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At least 487 records · Page 27

All sources NASA NTRS DOE OSTI

DOE OSTI2021

Macromolecular phasing using diffraction from multiple crystal forms

A phasing algorithm for macromolecular crystallography is proposed that utilizes diffraction data from multiple crystal forms – crystals of the same molecule with different unit-cell packings (different unit-cell parameters or space-group symmetries). The approach is based on the method of iterated projections, starting with no initial phase information. The practicality of the method is demonstrated by simulation using known structures that exist in multiple crystal forms, assuming some information on the molecular envelope and positional relationships between the molecules in the different unit cells. With incorporation of new or existing methods for determination of these parameters, the approach has potential as a method for ab initio phasing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

A Stochastic Quasi-Newton Method in the Absence of Common Random Numbers

We present Q-SASS, a quasi-Newton method for unconstrained stochastic optimization that does not rely on common random numbers. Most existing quasi-Newton approaches leverage common random numbers to construct second-order updates. However, motivated by challenges in variational quantum algorithms—where such coordination is not possible—we consider the setting in which function values and gradients are accessible only through noisy probabilistic zeroth- and first-order oracles, and no common random numbers can be exploited. We derive high-probability tail bounds on the iteration complexity of our algorithm for nonconvex, convex, and strongly convex (more generally, those satisfying the PL condition) objective functions. Finally, we demonstrate the empirical benefits of our quasi-Newton updating scheme on both synthetic and quantum chemistry problems.

Complexity bound↗

NASA NTRS1988

Fast polar decomposition of an arbitrary matrix

The polar decomposition of an m x n matrix A of full rank, where m is greater than or equal to n, can be computed using a quadratically convergent algorithm. The algorithm is based on a Newton iteration involving a matrix inverse. With the use of a preliminary complete orthogonal decomposition the algorithm can be extended to arbitrary A. How to use the algorithm to compute the positive semi-definite square root of a Hermitian positive semi-definite matrix is described. A hybrid algorithm which adaptively switches from the matrix inversion based iteration to a matrix multiplication based iteration due to Kovarik, and to Bjorck and Bowie is formulated. The decision when to switch is made using a condition estimator. This matrix multiplication rich algorithm is shown to be more efficient on machines for which matrix multiplication can be executed 1.5 times faster than matrix inversion.

Higham, Nicholas J.↗

DOE OSTI2024

Active learning for SNAP interatomic potentials via Bayesian predictive uncertainty

Bayesian inference with a simple Gaussian error model is used to efficiently compute prediction variances for energies, forces, and stresses in the linear SNAP interatomic potential. Here, the prediction variance is shown to have a strong correlation with the absolute error over approximately 24 orders of magnitude. Using this prediction variance, an active learning algorithm is constructed to iteratively train a potential by selecting the structures with the most uncertain properties from a pool of candidate structures. The relative importance of the energy, force, and stress errors in the objective function is shown to have a strong impact upon the trajectory of their respective net error metrics when running the active learning algorithm. Batched training of different batch sizes is also tested against singular structure updates, and it is found that batches can be used to significantly reduce the number of retraining steps required with only minor impact on the active learning trajectory.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2008

Dependence of Adaptive Cross-correlation Algorithm Performance on the Extended Scene Image Quality

Recently, we reported an adaptive cross-correlation (ACC) algorithm to estimate with high accuracy the shift as large as several pixels between two extended-scene sub-images captured by a Shack-Hartmann wavefront sensor. It determines the positions of all extended-scene image cells relative to a reference cell in the same frame using an FFT-based iterative image-shifting algorithm. It works with both point-source spot images as well as extended scene images. We have demonstrated previously based on some measured images that the ACC algorithm can determine image shifts with as high an accuracy as 0.01 pixel for shifts as large 3 pixels, and yield similar results for both point source spot images and extended scene images. The shift estimate accuracy of the ACC algorithm depends on illumination level, background, and scene content in addition to the amount of the shift between two image cells. In this paper we investigate how the performance of the ACC algorithm depends on the quality and the frequency content of extended scene images captured by a Shack-Hatmann camera. We also compare the performance of the ACC algorithm with those of several other approaches, and introduce a failsafe criterion for the ACC algorithm-based extended scene Shack-Hatmann sensors.

wave-front sensing and control↗

NASA NTRS1989

Numerical optimization in Hilbert space using inexact function and gradient evaluations

Trust region algorithms provide a robust iterative technique for solving non-convex unstrained optimization problems, but in many instances it is prohibitively expensive to compute high accuracy function and gradient values for the method. Of particular interest are inverse and parameter estimation problems, since function and gradient evaluations involve numerically solving large systems of differential equations. A global convergence theory is presented for trust region algorithms in which neither function nor gradient values are known exactly. The theory is formulated in a Hilbert space setting so that it can be applied to variational problems as well as the finite dimensional problems normally seen in trust region literature. The conditions concerning allowable error are remarkably relaxed: relative errors in the gradient error condition is automatically satisfied if the error is orthogonal to the gradient approximation. A technique for estimating gradient error and improving the approximation is also presented.

Carter, Richard G.↗

DOE OSTI2023

Navigating the Dynamic Noise Landscape of Variational Quantum Algorithms with QISMET

In the Noisy Intermediate Scale Quantum (NISQ) era, the dynamic nature of quantum systems causes noise sources to constantly vary over time. Transient errors from the dynamic NISQ noise landscape are challenging to comprehend and are especially detrimental to classes of applications that are iterative and/or long-running, and therefore their timely mitigation is important for quantum advantage in real-world applications. The most popular examples of iterative long-running quantum applications are variational quantum algorithms (VQAs). Iteratively, VQA’s classical optimizer evaluates circuit candidates on an objective function and picks the best circuits towards achieving the application’s target. Noise fluctuation can cause a significant transient impact on the objective function estimation of the VQA iterations’ tuning candidates. This can severely affect VQA tuning and, by extension, its accuracy and convergence. Furthermore, this paper proposes QISMET: Quantum Iteration Skipping to Mitigate Error Transients, to navigate the dynamic noise landscape of VQAs. QISMET actively avoids instances of high fluctuating noise which are predicted to have a significant transient error impact on specific VQA iterations. To achieve this, QISMET estimates transient error in VQA iterations and designs a controller to keep the VQA tuning faithful to the transient-free scenario. By doing so, QISMET efficiently mitigates a large portion of the transient noise impact on VQAs and is able to improve the fidelity by 1.3x-3x over a traditional VQA baseline, with 1.6-2.4x improvement over alternative approaches, across different applications and machines.

Ravi, Gokul Subramanian↗

DOE OSTI2022

Low-synch Gram–Schmidt with delayed reorthogonalization for Krylov solvers

The parallel strong-scaling of iterative methods is often determined by the number of global reductions at each iteration. Low-synch Gram-Schmidt algorithms are applied here to the Arnoldi algorithm to reduce the number of global reductions and therefore to improve the parallel strong-scaling of iterative solvers for nonsymmetric matrices such as the GMRES and the Krylov-Schur iterative methods. In the Arnoldi context, the factorization is "left-looking" and processes one column at a time. Among the methods for generating an orthogonal basis for the Arnoldi algorithm, the classical Gram-Schmidt algorithm, with reorthogonalization (CGS2) requires three global reductions per iteration. A new variant of CGS2 that requires only one reduction per iteration is presented and applied to the Arnoldi algorithm. Delayed CGS2 (DCGS2) employs the minimum number of global reductions per iteration (one) for a one-column at-a-time algorithm. The main idea behind the new algorithm is to group global reductions by rearranging the order of operations. DCGS2 must be carefully integrated into an Arnoldi expansion or a GMRES solver. Numerical stability experiments assess robustness for Krylov-Schur eigenvalue computations. Performance experiments on the ORNL Summit supercomputer then establish the superiority of DCGS2 over CGS2.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Mixed-precision numerics in scientific applications: survey and perspectives

The explosive demand for artificial intelligence (AI) workloads has led to a significant increase in silicon area dedicated to lower-precision computations on recent high-performance computing hardware designs. However, mixed-precision capabilities, which can achieve performance improvements of up to 8x compared to double-precision in extreme compute-intensive workloads, remain largely untapped in most scientific applications. A growing number of efforts have shown that mixed-precision algorithmic innovations can deliver superior performance without sacrificing accuracy. These developments should prompt computational scientists to seriously consider whether their scientific modeling and simulation applications could benefit from the acceleration offered by new hardware and mixed-precision algorithms. In this survey, we (1) review progress across diverse scientific domains—fluid dynamics, weather and climate, quantum chemistry, and computational genomics—that have begun adopting mixed-precision strategies; (2) examine state-of-the-art algorithmic techniques such as iterative refinement, splitting and emulation schemes, and adaptive precision solvers; (3) assess their implications for accuracy, performance, and resource utilization; and (4) survey the emerging software ecosystem that enables mixed-precision methods at scale. We conclude with perspectives and recommendations on cross-cutting opportunities, domain-specific challenges, and the role of co-design between application scientists, numerical analysts, and computer scientists. Collectively, this survey underscores that mixed-precision numerics can reshape computational science by aligning algorithms with the evolving landscape of hardware capabilities.

Graphics processing units↗

NASA NTRSDate not supplied

Control Effector Unsaturation Modification to the Cascading Generalized Inverse Control Allocation Algorithm

Control allocation has sufficiently progressed such that it is used in front-line fighter aircraft such as the F-18Superhornet and the F-35 Joint Strike Fighter. Published literature shows the F-35 utilizes Nonlinear Dynamic Inversion in conjunction with an Effector Blender that incorporates the Cascading Generalized Inverse control allocation algorithm. While the Cascading Generalized Inverse algorithm is one of the premier generalized inverse methods, it does suffer from three deficiencies. In particular, it suffers from an inability to achieve some desired outcomes, it intermittently provides non-optimal solutions and generally fails to preserve moment direction near maximal achievable moments. An effector unsaturation method based on a Scalar Difference Quadratic was first introduced and implemented on the iterative Prediction Method control allocation algorithm which was shown to consistently achieve optimal (weighted) control allocation solutions throughout the entire Attainable Moment Set while preserving desired moment direction. In this paper, the shortcomings of the Cascading Generalized Inverse algorithm are addressed by augmenting the baseline algorithm with Scalar Difference Quadratic unsaturation identification and location at each iteration. Numerical case studies demonstrate that the Modified Cascading Generalized Inverse algorithm resolves the aforementioned deficiencies.

Michael J Acheson↗

DOE OSTI2026

ReMU: regional minimal updating for model-based derivative-free optimization

Derivative-free optimization (DFO) problems are optimization problems where derivative information is unavailable or extremely difficult to obtain. Model-based DFO solvers have been applied extensively in scientific computing. Powell's NEWUOA (2004) [Powell, The NEWUOA software for unconstrained optimization without derivatives, in Large-Scale Nonlinear Optimization, Nonconvex Optimization and its Applications Vol. 83, G. Di Pillo and M. Roma, eds., Springer, 2006, pp. 255–297] and Wild's POUNDerS (2014) [Wild, Solving derivative-free nonlinear least squares problems with POUNDERS, in Advances and Trends in Optimization with Engineering Applications, T. Terlaky, M.F. Anjos, and S. Ahmed, eds., SIAM, 2017, pp. 529–540] explore the numerical power of the minimal norm Hessian (MNH) model for DFO and contributed to the open discussion on building better models with fewer data to achieve faster numerical convergence. Another decade later, we propose the regional minimal updating (ReMU) models, and extend the previous models into a broader class, including the H 2 norm models [Xie and Yuan, Least H 2 norm updating of quadratic interpolation models for derivative-free trust-region algorithms, IMA J. Numer. Anal. 46 (2025), pp. 21–50]. This paper shows motivation behind ReMU models, computational details, theoretical and numerical results on particular extreme points and the barycentre of ReMU's weight coefficient region, and the associated KKT matrix error and distance. Novel metrics, such as the truncated Newton step error, are proposed to numerically understand the new models' properties. A new algorithmic strategy, based on iteratively adjusting the ReMU model type, is also proposed, and shows numerical advantages by combining and switching between the barycentric model and the classic least Frobenius norm model in an online fashion.

derivative-free trust-region methods↗

NASA NTRS1981

An evaluation of ISOCLS and CLASSY clustering algorithms for forest classification in northern Idaho

Both the iterative self-organizing clustering system (ISOCLS) and the CLASSY algorithms were applied to forest and nonforest classes for one 1:24,000 quadrangle map of northern Idaho and the classification and mapping accuracies were evaluated with 1:30,000 color infrared aerial photography. Confusion matrices for the two clustering algorithms were generated and studied to determine which is most applicable to forest and rangeland inventories in future projects. In an unsupervised mode, ISOCLS requires many trial-and-error runs to find the proper parameters to separate desired information classes. CLASSY tells more in a single run concerning the classes that can be separated, shows more promise for forest stratification than ISOCLS, and shows more promise for consistency. One major drawback to CLASSY is that important forest and range classes that are smaller than a minimum cluster size will be combined with other classes. The algorithm requires so much computer storage that only data sets as small as a quadrangle can be used at one time.

Werth, L. F.↗

NASA NTRS2010

Fast Solution in Sparse LDA for Binary Classification

An algorithm that performs sparse linear discriminant analysis (Sparse-LDA) finds near-optimal solutions in far less time than the prior art when specialized to binary classification (of 2 classes). Sparse-LDA is a type of feature- or variable- selection problem with numerous applications in statistics, machine learning, computer vision, computational finance, operations research, and bio-informatics. Because of its combinatorial nature, feature- or variable-selection problems are NP-hard or computationally intractable in cases involving more than 30 variables or features. Therefore, one typically seeks approximate solutions by means of greedy search algorithms. The prior Sparse-LDA algorithm was a greedy algorithm that considered the best variable or feature to add/ delete to/ from its subsets in order to maximally discriminate between multiple classes of data. The present algorithm is designed for the special but prevalent case of 2-class or binary classification (e.g. 1 vs. 0, functioning vs. malfunctioning, or change versus no change). The present algorithm provides near-optimal solutions on large real-world datasets having hundreds or even thousands of variables or features (e.g. selecting the fewest wavelength bands in a hyperspectral sensor to do terrain classification) and does so in typical computation times of minutes as compared to days or weeks as taken by the prior art. Sparse LDA requires solving generalized eigenvalue problems for a large number of variable subsets (represented by the submatrices of the input within-class and between-class covariance matrices). In the general (fullrank) case, the amount of computation scales at least cubically with the number of variables and thus the size of the problems that can be solved is limited accordingly. However, in binary classification, the principal eigenvalues can be found using a special analytic formula, without resorting to costly iterative techniques. The present algorithm exploits this analytic form along with the inherent sequential nature of greedy search itself. Together this enables the use of highly-efficient partitioned-matrix-inverse techniques that result in large speedups of computation in both the forward-selection and backward-elimination stages of greedy algorithms in general.

Moghaddam, Baback↗

DOE OSTI2023

Latency considerations for stochastic optimizers in variational quantum algorithms

Variational quantum algorithms, which have risen to prominence in the noisy intermediate-scale quantum setting, require the implementation of a stochastic optimizer on classical hardware. To date, most research has employed algorithms based on the stochastic gradient iteration as the stochastic classical optimizer. In this work we propose instead using stochastic optimization algorithms that yield stochastic processes emulating the dynamics of classical deterministic algorithms. This approach results in methods with theoretically superior worst-case iteration complexities, at the expense of greater per-iteration sample (shot) complexities. We investigate this trade-off both theoretically and empirically and conclude that preferences for a choice of stochastic optimizer should explicitly depend on a function of both latency and shot execution times.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Spread Spectrum Time Domain Reflectometry and Steepest Descent Inversion to Measure Complex Impedance

In this paper, we present a method for estimating complex impedances using reflectometry and a modified steepest descent inversion algorithm. We simulate spread spectrum time domain reflectometry (SSTDR), which can measure complex impedances on energized systems for an experimental setup with resistive and capacitive loads. A parametric function, which includes both a misfit function and stabilizer function, is created. The misfit function is a least squares estimate of how close the model data matches observed data. The stabilizer function prevents the steepest descent algorithm from becoming unstable and diverging. Steepest descent iteratively identifies the model parameters that minimize the parametric function. We validate the algorithm by correctly identifying the model parameters (capacitance and resistance) associated with simulated SSTDR data, with added 3 dB white Gaussian noise. With the stabilizer function, the steepest descent algorithm estimates of the model parameters are bounded within a specified range. Furthermore, the errors for capacitance (220pF to 820pF) and resistance (50 Ω to 270 Ω) are < 10%, corresponding to a complex impedance magnitude |R +1/jωC| of 53 Ω to 510 Ω.

14 SOLAR ENERGY↗

DOE OSTI2026

Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method

While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to improve the accuracy of deep learning-based solutions for time-dependent PDEs is to use the learned model as the coarse propagator in the Parareal method and a traditional numerical method as the fine solver. However, successful integration of deep learning into the Parareal method requires consistency between the coarse and fine solvers, particularly for PDEs exhibiting rapid changes such as sharp transitions. Here, to ensure this consistency, we propose using convolutional neural networks (CNNs) to learn the fully discrete time-stepping operator defined by the same numerical scheme employed as the fine solver. We demonstrate the effectiveness of the proposed method in solving the classical and mass-conservative Allen–Cahn (AC) equations. Through iterative updates in the Parareal algorithm, our approach achieves a significant computational speedup compared to traditional fine solvers while converging to high-accuracy solutions. Our results highlight that the proposed hybrid Parareal algorithm effectively accelerates simulations, particularly when implemented on multiple GPUs, and converges to the desired accuracy in only a few iterations. Another advantage of our method is that the CNN model is trained on trajectory-based data generated from random initial conditions, such that the trained model can be used to solve the AC equations with various initial conditions without retraining. This work demonstrates the potential of integrating neural network methods into parallel-in-time frameworks for efficient and accurate simulations of time-dependent PDEs.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1989

Parallel conjugate gradient algorithms for manipulator dynamic simulation

Parallel conjugate gradient algorithms for the computation of multibody dynamics are developed for the specialized case of a robot manipulator. For an n-dimensional positive-definite linear system, the Classical Conjugate Gradient (CCG) algorithms are guaranteed to converge in n iterations, each with a computation cost of O(n); this leads to a total computational cost of O(n sq) on a serial processor. A conjugate gradient algorithms is presented that provide greater efficiency using a preconditioner, which reduces the number of iterations required, and by exploiting parallelism, which reduces the cost of each iteration. Two Preconditioned Conjugate Gradient (PCG) algorithms are proposed which respectively use a diagonal and a tridiagonal matrix, composed of the diagonal and tridiagonal elements of the mass matrix, as preconditioners. Parallel algorithms are developed to compute the preconditioners and their inversions in O(log sub 2 n) steps using n processors. A parallel algorithm is also presented which, on the same architecture, achieves the computational time of O(log sub 2 n) for each iteration. Simulation results for a seven degree-of-freedom manipulator are presented. Variants of the proposed algorithms are also developed which can be efficiently implemented on the Robot Mathematics Processor (RMP).

Fijany, Amir↗

DOE OSTI2021

An extended numerical manifold method for unsaturated soil-water interaction analysis at micro-scale

To investigate unsaturated soil-water interaction at micro-scale, this work extends the numerical manifold method (NMM) by incorporating a soil-water coupling model considering specific capillary water distribution and capillary force calculation. The soil skeleton is constructed by a soil skeleton generation algorithm with random polygons. To more realistically capture the interaction between soil grains and capillary water, a capillary mechanics-based geometric algorithm is proposed to iteratively calculate the capillary water distribution. The capillary forces corresponding to the capillary water distribution are calculated based on the Young-Laplace equation. The proposed capillary water solving framework is first verified by reproducing the soil-water characteristic curve and the capillary water distribution of an ideal contact-disk model against analytical solutions. To further validate the ability of the capillary water solving framework to predict hydraulic behavior of the real soil, a laboratory test on the Toyoura sand is reproduced numerically. Then an ideal direct shear test is performed to further validate the two-way soil-water coupling procedure, in which a comparison between the numerical and analytical results regarding the shear strength and matric suction is presented. Finally, microscopic hydraulic and compression tests are conducted on two soil specimens with the same porosity and mean grain diameter but different uniformity coefficients. The results elucidate that the extended method is a potential tool to explore unsaturated soil behaviors at micro-scale.

58 GEOSCIENCES↗