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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement

The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision iterative refinement to enhance methods for sparse systems based on approximate sparse factorizations. In doing so, we first develop a new error analysis for LU- and GMRES-based iterative refinement under a general model of LU factorization that accounts for the approximation methods typically used by modern sparse solvers, such as low-rank approximations or relaxed pivoting strategies. We then provide a detailed performance analysis of both the execution time and memory consumption of different algorithms, based on a selected set of iterative refinement variants and approximate sparse factorizations. Our performance study uses the multifrontal solver MUMPS, which can exploit block low-rank factorization and static pivoting. We evaluate the performance of the algorithms on large, sparse problems coming from a variety of real-life and industrial applications showing that mixed-precision iterative refinement combined with approximate sparse factorization can lead to considerable reductions of both the time and memory consumption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Multistage mixed precision iterative refinement

Abstract Low precision arithmetic, in particular half precision (16‐bit) floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings in energy. Motivated by this, there has been a renewed interest in mixed precision iterative refinement schemes for solving linear systems , and new variants of GMRES‐based iterative refinement have been developed. Each particular variant with a given combination of precisions leads to different condition number‐based constraints for convergence of the backward and forward errors, and each has different performance costs. The constraints for convergence given in the literature are, as an artifact of the analyses, often overly strict in practice, and thus could lead a user to select a more expensive variant when a less expensive one would have sufficed. In this work, we develop a multistage mixed precision iterative refinement solver which aims to combine existing mixed precision approaches to balance performance and accuracy and improve usability. For a user‐specified initial combination of precisions, the algorithm begins with the least expensive approach and convergence is monitored via inexpensive computations with quantities produced during the iteration. If slow convergence or divergence is detected using particular stopping criteria, the algorithm switches to use a more expensive, but more reliable variant. A novel aspect of our approach is that, unlike existing implementations, our algorithm first attempts to use “stronger” GMRES‐based solvers for the solution update before resorting to increasing the precision(s). In some scenarios, this can avoid the need to refactorize the matrix in higher precision. We perform extensive numerical experiments on a variety of random dense problems and problems from real applications which confirm the benefits of the multistage approach.

Oktay, Eda↗
DOE OSTI2025

ARCS: Agentic Retrieval-Augmented Code Synthesis with Iterative Refinement

Agentic Retrieval-Augmented Code Synthesis with Iterative RefinementIn supercomputing, efficient and optimized code generation is essential to leverage high-performance systems effectively. We have developed Agentic Retrieval-Augmented Code Synthesis (ARCS), an advanced framework for accurate, robust, and efficient code generation, completion, and translation. ARCS integrates Retrieval-Augmented Generation (RAG) with Chain-of-Thought (CoT) reasoning to systematically break down and iteratively refine complex programming tasks. An agent-based RAG mechanism retrieves relevant code snippets, while real-time execution feedback drives the synthesis of candidate solutions. This process is formalized as a state-action search tree optimization, balancing code correctness with editing efficiency. Evaluations on the Geeks4Geeks and HumanEval benchmarks demonstrate that ARCS significantly outperforms traditional prompting methods in translation and generation quality. By enabling scalable and precise code synthesis, ARCS offers transformative potential for automating and optimizing code development in supercomputing applications, enhancing computational resource utilization

Bhattarai, Manish [Los Alamos National Labs]↗
DOE OSTI2020

Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems

Double-precision floating-point arithmetic (FP64) has been the de facto standard for engineering and scientific simulations for several decades. Problem complexity and the sheer volume of data coming from various instruments and sensors motivate researchers to mix and match various approaches to optimize compute resources, including different levels of floating-point precision. In recent years, machine learning has motivated hardware support for half-precision floating-point arithmetic. A primary challenge in high-performance computing is to leverage reduced-precision and mixed-precision hardware. We show how the FP16/FP32 Tensor Cores on NVIDIA GPUs can be exploited to accelerate the solution of linear systems of equations Ax = b without sacrificing numerical stability. The techniques we employ include multiprecision LU factorization, the preconditioned generalized minimal residual algorithm (GMRES), and scaling and auto-adaptive rounding to avoid overflow. We also show how to efficiently handle systems with multiple right-hand sides. On the NVIDIA Quadro GV100 (Volta) GPU, we achieve a 4×-5× performance increase and 5× better energy efficiency versus the standard FP64 implementation while maintaining an FP64 level of numerical stability.

GMRES↗
NASA NTRS1992

Iterative refinement scheduling

We present a heuristics-based approach to deep space mission scheduling which is modeled on the approach used by expert human schedulers in producing schedules for planetary encounters. New chronological evaluation techniques are used to focus the search by using information gained during the scheduling process to locate, classify, and resolve regions of conflict. Our approach is based on the assumption that during the construction of a schedule there exist several disjunct temporal regions where the demand for one resource type or a single temporal constraint dominates (bottleneck regions). If the scheduler can identify these regions and classify them based on their dominant constraint, then the scheduler can select the scheduling heuristic.

Biefeld, Eric↗
NASA NTRS1998

Progressive content-based retrieval of image and video with adaptive and iterative refinement

A method and apparatus for minimizing the time required to obtain results for a content based query in a data base. More specifically, with this invention, the data base is partitioned into a plurality of groups. Then, a schedule or sequence of groups is assigned to each of the operations of the query, where the schedule represents the order in which an operation of the query will be applied to the groups in the schedule. Each schedule is arranged so that each application of the operation operates on the group which will yield intermediate results that are closest to final results.

Li, Chung-Sheng↗
DOE OSTI2022

A workflow for automatic generation and efficient refinement of individual pressure-dependent networks

Manual chemical kinetic model construction often requires modelists to at least implicitly guess all possible decay pathways and their relative fluxes for all important species. We present a workflow and associated tool for automatic generation and re finement of pressure-dependent networks that should enable modelists to efficiently and comprehensively identify decay pathways and estimate respective parameters for chemical species. This tool combines the capabilities of the Reaction Mechanism Generator (RMG) software to generate possible reaction paths, determine thermochemistry, approximate rate coefficients and estimate frequencies with the capabilities of the Arkane software to use quantum chemical parameters to compute thermochemistry and pressure dependent rates. A flux-based algorithm is used to decide which isomers to add to the network. Isomers added to the network are reacted to form other channels. When enough of the flux is accounted for by the isomers and bimolecular product channels, the generation process terminates to yield a comprehensive network. Network sensitivity analysis is applied to the network to identify the most important wells and barriers that can be refined using quantum chemistry calculations. Iterative refinement can then be used to achieve accuracy. The comprehensive network can be easily reduced using energy and flux-based algorithms to the most important channels and isomers in the network.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1991

Intelligent perturbation algorithms for space scheduling optimization

Intelligent perturbation algorithms for space scheduling optimization are presented in the form of the viewgraphs. The following subject areas are covered: optimization of planning, scheduling, and manifesting; searching a discrete configuration space; heuristic algorithms used for optimization; use of heuristic methods on a sample scheduling problem; intelligent perturbation algorithms are iterative refinement techniques; properties of a good iterative search operator; dispatching examples of intelligent perturbation algorithm and perturbation operator attributes; scheduling implementations using intelligent perturbation algorithms; major advances in scheduling capabilities; the prototype ISF (industrial Space Facility) experiment scheduler; optimized schedule (max revenue); multi-variable optimization; Space Station design reference mission scheduling; ISF-TDRSS command scheduling demonstration; and example task - communications check.

Kurtzman, Clifford R.↗
NASA NTRS2005

Apex Reference Manual 3.0 Beta

Apex is a toolkit for constructing software that behaves intelligently and responsively in demanding task environments. Reflecting its origin at NASA where Apex continues to be developed, current applications include: a) Providing autonomous mission management and tactical control capabilities for unmanned aerial vehicles including an autonomous surveillance helicopter and a simulation prototype of an unmanned fixed-wing aircraft to be used for wildfire mapping; b) Simulating human air traffic controllers, pilots and astronauts to help predict how people might respond to changes in equipment or procedures; and c) Predicting the precise duration and sequence of routine human behaviors based on a human-computer interaction engineering technique called CPM-GOMS. Among Apex s components are a set of implemented reasoning services, such as those for reactive planning and temporal pattern recognition; a software architecture that embeds and integrates these services and allows additional reasoning elements to be added as extensions; a formal language for specifying agent knowledge; a simulation environment to facilitate prototyping and analysis; and Sherpa, a set of tools for visualizing autonomy logic and runtime behavior. In combination, these are meant to provide a flexible and usable framework for creating, testing, and deploying intelligent agent software. Overall, our goal in developing Apex is to lower economic barriers to developing intelligent software agents. New ideas about how to extend or modify the system are evaluated in terms of their impact in reducing the time, expertise, and inventiveness required to build and maintain applications. For example, potential enhancements to the AI reasoning capabilities in the system are reviewed not only for usefulness and distinctiveness, but also for their impact on the readability and general usability of Apex s behavior representation language (PDL) and on the transparency of resulting behavior. A second central part of our approach is to iteratively refine Apex based on lessons learned from as diverse a set of applications as possible. Many applications have been developed by users outside the core development team including engineers, researchers, and students. Usability is thus a central concern for every aspect of Apex visible to a user, including PDL, Sherpa, the Apex installation process, APIs, and user documentation. Apex users vary in their areas of expertise and in their familiarity with autonomy technology. Focusing on usability, a development philosophy summarized by the project motto "Usable Autonomy," has been important part of enabling diverse users to employ Apex successfully and to provide feedback needed to guide iterative, user-centered refinement.

Freed, Michael A.↗
NASA NTRSDate not supplied

VIPER Lunar Rover Agile Mission Systems

Agile development methods, which have gone from outlier to mainstream in software development, are poised to expand into all aspects of space mission development. Modern software development operates on a principle of continuous deployment, where progress is verified not with conventional metrics, but with a continuous build, available to key stakeholders, enabling direct examination of the state of the code base, and assessment of progress through demonstration of capability. Delivery times are measured in weeks, not months. Stakeholders are part of the process on an ongoing basis. The cost of change is comparatively low and requirements, which often are not precisely defined at the start of a project, may be iteratively refined in a series of agile development cycles. Agile methods are compatible with traditional system engineering methods and may be tailored to the space operations environment. The low cost of change and iterative development cycles of agile enable requirements to be defined as outcomes and constraints, with design details to be refined during the development cycle. We are now at a point where agile methods may be extended beyond software, to Mission Systems, including the Mission Operations System and the Ground Data System. For NASA’s VIPER Lunar Rover Mission, scheduled to land at a lunar pole in late 2023, we are developing the Mission System using agile methods. As in agile software, where the measure of progress is working code, in agile mission system development, the measure of capability is what we can demonstrate. Demonstrations over presentations. We demonstrate mission system capability using simulations. The concept of operations, from commanding, to driving the rover, to how we downlink images for evaluation for a near-real time command cycle, will be tested and proven in simulation, years before we begin the traditional simulation cycle for training. “Say it then simulate it.” We develop and refine our designs using simulations, with an emphasis on new components of the system that are not well known early. For example, the required duration of a mission planning cycle for a lunar surface asset such as VIPER, that operates twenty-four hours a day, seven days a week, with continuous communications and a unique set of constraints based on the physics of the lunar poles and the line of site to Earth, is a unique problem in mission planning that is unlikely to be solved in a series of meetings. A small number of requirements specifying the outcomes may serve as the jumping off point to an agile development cycle, with demonstration in simulations. We have already demonstrated this process with simulations of rover driver decision time. VIPER is driven using near-real time command and control to waypoints. The driver decision time between waypoints is a fundamental enabling unit of productivity to accomplish the mission timeline. We have validated driver decision time in simulations of rover driving at the lunar South Pole, using the prototype mission tools for driving, command and control. The capability to develop and refine designs using simulations as part of agile Mission System development cycle changes the nature of team interactions, creating a focus on doing, rather than analyzing and documenting. Waterfall development cycles were, in part, a product of the significant cost of change in the early days of spaceflight. When the cost of change is high, it is vital to get your requirements right at the outset, because the system will be built to those specifications, and, when change is expensive, you better get it right early. However, modern technology has greatly lowered the cost of change, enabling iterative, rapid development cycles, in which key operations concepts may be tested and refined during development. Extending agile development to the Mission System for VIPER is a significant step in moving agile development methods for space operations beyond software, to the Mission System.

Agile↗
NASA NTRS2008

Automated Assume-Guarantee Reasoning by Abstraction Refinement

Current automated approaches for compositional model checking in the assume-guarantee style are based on learning of assumptions as deterministic automata. We propose an alternative approach based on abstraction refinement. Our new method computes the assumptions for the assume-guarantee rules as conservative and not necessarily deterministic abstractions of some of the components, and refines those abstractions using counter-examples obtained from model checking them together with the other components. Our approach also exploits the alphabets of the interfaces between components and performs iterative refinement of those alphabets as well as of the abstractions. We show experimentally that our preliminary implementation of the proposed alternative achieves similar or better performance than a previous learning-based implementation.

Pasareanu, Corina S.↗
NASA NTRS1987

A new art code for tomographic interferometry

A new algebraic reconstruction technique (ART) code based on the iterative refinement method of least squares solution for tomographic reconstruction is presented. Accuracy and the convergence of the technique is evaluated through the application of numerically generated interferometric data. It was found that, in general, the accuracy of the results was superior to other reported techniques. The iterative method unconditionally converged to a solution for which the residual was minimum. The effects of increased data were studied. The inversion error was found to be a function of the input data error only. The convergence rate, on the other hand, was affected by all three parameters. Finally, the technique was applied to experimental data, and the results are reported.

Tan, H.↗
DOE OSTI2021

RISE: robust iterative surface extension for sub-nanometer X-ray mirror fabrication

Precision optics have been widely required in many advanced technological applications. X-ray mirrors, as an example, serve as the key optical components at synchrotron radiation and free electron laser facilities. They are rectangular silicon or glass substrates where a rectangular Clear Aperture (CA) needs to be polished to sub-nanometer Root Mean Squared (RMS) to keep the imaging capability of the incoming X-ray wavefront at the diffraction limit. The convolutional polishing model requires a CA to be extended with extra data, from which the dwell time is calculated via deconvolution. However, since deconvolution is very sensitive to boundary errors and noise, the existing surface extension methods can hardly fulfill the sub-nanometer requirement. On one hand, the figure errors in a CA were improperly modeled during the extension, leading to continuity issues along the boundary. On the other hand, uncorrectable high-frequency errors and noise were also extended. In this study, we propose a novel Robust Iterative Surface Extension (RISE) method that resolves these problems with a data fitting strategy. RISE models the figure errors in a CA with orthogonal polynomials and ensures that only correctable errors are fit and extended. Combined with boundary conditions, an iterative refinement of dwell time is then proposed to compensate the errors brought by the extension and deconvolution, which drastically reduces the estimated figure error residuals in a CA while the increase of total dwell time is negligible. To our best knowledge, RISE is the first data fitting-based surface extension method and is the first to optimize dwell time based on iterative extension. An experimental verification of RISE is given by fabricating two elliptic cylinders (10 mm × 80 mm CAs) starting from a sphere with a radius of curvature around 173 m using ion beam figuring. The figure errors in the two CAs greatly improved from 204.96 nm RMS and 190.28 nm RMS to 0.62 nm RMS and 0.71 nm RMS, respectively, which proves that RISE is an effective method for sub-nanometer level X-ray mirror fabrication.

36 MATERIALS SCIENCE↗
NASA NTRS2006

Humanoid Mobile Manipulation Using Controller Refinement

An important class of mobile manipulation problems are move-to-grasp problems where a mobile robot must navigate to and pick up an object. One of the distinguishing features of this class of tasks is its coarse-to-fine structure. Near the beginning of the task, the robot can only sense the target object coarsely or indirectly and make gross motion toward the object. However, after the robot has located and approached the object, the robot must finely control its grasping contacts using precise visual and haptic feedback. This paper proposes that move-to-grasp problems are naturally solved by a sequence of controllers that iteratively refines what ultimately becomes the final solution. This paper introduces the notion of a refining sequence of controllers and characterizes this type of solution. The approach is demonstrated in a move-to-grasp task where Robonaut, the NASA/JSC dexterous humanoid, is mounted on a mobile base and navigates to and picks up a geological sample box. In a series of tests, it is shown that a refining sequence of controllers decreases variance in robot configuration relative to the sample box until a successful grasp has been achieved.

Platt, Robert↗