress in the other collaborating institutions when needed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Development and Validation of Algorithms That Analyze Communicating Thermostat Data to Identify Enclosure Retrofit Opportunities

Annual energy savings of up to $\$ 4$ to $\$ 5$ billion could be achieved nationwide through basic insulation and heating system retrofits of existing homes. However, current utility energy efficiency programs are costly and challenging to scale. Customer acquisition occurs primarily through energy bill mailers, mass media, and online advertising that lack specificity about home-specific retrofit opportunities, expected energy savings, and cost-effectiveness. Specific retrofit opportunities are identified via on-site home energy assessments (HEAs) that are inconvenient to homeowners, expensive, and of variable accuracy. We developed computational algorithms that automatically analyze communicating thermostat (CT) heating data that could be used to increase the customer uptake of insulation and air sealing energy conservation measures (ECMs) by identifying homes with the most significant retrofit opportunities, estimating post-retrofit energy savings, and formulating home-specific outreach. The algorithms are based on an extended second-order grey-box model that characterizes a building’s thermal response using lumped elements, coupled with an empirical model of infiltration that accounts for both wind and stack effects. The basic parameters of the model correspond to actual physical parameters of the home, i.e., the home’s overall R-value of and the building envelope ACH50. Unlike the conventional approach, which estimates model parameters based on the best fit to the observed time-dependent room temperature, our approach derives correlations between the daily heating system runtime and temperature difference (indoor-outdoor) that are more robust to data quality issues in real-world applications. We also used HEA data for algorithm development and validation. With the help of our utility partners, Eversource and National Grid, we obtained data sets for hundreds of Massachusetts homes. For each home, these data sets included three sets of information anonymized by the utility: (1) CT data (HVAC runtime, room temperature, and, for some vendors, outdoor temperature and wind speed) collected by the CT vendor (one of three) over a heating season, (2) HEA report performed by the HEA vendor (same vendor for all homes), (3) Monthly utility gas bills coincident with the CT data (3 to 24 per home, depending on availability). For some homes, we also obtained blower-door test results. Initially, we applied the algorithms developed to homes with a single CT and then extended them to homes with two CTs by using an equivalent home approach. Finally, we developed algorithms for prediction of energy savings and a methodology of comparing our predictions with those generated by HEAs. The main technical results indicate that we can reliably identify homes with insulation and/or air sealing retrofit opportunities and provide accurate savings predictions. Our hypothesis is that the algorithms could be applied to utility energy efficiency programs to identify homes that could realize significant energy savings from insulation and/or air sealing retrofits. This information could then be used to reach out to those homes with highly customized outreach, thereby delivering increased program energy savings and cost-effectiveness. This would: Significantly increase the uptake rate of on-site HEAs, and Significantly increase the fraction of HEAs resulting in ECM implementation. To test these hypotheses, we designed and conducted a randomized controlled trial (RCT). The RCT results suggest that personal messaging leads to a two- to five-fold increase in the HEA uptake rate.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Experience with the alpaka performance portability library in the CMS software

ion Library for Parallel Kernel Acceleration) is a header-only C++ library that provides performance portability across different back-ends, abstracting the underlying levels of parallelism. It supports serial and parallel execution on CPUs, and extremely parallel execution on NVIDIA, AMD and Intel GPUs.This contribution will show how alpaka is used in the CMS software to develop and maintain a single code base; to use different toolchains to build the code for each supported back-end, and link them into a single application; to seamlessly select the best backend at runtime, and implement portable reconstruction algorithms that run efficiently on CPUs and GPUs from different vendors. It will describe the validation and deployment of the alpaka-based implementation in the CMS High Level Trigger, and highlight how it achieves near-native performance.

Alawieh, Jaafar [CERN]↗
DOE OSTI2020

Locality-Aware Scheduling for Scalable Heterogeneous Environments

Heterogeneous computing promise boost performance of scientific applications by allowing massively parallel execution of computational tasks. However, manually managing extremely heterogeneous, multi-device systems is complicated and may result in sub-optimal performance. Specifically, data management is an extremely challenging problem on multi-device systems. In this work, we introduce two locality-aware schedulers for the Minos Computing Library (MCL), an asynchronous, task-based programming model and runtime for extremely heterogeneous systems. The first scheduler implements a pure locality-aware algorithm to maximize data reuse, though it might incur in ”hot-spots” that limit system utilization. The second scheduler mitigates this drawback by dynamically targeting between locality-awareness and system utilization based on the current workload and available computing devices. Our results show that locality-awareness greatly benefit applications that exhibit data reuse, providing up to 6.9x and 7.9x over the original MCL scheduler and equivalent OpenCL implementations, respectively. Moreover, our schedulers introduce negligible overhead compared with the original MCL scheduler and achieve similar performance for applications that don’t benefit from data locality.

Architecture, co-design, Task-based programming mo↗
DOE OSTI2020

Pulsed Thermal Tomography Nondestructive Examination of Additively Manufactured Reactor Materials (Second Annual Progress Report)

Additive manufacturing (AM) is an emerging method for cost-efficient fabrication of nuclear reactor parts. AM of metallic structures for nuclear energy applications is currently based on laser powder bed fusion (LPBF) process, which can introduce internal material flaws, such as pores and anisotropy. Integrity of AM structures needs to be evaluated nondestructively because material flaws could lead to premature failures due to exposure to high temperature, radiation and corrosive environment in a nuclear reactor. Thermal tomography (TT) provides a capability for non-destructive evaluation of sub-surface defects in arbitrary size structures. Thermal tomography is a computational method for heat diffusion-based imaging of solids, which provides 3D visualization of data from flash thermography measurements. We investigate thermal tomography imaging and nondestructive evaluation of stainless steel and nickel super alloy metallic structures produced with laser powder bed fusion (LPBF) additive manufacturing (AM) process. Metallic structures produced with LPBF contain defects, and there are limited capabilities to evaluate these structures non-destructively. Thermal tomography reconstruction of 3D apparent spatial effusivity provides information about AM structure geometry and internal material flaws. We study performance of thermal tomography in imaging of metallic structures through COMSOL computer simulations of transient heat transfer, and through reconstruction of data obtained from experimental measurements. Reconstruction of internal defects is investigated using a stainless steel 316L specimen with flat bottom hole (FBH) indentations, and Inconel 718 plate produced with laser powder bed fusion (LPBF) method, which contains imprinted hemispherical shape low density regions containing non-sintered metallic powder. The FBH’s have the same sizes as the imprinted defects in the LPBF specimens, but offer better imaging contrast. Thermal tomography reconstructions provide visualizations of internal defects, and allow for estimation of their sizes and locations. Detection sensitivity of TT is limited by noises. We investigate separation of signal from noise in thermography images using several machine learning (ML) methods, including new spatio-temporal blind source separation (STBSS) and spatio-temporal sparse dictionary learning (STSDL) methods. Performance of the ML methods is benchmarked using thermography data obtained from imaging stainless steel 316L and Inconel 718 specimens produced LPBF method with imprinted calibrated porosity defects. The ML methods are ranked by F-score and execution runtime. Finally, we investigate TT of AM stainless steel 316L specimen with imprinted internal porosity defects using relatively low-cost, small form factor infrared (IR) camera based on uncooled micro bolometer detector. Sparse coding related K-means singular value decomposition (SVD) machine learning, image processing algorithms are developed to improve quality of TT images through removal of Additive white Gaussian noise without blurring the images. Following initial qualification of an AM component for deployment in a nuclear reactor, a compact TT can also be used for in-service nondestructive evaluation (NDE). With capability to perform in-service NDE of the AM component lifecycle, TT data can be used for development of a component digital twin.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Intercomparison of flood inundation models across land use types and hydrological flood stages

Flood Inundation Mapping (FIM) model selection is a key operational decision because accurate, rapid mapping underpins early warning and resource allocation. FIM performance is context-dependent and can vary with hydrograph phase, land-use/land-cover (LULC), and the evaluation benchmark. Intercomparison studies typically assess a single near-peak snapshot against one reference dataset. Here, we provide a context-stratified intercomparison across (i) multiple hydrograph phases, (ii) LULC classes, and (iii) benchmark types, for five FIM approaches spanning a wide range of physical complexity and operational cost (TRITON, LISFLOOD-FP, HEC-RAS 2D, ARC-Curve2Flood, and OWP HAND-FIM). We use the Hurricane Matthew flood (2016) in the Neuse River Basin, North Carolina, USA, as a case study. Using high-resolution remote sensing-derived flood inundation maps, hand-labeled points, and building footprints, we assess model skill across two rising and two falling hydrograph limbs and across major LULC types. Results show that model rankings shift systematically across contexts: LISFLOOD-FP ranks highest in three of four flood phases, while TRITON leads during one rising limb phase; LISFLOOD-FP performs best in vegetated areas, whereas HEC-RAS improves relative performance in agricultural and urban areas; and benchmark choice influences conclusions, with LISFLOOD-FP performing best for flooded-building detection in the late falling limb, while TRITON ranks highest against hand-labeled points. We also report representative wall-clock runtimes for each workflow to provide use-case context for operational feasibility. Together, these results offer transferable guidance for model selection and for designing large-scale, benchmark-aware FIM intercomparison studies.

Nikrou, Parvaneh [University of Alabama]↗
DOE OSTI2017

Aces4: A Platform for Computational Chemistry Calculations with Extremely Large Block-Sparse Arrays

Aces4 is a parallel programming platform comprising a DSL for Computational Chemistry and its runtime system. It offers a convenient way to express parallelism together with extensive support for extremely large, possibly sparse, distributed arrays. It aids scientists in the creation of performant, scalable, massively parallel programs that can effectively take advantage of leadership class computing systems to address important scientific questions. Aces4 has enabled the development and implementation of new methods in electronic structure theory which are breaking new ground in their ability to perform highly accurate calculations on ever larger molecular systems. In this paper the design of Aces4, which is based on the the Super Instruction Architecture approach, is described. Experimental scaling results for Molecular Cluster Perturbation Theory, a new method enabled by Aces4, and CCSD, a widely used computational chemistry method are given.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗