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

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Revisiting the ODE Method for Recursive Algorithms: Fast Convergence Using Quasi Stochastic Approximation

Several decades ago, Profs. Sean Meyn and Lei Guo were postdoctoral fellows at ANU, where they shared interest in recursive algorithms. It seems fitting to celebrate Lei Guo's 60th birthday with a review of the ODE Method and its recent evolution. The method has been regarded as a technique for algorithm analysis. It is argued that this viewpoint is backwards: The original stochastic approximation method was surely motivated by an ODE, and tools for analysis came much later (based on establishing robustness of Euler approximations). The paper presents a brief survey of recent research in machine learning that shows the power of algorithm design in continuous time, following by careful approximation to obtain a practical recursive algorithm. While these methods are usually presented in a stochastic setting, this is not a prerequisite. In fact, recent theory shows that rates of convergence can be dramatically accelerated by applying techniques inspired by quasi Monte-Carlo. Subject to conditions, the optimal rate of convergence can be obtained by applying the averaging technique of Polyak and Ruppert. The conditions are not universal, but theory suggests alternatives to achieve acceleration. The theory is illustrated with applications to gradient-free optimization, and policy gradient algorithms for reinforcement learning.

learning and adaptive systems in artificial intell↗
DOE OSTI2021

SDSS-V Algorithms: Fast, Collision-free Trajectory Planning for Heavily Overlapping Robotic Fiber Positioners

Robotic fiber positioner (RFP) arrays are becoming heavily adopted in wide-field massively multiplexed spectroscopic survey instruments. RFP arrays decrease nightly operational overheads through rapid reconfiguration between fields and exposures. In comparison to similar instruments, SDSS-V has selected a very dense RFP packing scheme where any point in a field is typically accessible to three or more robots. This design provides flexibility in target assignment. However, the task of collisionless trajectory planning is especially challenging. We present two multiagent distributed control strategies that are highly efficient and computationally inexpensive for determining collision-free paths for RFPs in heavily overlapping workspaces. We demonstrate that a reconfiguration path between two arbitrary robot configurations can be efficiently found if a “folded” state, in which all robot arms are retracted and aligned in a lattice-like orientation, is inserted between the initial and final states. Although developed for SDSS-V, the approach we describe is generic and thus applicable to a wide range of RFP designs and layouts. Robotic fiber positioner technology continues to advance rapidly, and in the near future ultra-densely packed RFP designs may be feasible. Our algorithms are especially capable in routing paths in very crowded environments, where we see efficient results even in regimes significantly more crowded than the SDSS-V RFP design.

42 ENGINEERING↗
DOE OSTI2026

A Fast Algorithm for Computing Zigzag Representatives

Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtrations encode the evolution of homological features. Although one can locate a particular feature at any index in the filtration using existing algorithms, the resulting representatives may not be compatible with the zigzag: a representative cycle at one index may not map into a representative cycle at its neighbor. For this, one needs to compute compatible representative cycles along each bar in the barcode. It is known that the barcode for a zigzag filtration with m insertions and deletions can be computed $O(m^ω)$ in time, where $ω < 2.373$ is the matrix multiplication exponent. However, it is not known how to compute the compatible representatives so efficiently. For a non-zigzag filtration, the classical matrix-based algorithm provides representatives in $O(m^3)$ time, which can be improved to $O(m^ω)$. However, no known algorithm for zigzag filtrations computes the representatives with the $O(m^3)$ time bound. We present an $O(m^3 n)$ time algorithm for this problem, where $n ≤ m$ is the size of the largest complex in the filtration.

Persistent homology↗
DOE OSTI2021

A Fast Algorithm for Scanning Transmission Electron Microscopy Imaging and 4D-STEM Diffraction Simulations

Scanning transmission electron microscopy (STEM) is an extremely versatile method for studying materials on the atomic scale. Many STEM experiments are supported or validated with electron scattering simulations. However, using the conventional multislice algorithm to perform these simulations can require extremely large calculation times, particularly for experiments with millions of probe positions as each probe position must be simulated independently. Recently, the plane-wave reciprocal-space interpolated scattering matrix (PRISM) algorithm was developed to reduce calculation times for large STEM simulations. Here, we introduce a new method for STEM simulation: partitioning of the STEM probe into “beamlets,” given by a natural neighbor interpolation of the parent beams. This idea is compatible with PRISM simulations and can lead to even larger improvements in simulation time, as well requiring significantly less computer random access memory (RAM). We have performed various simulations to demonstrate the advantages and disadvantages of partitioned PRISM STEM simulations. We find that this new algorithm is particularly useful for 4D-STEM simulations of large fields of view. We also provide a reference implementation of the multislice, PRISM, and partitioned PRISM algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Fast Algorithms for Scientific Data Compression

Many scientific simulations and experiments generate terabytes to petabytes of data daily, necessitating data compression techniques. Unlike video and image compression, scientists require methods that accurately preserve primary data (PD) and derived quantities of interest (QoIs). In our previous work, we demonstrated the effectiveness of hybrid compression techniques that combine machine learning with traditional approaches. This paper presents innovative computational techniques aimed at expediting the compression pipeline. Our experiments, conducted on two distinct platforms with a large-scale XGC-based fusion simulation, demonstrate that the overhead incurred by these new approaches is less than one percent of the computational resources needed for the simulation.

Banerjee, Tania↗
DOE OSTI2024

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Retrieval of temperature and humidity profiles from ground-based high-resolution infrared observations using an adaptive fast iterative algorithm

Various retrieval algorithms have been developed for retrieving temperature and water vapor profiles from Atmospheric Emitted Radiance Interferometer (AERI) observations. The physical retrieval algorithm, named AERI Optimal Estimation (AERIoe), outperforms other retrieval algorithms in many aspects except the retrieval time, which is significantly increased due to the complex radiative transfer process. The calculation of the Jacobian matrix is the most computationally intensive step of the physical retrieval algorithm. Interestingly, an analysis of the change in AERI observations' information content with respect to Jacobians revealed that the AERIoe algorithm's performance presents negligible dependence on these metrics. Thus, the Jacobian matrix could remain unchanged when the variation in the atmospheric state is small in the retrieval process to reduce the most time-consuming computation. On the basis of the above findings, a fast physical–iterative retrieval algorithm was proposed by adaptively recalculating Jacobians in keeping with the changes in the atmospheric state. Experiments with synthetic observations demonstrate that the proposed method experiences an average reduction in retrieval time by an impressive 59 % compared to the original AERIoe algorithm while achieving maximum root-mean-square errors of less than 0.95 K and 0.22 log(ppmv) for heights below 3 km for the temperature and water vapor profile, respectively. Further analyses revealed that the fast-retrieval algorithm reached an acceptable convergence rate of 98.7 %, marginally lower than AERIoe's 99.9 % convergence rate for the 826 cases used in this study.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Sempervirens: A Fast Reconstruction Algorithm for Noisy and Incomplete Binary Matrix Representations of Trees

Applications such as reconstructing cell lineage trees (represented as phylogenetic trees) from single-cell sequencing data require reconstructing a {0,1}-matrix that has many errors and missing entries. We introduce Sempervirens, a very fast matrix reconstruction algorithm for noisy and incomplete matrix representations of phylogenetic trees. Sempervirens uses an iterative maximum-likelihood approach to determine the topology tree represented by the corrupted data. We show that Sempervirens is at least three orders of magnitude faster than other methods on thousand by thousand matrices, with the speed gap widening with larger matrices. We also show that Sempervirens matches state-of-the-art methods in reconstruction accuracy. The speed of Sempervirens enables it to be tractably applied to reconstructing much larger matrices than those that other methods can reconstruct. In addition to experimental results, we justify the algorithm with a mathematical treatment of its subprocedures.

algorithms↗
DOE OSTI2023

AlignOT: An Optimal Transport Based Algorithm for Fast 3D Alignment With Applications to Cryogenic Electron Microscopy Density Maps

Aligning electron density maps from Cryogenic electron microscopy (cryo-EM) is a first key step for studying multiple conformations of a biomolecule. As this step remains costly and challenging, with standard alignment tools being potentially stuck in local minima, we propose here a new procedure, called AlignOT, which relies on the use of computational optimal transport (OT) to align EM maps in 3D space. By embedding a fast estimation of OT maps within a stochastic gradient descent algorithm, our method searches for a rotation that minimizes the Wasserstein distance between two maps, represented as point clouds. Here, we quantify the impact of various parameters on the precision and accuracy of the alignment, and show that AlignOT can outperform the standard local alignment methods, with an increased range of rotation angles leading to proper alignment. We further benchmark AlignOT on various pairs of experimental maps, which account for different types of conformational heterogeneities and geometric properties. As our experiments show good performance, we anticipate that our method can be broadly applied to align 3D EM maps.

3D alignment↗
DOE OSTI2025

Ensemble Simulation Techniques and Fast Randomized Algorithms

The major goals of the project were to develop and analyze new ensemble simulation techniques, including trajectory stratification and preconditioned MCMC techniques, as well as develop fast numerical linear algebra techniques closely related to ensemble simulation ideas. The trajectory stratification techniques involve simulating in parallel short trajectory fragments of a Markov process confined to a specific region of space‐time and then patching together the statistics gathered to assemble estimates of very general dynamical properties. We have also developed this approach for rare event simulation and extended the techniques to applications requiring a more general framework (such as electronic structure calculations). The preconditioned MCMC techniques involve simulating multiple Markov chains in parallel and then using information from the ensemble to speed the mixing of each individual chain. The fast randomized linear algebra methods are motivated by the diffusion Monte Carlo technique, but are applicable to finding the dominant eigenvalue of (almost) general matrices. For most non‐negative matrices, the schemes result in an error (compared to the power method) that is constant in the dimension of the problem. For more general matrices, we see a very clear sublinear cost trend in computational tests.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Fast Computational Algorithms for Partial Differential Equations and Uncertainty Quantifications

This project concerned the construction, testing and analysis of computational algorithms for solving parameterized and stochastic partial differential equations. The study and understanding of equations of this type is of fundamental importance in numerous engineering and scientific applications. Examples include simulation of plasma dynamics in models of electric propulsion and nuclear fusion, simulation of multiphase flows, such as the flow of water, gas and oil in reservoirs, and structural analysis of the dependence of structures on materials. Parametrization is used in such settings when properties of the models such as viscosity of fluids or electric resistivity of materials are not precisely understood and instead are treated as random variables. The resulting solutions are themselves random, and having such solutions will enable engineers to use probabilistic methods to assess the likelihood of events, for example, whether a pollutant in a liquid will exceed a limit, and to use such analyses to develop ways to ensure positive outcomes. Construction of accurate (high resolution) computational solutions is expensive, requiring significant computer time and computational resources, and there is need to reduce computational cost to make simulation useful and effective. The aim of the project was to construct algorithms to efficiently compute surrogate solutions to parameterized problems to allow for efficient and accurate simulation. The technical approach used focused on two related strategies, based on rank-reduction methods and reduced-order models. These methods construct surrogate solutions of parameter-dependent models by projection or interpolation into low-dimensional approximation spaces. Cost savings are achieved if the low-dimensional spaces can be identified and constructed efficiently and if the resulting low-dimensional algebraic systems can be solved cheaply. Accomplishments include: Theoretical and empirical demonstration of the effectiveness of fast multigrid solution strategies for computing low-rank representations of parameter-dependent solutions to discrete partial differential equations, including the first proof establishing so-called textbook convergence properties for low-rank methods. Development of efficient solution algorithms for solving nonlinear parameter-dependent partial differential equations used in models of fluid dynamics. Developent of efficient algorithms for low-rank representation of solutions of time-dependent simulations of fluid dynamics using multi-dimensional tensor representations of solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Fast inversion, preconditioned quantum linear system solvers, fast Green's-function computation, and fast evaluation of matrix functions

Preconditioning is the most widely used and effective way for treating ill-conditioned linear systems in the context of classical iterative linear system solvers. We introduce a quantum primitive called fast inversion, which can be used as a preconditioner for solving quantum linear systems. The key idea of fast inversion is to directly block encode a matrix inverse through a quantum circuit implementing the inversion of eigenvalues via classical arithmetics. We demonstrate the application of preconditioned linear system solvers for computing single-particle Green's functions of quantum many-body systems, which are widely used in quantum physics, chemistry, and materials science. We analyze the complexities in three scenarios: the Hubbard model, the quantum many-body Hamiltonian in the plane-wave-dual basis, and the Schwinger model. We also provide a method for performing Green's function calculation in second quantization within a fixed-particle manifold and note that this approach may be valuable for simulation more broadly. Aside from solving linear systems, fast inversion also allows us to develop fast algorithms for computing matrix functions, such as the efficient preparation of Gibbs states. Furthermore, we introduce two efficient approaches for such a task, based on the contour-integral formulation and the inverse transform, respectively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

QCLAB v0.1

QCLAB is an object-oriented MATLAB package for creating and representing quantum circuits. QCLAB can be used for rapid prototyping and testing of quantum algorithms, and allows for fast algorithm development and discovery. QCLAB provides I/O through openQASM making it compatible with quantum hardware. It is uniquely targeted at MATLAB users who so far didn't have any native MATLAB options for developing quantum computing applications.

Van Beeumen, RoelMaria Franciscus↗