The recent successes of parallel-in-time (PinT) integration have established its potential as a powerful algorithmic paradigm, which can be used in conjunction with other forms of parallelism to enhance the performance of Exascale systems. However, the parallel efficiency of PinT methods is currently constrained by two primary factors:

  1. The iterative nature of these methods increases total computation time despite reductions in wall-clock time through parallelism.
  2. The serial step within the PinT methods poses a significant bottleneck to scaling.

This Innovation Study aims to address these limitations for systems described by high-dimensional multiscale partial differential equations (PDEs) and simulated using Monte Carlo methods. To alleviate the serial bottleneck in PinT methods, this study employs approximate, low-dimensional models during the serial step. This approach reduces the computational load without compromising accuracy.

Furthermore, the PinT methods have been designed with uncertainty quantification and data assimilation in mind, which are iterative processes. By integrating these iterations within the PinT framework, this study anticipates a significant reduction in computational overhead. The focus will be on algorithm design and analysis, building upon conceptual ideas developed by the project partners during the EuroHPC Time-X project on time-parallel time integration methods.

The objective of this study is to implement these novel ideas into prototype software, thereby advancing the technology readiness level (TRL) from TRL1 to TRL5. This is in response to the specific requirements of the Inno4Scale initiative. In order to maximise impact, the developed methods will be applied to a highly relevant societal application: the design of electrical machines. Furthermore, the resulting open-source software will provide a non-intrusive wrapper around existing simulation codes and serve as a guideline for implementing the methods into other simulation software.

By addressing the critical issues of iterative overhead and serial bottlenecks in PinT methods, MLMC-PinT4Data aims to enhance the computational efficiency and scalability of Exascale systems, enabling more sophisticated and timely simulations across a range of scientific and engineering applications.