Mixed precision algorithms for High Performance Computing – MixHPC

The year 2022 has witnessed the advent of the first supercomputer able to perform over 10^18 floating-point operations per second, officially launching the exascale computing era. While exascale computing holds promises of unprecedented computational power, it also brings numerous significant challenges. Supercomputers have grown larger, more heterogeneous, and more power hungry, and so it has become much harder for complex numerical algorithms to achieve high performance and scalability. This project, MixHPC, confronts these challenges by harnessing the power of lower precision arithmetics, whose recent emergence on modern hardware represents one of the most significant developments of the High Performance Computing (HPC) landscape of the last few years. Reducing the precision makes computations faster, communications lighter, and power consumption greener. However, reducing the precision is also a risky approach that requires major algorithmic innovations
in order to avoid compromising the accuracy and robustness of the algorithms.

With MixHPC I propose to tackle this challenge by rethinking the role of precision in HPC: rather than viewing it as a fixed, static parameter, MixHPC will dynamically and adaptively employ multiple precisions, strategically mixing them to obtain novel mixed precision algorithms. This research encompasses both fundamental and applied science, spanning the fields of HPC, numerical linear algebra, data science, and numerical analysis. Indeed, I believe that the key to develop effective mixed precision algorithms is to combine knowledge and skills from all these fields. I aim to leverage my double experience both as a numerical analyst and an HPC practitioner to develop innovative algorithms that are fast, numerically sound, provably robust, and able to scale on large problems and on exascale computers with modern hardware.