Project description
Understanding the limits of inexactness could lead to more efficient algorithms for exascale
Matrix computations are common in many fields. We are moving towards the age of exascale computing – and exascale-size matrices – which will require nearly unfathomable workloads. A common way to reduce this workload is to introduce inexact or approximate matrix computations. But to ensure that inexactness from multiple sources propagating through exascale matrix computations does not confound the conclusions we draw from the results, we need a systematic approach for analysing multiple sources of inexactness together and studying their interaction. Funded by the European Research Council, the inEXASCALE project will rigorously analyse the combination of errors from multiple sources and evaluate their effect on numerical behaviour and solution quality in matrix computations. This could lead to new algorithms for exascale problems that exploit inexactness to balance performance and accuracy.
Objective
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 inexactness
WP2: Development of new algorithms that exploit inexactness that are both fast and provably accurate
WP3: Making error analysis of exascale computations meaningful in practice
WP4: Exploring emerging sources of inexactness beyond the exascale era
Our approach will lead to new methodologies that can change current paradigms.
Fields of science
Keywords
Programme(s)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Topic(s)
Funding Scheme
HORIZON-ERC - HORIZON ERC GrantsHost institution
116 36 Praha 1
Czechia