arXiv subjects

Roman Iakymchuk

Publications and source records attributed to Roman Iakymchuk.

13 recordsLinked to original sources

arXiv2026

An HPC Approach to Accelerate Tensor Decompositions

Quantum systems grow in complexity so rapidly that even modest models become difficult to simulate, creating a strong need for methods that can handle high-dimensional data, also known as tensors. In this work, we investigate a novel Jacobi-type tensor algorithm for tensor decomposition and develop a CUDA-based algorithm that supports tensors of arbitrary order on a single GPU. We test the implementation on NVIDIA H100 GPUs and show that the algorithm converges correctly for diagonalizable tensors up to nine dimensions, with runtime scaling in a predictable way as tensor order grows. Finally, our general algorithm outperforms the original MATLAB reference by more than two orders of magnitude.

cs.DC↗

arXiv2026

Mixed-Precision SEM-Based CFD Simulations on GPUs: A Taylor-Green Vortex case

Mixed precision is a promising approach for reducing the computational cost and energy consumption of Computation Fluid Dynamics (CFD) simulations, but its effectiveness depends strongly on where precision is reduced within the full simulation pipeline. In this work, we study Taylor-Green vortex case using Neko, a matrix-free CFD solver based on the spectral element method (SEM). Profiling shows that the fluid time step is not dominated by Krylov convergence alone: the velocity and pressure solvers require only a small number of iterations per step, while a substantial fraction of runtime is spent in other SEM operators and solver components. Motivated by this structure, we propose a three-level hierarchical mixed-precision control model. Two groups of configurations are evaluated in environments bounded by 64-bit floating-point (fp64) and 32-bit floating-point (fp32) precision, respectively. The fp64-bounded group identifies accuracy sensitive components and shows that SEM-focused fp32 computation is a promising direction for future optimization. The fp32-bounded group provides the main practical benefit. For the high Reynolds number case studied, selected configurations reduce both time- and energy-to-solution by about 34% relative to the fp64 baseline, while improving robustness compared with global fp32. Targeted fp16 kernel overrides are also explored, showing potential for selected operations but increased sensitivity in gradient-based quantities such as enstrophy. Overall, these results indicate that mixed-precision for matrix-free SEM-based CFD should be treated as a simulation-level control problem rather than solely as a Krylov-solver optimization.

cs.DC↗

arXiv2026

Mixed-Precision For Energy Efficient Computations

As simulations grow more realistic, the pursuit of higher accuracy results in extended computation times and substantial power consumption. This study explores mixed-precision computing as a promising strategy to address these challenges, leveraging computer arithmetic tools to optimize performance. Using Reactor Simulator and LULESH benchmarks as case studies, we evaluated the potential of mixed-precision strategies to reduce both time-to-solution and energy-to-solution. For Reactor Simulator, we achieved a 30% reduction in both metrics without compromising accuracy. Similarly, for LULESH, results demonstrated up to a 30% improvement in time-to-solution and a 25% reduction in energy-to-solution.

cs.PF↗

arXiv2025

Harvesting energy consumption on European HPC systems: Sharing Experience from the CEEC project

Energy efficiency has emerged as a central challenge for modern high-performance computing (HPC) systems, where escalating computational demands and architectural complexity have led to significant energy footprints. This paper presents the collective experience of the EuroHPC JU Center of Excellence in Exascale CFD (CEEC) in measuring, analyzing, and optimizing energy consumption across major European HPC systems. We briefly review key methodologies and tools for energy measurement as well as define metrics for reporting results. Through case studies using representative CFD applications (waLBerla, FLEXI/GAL{\AE}XI, Neko, and NekRS), we evaluate energy-to-solution and time-to-solution metrics on diverse architectures, including CPU- and GPU-based partitions of LUMI, MareNostrum5, MeluXina, and JUWELS Booster. Our results highlight the advantages of accelerators and mixed-precision techniques for reducing energy consumption while maintaining computational accuracy. Finally, we advocate the need to facilitate energy measurements on HPC systems in order to raise awareness, teach the community, and take actions toward more sustainable exascale computing.

cs.DC↗

arXiv2025

Enabling mixed-precision in spectral element codes

Mixed-precision computing has the potential to significantly reduce the cost of exascale computations, but determining when and how to implement it in programs can be challenging. In this article, we propose a methodology for enabling mixed-precision with the help of computer arithmetic tools, roofline model, and computer arithmetic techniques. As case studies, we consider Nekbone, a mini-application for the Computational Fluid Dynamics (CFD) solver Nek5000, and a modern Neko CFD application. With the help of the Verificarlo tool and computer arithmetic techniques, we introduce a strategy to address stagnation issues in the preconditioned Conjugate Gradient method in Nekbone and apply these insights to implement a mixed-precision version of Neko. We evaluate the derived mixed-precision versions of these codes by combining metrics in three dimensions: accuracy, time-to-solution, and energy-to-solution. Notably, mixed-precision in Nekbone reduces time-to-solution by roughly 1.62x and energy-to-solution by 2.43x on MareNostrum 5, while in the real-world Neko application, the gain is up to 1.3x in both time and energy, with the accuracy that matches double-precision results.

cs.MS↗

arXiv2024

Verificarlo CI: continuous integration for numerical optimization and debugging

Floating-point accuracy is an important concern when developing numerical simulations or other compute-intensive codes. Tracking the introduction of numerical regression is often delayed until it provokes unexpected bug for the end-user. In this paper, we introduce Verificarlo CI, a continuous integration workflow for the numerical optimization and debugging of a code over the course of its development. We demonstrate applicability of Verificarlo CI on two test-case applications.

cs.SE↗

arXiv2024

Enabling mixed-precision with the help of tools: A Nekbone case study

Mixed-precision computing has the potential to significantly reduce the cost of exascale computations, but determining when and how to implement it in programs can be challenging. In this article, we consider Nekbone, a mini-application for the CFD solver Nek5000, as a case study, and propose a methodology for enabling mixed-precision with the help of computer arithmetic tools and roofline model. We evaluate the derived mixed-precision program by combining metrics in three dimensions: accuracy, time-to-solution, and energy-to-solution. Notably, the introduction of mixed-precision in Nekbone, reducing time-to-solution by 40.7% and energy-to-solution by 47% on 128 MPI ranks.

cs.MS↗

arXiv2024

Robustness and Accuracy in Pipelined Bi-Conjugate Gradient Stabilized Method: A Comparative Study

In this article, we propose an accuracy-assuring technique for finding a solution for unsymmetric linear systems. Such problems are related to different areas such as image processing, computer vision, and computational fluid dynamics. Parallel implementation of Krylov subspace methods speeds up finding approximate solutions for linear systems. In this context, the refined approach in pipelined BiCGStab enhances scalability on distributed memory machines, yielding to substantial speed improvements compared to the standard BiCGStab method. However, it's worth noting that the pipelined BiCGStab algorithm sacrifices some accuracy, which is stabilized with the residual replacement technique. This paper aims to address this issue by employing the ExBLAS-based reproducible approach. We validate the idea on a set of matrices from the SuiteSparse Matrix Collection.

cs.MS↗

arXiv2023

General framework for re-assuring numerical reliability in parallel Krylov solvers: A case of BiCGStab methods

Parallel implementations of Krylov subspace methods often help to accelerate the procedure of finding an approximate solution of a linear system. However, such parallelization coupled with asynchronous and out-of-order execution often enlarge the non-associativity impact in floating-point operations. These problems are even amplified when communication-hiding pipelined algorithms are used to improve the parallelization of Krylov subspace methods. Introducing reproducibility in the implementations avoids these problems by getting more robust and correct solutions. This paper proposes a general framework for deriving reproducible and accurate variants of Krylov subspace methods. The proposed algorithmic strategies are reinforced by programmability suggestions to assure deterministic and accurate executions. The framework is illustrated on the preconditioned BiCGStab method and its pipelined modification, which in fact is a distinctive method from the Krylov subspace family, for the solution of non-symmetric linear systems with message-passing. Finally, we verify the numerical behaviour of the two reproducible variants of BiCGStab on a set of matrices from the SuiteSparse Matrix Collection and a 3D Poisson's equation.

cs.MS↗

arXiv2022

Efficient and Eventually Consistent Collective Operations

Collective operations are common features of parallel programming models that are frequently used in High-Performance (HPC) and machine/ deep learning (ML/ DL) applications. In strong scaling scenarios, collective operations can negatively impact the overall application performance: with the increase in core count, the load per rank decreases, while the time spent in collective operations increases logarithmically. In this article, we propose a design for eventually consistent collectives suitable for ML/ DL computations by reducing communication in Broadcast and Reduce, as well as by exploring the Stale Synchronous Parallel (SSP) synchronization model for the Allreduce collective. Moreover, we also enrich the GASPI ecosystem with frequently used classic/ consistent collective operations -- such as Allreduce for large messages and AlltoAll used in an HPC code. Our implementations show promising preliminary results with significant improvements, especially for Allreduce and AlltoAll, compared to the vendor-provided MPI alternatives.

cs.DC↗

arXiv2020

Reproducibility of Parallel Preconditioned Conjugate Gradient in Hybrid Programming Environments

The Preconditioned Conjugate Gradient method is often employed for the solution of linear systems of equations arising in numerical simulations of physical phenomena. While being widely used, the solver is also known for its lack of accuracy while computing the residual. In this article, we propose two algorithmic solutions that originate from the ExBLAS project to enhance the accuracy of the solver as well as to ensure its reproducibility in a hybrid MPI + OpenMP tasks programming environment. One is based on ExBLAS and preserves every bit of information until the final rounding, while the other relies upon floating-point expansions and, hence, expands the intermediate precision. Instead of converting the entire solver into its ExBLAS-related implementation, we identify those parts that violate reproducibility/non-associativity, secure them, and combine this with the sequential executions. These algorithmic strategies are reinforced with programmability suggestions to assure deterministic executions. Finally, we verify these approaches on two modern HPC systems: both versions deliver reproducible number of iterations, residuals, direct errors, and vector-solutions for the overhead of less than 37.7 % on 768 cores.

cs.DC↗

arXiv2020

White Paper from Workshop on Large-scale Parallel Numerical Computing Technology (LSPANC 2020): HPC and Computer Arithmetic toward Minimal-Precision Computing

In numerical computations, precision of floating-point computations is a key factor to determine the performance (speed and energy-efficiency) as well as the reliability (accuracy and reproducibility). However, precision generally plays a contrary role for both. Therefore, the ultimate concept for maximizing both at the same time is the minimal-precision computing through precision-tuning, which adjusts the optimal precision for each operation and data. Several studies have been already conducted for it so far (e.g. Precimoniuos and Verrou), but the scope of those studies is limited to the precision-tuning alone. Hence, we aim to propose a broader concept of the minimal-precision computing system with precision-tuning, involving both hardware and software stack. In 2019, we have started the Minimal-Precision Computing project to propose a more broad concept of the minimal-precision computing system with precision-tuning, involving both hardware and software stack. Specifically, our system combines (1) a precision-tuning method based on Discrete Stochastic Arithmetic (DSA), (2) arbitrary-precision arithmetic libraries, (3) fast and accurate numerical libraries, and (4) Field-Programmable Gate Array (FPGA) with High-Level Synthesis (HLS). In this white paper, we aim to provide an overview of various technologies related to minimal- and mixed-precision, to outline the future direction of the project, as well as to discuss current challenges together with our project members and guest speakers at the LSPANC 2020 workshop; https://www.r-ccs.riken.jp/labs/lpnctrt/lspanc2020jan/.

cs.DC↗

arXiv2018

Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures

Feltor is a modular and free scientific software package. It allows developing platform independent code that runs on a variety of parallel computer architectures ranging from laptop CPUs to multi-GPU distributed memory systems. Feltor consists of both a numerical library and a collection of application codes built on top of the library. Its main target are two- and three-dimensional drift- and gyro-fluid simulations with discontinuous Galerkin methods as the main numerical discretization technique. We observe that numerical simulations of a recently developed gyro-fluid model produce non-deterministic results in parallel computations. First, we show how we restore accuracy and bitwise reproducibility algorithmically and programmatically. In particular, we adopt an implementation of the exactly rounded dot product based on long accumulators, which avoids accuracy losses especially in parallel applications. However, reproducibility and accuracy alone fail to indicate correct simulation behaviour. In fact, in the physical model slightly different initial conditions lead to vastly different end states. This behaviour translates to its numerical representation. Pointwise convergence, even in principle, becomes impossible for long simulation times. In a second part, we explore important performance tuning considerations. We identify latency and memory bandwidth as the main performance indicators of our routines. Based on these, we propose a parallel performance model that predicts the execution time of algorithms implemented in Feltor and test our model on a selection of parallel hardware architectures. We are able to predict the execution time with a relative error of less than 25% for problem sizes between 0.1 and 1000 MB. Finally, we find that the product of latency and bandwidth gives a minimum array size per compute node to achieve a scaling efficiency above 50% (both strong and weak).

physics.comp-ph↗