Benson, Austin R. | Search NASA

NASA NTRS2019

Automated Grain Yield Behavior Classification

A method for classifying grain stress evolution behaviors using unsupervised learning techniques is presented. The method is applied to analyze grain stress histories measured in-situ using high-energy X-ray diffraction microscopy (HEDM) from the aluminum-lithium alloy Al-Li 2099 at the elastic-plastic transition (yield). The unsupervised learning process automatically classified the grain stress histories into four groups: major softening, no work-hardening or softening, moderate work-hardening, and major work-hardening. The orientation and spatial dependence of these four groups are discussed. In addition, the generality of the classification process to other samples is explored.

Pagan, Darren C↗

DOE OSTI2016

Improving the Numerical Stability of Fast Matrix Multiplication

Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few fast algorithms have been efficiently implemented or used in practical applications. However, there exist many practical alternatives to Strassen's algorithm with varying performance and numerical properties. Fast algorithms are known to be numerically stable, but because their error bounds are slightly weaker than the classical algorithm, they are not used even in cases where they provide a performance benefit. We argue in this study that the numerical sacrifice of fast algorithms, particularly for the typical use cases of practical algorithms, is not prohibitive, and we explore ways to improve the accuracy both theoretically and empirically. The numerical accuracy of fast matrix multiplication depends on properties of the algorithm and of the input matrices, and we consider both contributions independently. We generalize and tighten previous error analyses of fast algorithms and compare their properties. We discuss algorithmic techniques for improving the error guarantees from two perspectives: manipulating the algorithms, and reducing input anomalies by various forms of diagonal scaling. In conclusion, we benchmark performance and demonstrate our improved numerical accuracy.

97 MATHEMATICS AND COMPUTING↗