Building on Time-X results, the Inno4Scale project MLMC-PinT4Data will develop parallel-in-time micro-macro Monte Carlo methods for uncertainty quantification and data assimilation.
With the exponential increase of computational power, numerical simulation has become a routine tool in many scientific domains. However, the shift towards massive parallelism poses numerous challenges for algorithm design: parallelization must be considered from the outset of algorithm design. Recent successes have established the potential of parallel-in-time (PinT) integration as a powerful algorithmic paradigm, in addition to other forms of parallelism, to unlock the performance of Exascale systems. The parallel efficiency of PinT methods, however, is currently limited by two factors: (i) they are iterative, which increases the total computation time (even if the parallelism reduces wall-clock time); and (ii) their serial step forms a scaling bottleneck.
In this project, we will tackle these problems for systems that are described by high-dimensional multiscale partial differential equations and simulated with a Monte Carlo method. We will alleviate the serial bottleneck of PinT methods by considering approximate, low-dimensional models during the serial step. Moreover, we will design PinT methods for uncertainty quantification and data assimilation, which in themselves already require an iterative procedure. By combining those iterations, we will significantly reduce computational overhead.
The project focuses on algorithm design and analysis, further developing conceptual ideas that have been conceived by the project partners in a collaboration that started within the context of the EuroHPC Time-X project on time-parallel time integration methods. By implementing these ideas into prototype software, we will advance them from TRL1 to TRL5, replying to the specific request of the Inno4Scale. To maximize impact, the developed methods will be applied to an application with high societal relevance: the design of electrical machines and be made available in open-source software libraries. This open-source software will both allow including a non-intrusive wrapper around existing simulation codes, and serve as a guide to implement the methods into existing simulation software.