Predictive simulations are playing an increasingly important role in enhancing and complementing traditional scientific experimentation and theory. These simulations use numerical algorithms and are often so computationally demanding that they necessitate parallel supercomputers. Additionally, to maintain optimal efficiency, computational methods must be continually adapted to new advancements in computer architecture. Currently, emerging architectures achieve high performance by utilizing reduced floating-point precision. While this advancement is largely driven by the rapid progress in artificial intelligence, it also significantly impacts numerical and scientific computing.

Any computation involving reduced finite precision will inevitably involve a trade-off between efficiency and accuracy. Analyzing floating-point accuracy is essential for validating predictive simulations, particularly in safety-critical applications. Therefore, using reduced and mixed precision algorithms must often be justified through careful numerical analysis. To fully leverage the capabilities of new computer architectures and their reduced precision floating-point formats, we need to consider appropriate data structures, revisit algorithm design, and systematically study performance and energy consumption. Given these considerations, studying reduced and mixed precision computing is especially timely. Significant progress has already been made in mixed precision within numerical linear algebra, including the revival and refinement of classical techniques like iterative refinement for solving linear systems. Additionally, there is substantial potential for improving performance and energy efficiency in higher-level applications, such as computational fluid dynamics and weather and climate modeling.

A targeted Dagstuhl Seminar can significantly influence the community by serving as a forum to consolidate and direct the rapidly evolving field of research. For numerical algorithms involving mixed and reduced precision, there is an urgent need for research, along with a pressing requirement to exchange ideas and better coordinate overlapping global efforts. Additionally, the techniques and implications of classical numerical round-off error analysis must be communicated to a broader audience. Currently, many potential users of reduced precision hardware in science and engineering may not be fully aware of the complexities and challenges involved in this area.

Key questions for the seminar include identifying which language constructs are best suited for expressing mixed precision algorithms in software and determining the specific floating-point formats required. This could provide valuable feedback to hardware developers. Additionally, the seminar should address which tools can aid in and simplify the analysis of reduced precision computing, and what tools might be necessary to evaluate the benefits of these techniques. For instance, how can algorithm developers predict and quantify the energy savings achieved through the use of reduced precision?

The primary goal of this Dagstuhl Seminar is to unite researchers focused on and utilizing reduced and mixed precision in numerical simulations. The seminar seeks to promote international and interdisciplinary collaboration in creating a groundbreaking software paradigm that effectively leverages evolving architectures. We plan to achieve this by combining informal, brainstorming-style discussions with subsequent presentations.

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Erin Claire Carson, Jack Joseph Dongarra, Ulrich Rüde, and Linda Stals