The introduction of stdpar in C++ introduces parallel algorithms into the standard library, which allows developers to easily harness the power of parallelism in their applications, leading to potential performance improvements, scalability, increased productivity, and improved reproducibility in scientific computing tasks. At least theoretically, as its performance depends on the compiler in use. In this paper, we examine the usability of stdpar and demonstrate the significant differences between different stdpar compilers. To this end, we study a kernel matrix assembly algorithm and a BLAS level 3 SYMM function, both implemented in the Parallel Least Squares Support Vector Machine (PLSSVM) library. The same code is compiled with an NVIDIA nvc++, gcc, Intel oneAPI icpx, and AdaptiveCpp compiler. We analyzed the code on an NVIDIA A30 GPU, an AMD MI210 GPU, and a dual-socket AMD EPYC 9274F CPU machine. First, we report surprisingly large runtime differences between the different stdpar compilers: up to 11 percent on the NVIDIA A30 GPU and even up to 335% on two AMD EPYC 9274F. Second, we show how stdpar enables energy reduction by a factor of up to 20.7 with the very same implementation by utilizing different hardware platforms.The code, utility scripts, and documentation are all available on GitHub: https://github.com/SC-SGS/PLSSVM

High-dimensional grid-based simulations serve as both a tool and a challenge in researching various domains. The main challenge of these approaches is the well-known curse of dimensionality, amplified by the need for fine resolutions in high-fidelity applications. The combination technique (CT) provides a straightforward way of performing such simulations while alleviating the curse of dimensionality. Recent work demonstrated the potential of the CT to join multiple systems simultaneously to perform a single high-dimensional simulation. This paper shows how to extend this to three or more systems and addresses some remaining challenges: load balancing on heterogeneous hardware; utilizing compression to maximize the communication bandwidth; efficient I/O management through hardware mapping; and improving memory utilization through algorithmic optimizations. Combining these contributions, we demonstrate the feasibility of the CT for extreme-scale Superfacility scenarios of 46 trillion DOF on two systems and 35 trillion DOF on three systems. Scenarios at these resolutions would be intractable with full-grid solvers ($\gt1,000$ nonillion DOF each).

Grid-based simulations of hot fusion plasmas are often severely limited by computational and memory resources; the grids live in four- to six-dimensional space and thus suffer the curse of dimensionality. However, high resolutions are required to fully capture the physics of interest. The sparse grid combination technique is a multi-scale method in which many anisotropically coarse resolved grids are used to approximate a fine-scale solution---and it alleviates the curse of dimensionality.