inEXASCALE · Analyzing and Exploiting Inexactness in Exascale Matrix Computations

Scientific computing inherently involves multiple sources of inexactness, from discretization or simplification of the problem, to noisy data, to finite precision rounding errors, to approximations made to increase parallelism, to stopping computations intentionally to improve efficiency. The standard state-of-the-art approach is to analyze different sources of error separately. There is currently no solid foundation or systematic approach for combining multiple sources of inexactness together and studying their interaction. Developing reliable approaches for exascale requires filling this gap, which must start with establishing a new rigorous foundation for analyzing multiple sources of error in matrix computations. Without this basis, the quest for efficiency in areas vitally depending on matrix computations, including, for example, data science and machine learning, will remain reliant on a trial-and-error approach. This project aims to break the current modular approach to the analysis and design of algorithms for matrix computations by understanding how different sources of inexactness interact while being propagated through a computation and their effect on numerical behavior and solution quality. Our holistic approach, rooted in rigorous theoretical analysis, will reveal opportunities for developing new algorithms for exascale problems that exploit inexactness to balance performance and accuracy. The project is structured around four fundamental objectives: WP1: Analysis of exascale matrix computations subject to multiple sources of inexactnessWP2: Development of new algorithms that exploit inexactness that are both fast and provably accurateWP3: Making error analysis of exascale computations meaningful in practiceWP4: Exploring emerging sources of inexactness beyond the exascale eraOur approach will lead to new methodologies that can change current paradigms.