Scientific computing must integrate AI with simulation and focus on energy-efficient methods and systems.

Nominations for this new prize will be invited September to November 2026.

The block elimination with additive modifications (BEAM) method was recently proposed as a alternative to LU with partial pivoting requiring less communication. Because of the novelty of BEAM, the existing theoretical analysis is lacking. To that end, we analyze both the numerical stability of the underlying block LU factorization and the effects of additive modifications. For the block LU factorization, we are able to improve the previous results of Demmel et al. from being cubic in the element growth to merely quadratic. Furthermore, we propose an alternative measure of element growth that is better aligned with block LU; this new measure of growth allows our analysis to apply to matrices that cannot be factored with pointwise LU. In the second part, we analyzed the modifications produced by BEAM and the effect they have on the condition number and growth factor. Finally, we show that BEAM will not apply any modifications in some cases that regular block LU can safely factor.

We analyze the topic structure of 10,299 publications from the International Conference on Computational Science (ICCS) between 2001 and 2024 as well as the Journal of Computational Science (JoCS) between 2010 and 2023, using natural language processing techniques and network analysis. The computational science classification corpus was created into 15 main disciplines and 256 sub-disciplines sourced from Wikipedia. Among the 15 main disciplines, machine learning became the most popular topic after 2019, surpassing parallel & distributed computing, which peaked in the early 2010s. ICCS and JoCS show differences in research popularity in both first and second-level disciplines. Algorithm theory, Mathematical modeling, and network science are the most dominant topics in both ICCS and JoCS. Different disciplines present different trends in ICCS and JoCS. In the past 24 years, machine learning related topics have gained the most attention in both ICCS and JoCS. We also examined and compared the correlation between the trends in ICCS and Google search Trends. The collaboration of disciplinary networks of second-level disciplines exhibits a scale-free characteristic, and the network structures have undergone significant evolution over 24 years. Moreover, different disciplinary communities exhibit different ”introverted” and ”extroverted” community characteristics within the network. Additionally, we examined the life span of thematic workshops and the evolution of authors’ collaborations inside and after ICCS.

The embedding layer is essential in deep learning, transforming high-dimensional data into compact representations. However, growing datasets and model sizes pose challenges in training time, memory, and generalization. We propose a scalable method for embedding initialization via spectral dimensionality reduction using dominant eigenvector projections. The proposed approach leverages on MIRAMns, multiple implicitly restarted Arnoldi method with nested subspaces, to extract most informative directions from large and potentially sparse data representations. Unlike traditional embeddings or autoencoders, this proposed approach requires few tunable parameters and is inherently parallel. We apply MIRAMns to matrix representations such as covariance and co-occurrence matrices to compute low-dimensional embeddings that preserve data structure and variance. Experiments across diverse datasets showthat the proposed method achieves comparable or better accuracy with significantly reduced dimensionality, enabling smaller, faster deep networks. Additionally, our parallel implementation scales efficiently on HPC platforms, making it well-suited for large-scale scientific and AI workloads.

The evolution of GPUs has resulted in democratized access to increasingly powerful low-precision compute capabilities, designed for artificial intelligence (AI), particularly large language models (LLMs) and generative AI. These algorithms heavily utilize hardware units specialized for matrix multiplication, such as Tensor Cores, that have advanced since their introduction, offering improved functionality, throughput, and energy efficiency. Two key techniques: mixed-precision algorithms and floating-point emulation, leveraging these resources, have emerged. They enable scientific applications, many dependent upon high-precision linear algebra, to achieve dramatic gains in performance and power efficiency. Additionally, these methods facilitate innovation in areas such as fine-grained mixed-precision strategies and data compression, broadening their impact across diverse computing platforms. This paper explores the opportunities afforded by these developments. We highlight both evolutionary advances and revolutionary features, such as the enhanced scaling capabilities of the latest NVIDIA Blackwell architecture’s Tensor Cores, and present empirical results, demonstrating their effectiveness on these GPUs.

STATEMENT OF INTEREST to Communications readers: This material is highly relevant and valuable to readers of Communications because it provides a comprehensive historical perspective on how federal funding has directly influenced pivotal developments in computing. Understanding the origins and trajectories of crucial software libraries and high-performance computing paradigms helps computing professionals appreciate the broader context and strategic significance of sustained investment in computational infrastructure. The discussion on current challenges and future policy recommendations offers actionable insights and frameworks essential for researchers, policymakers, educators, and industry leaders who play pivotal roles in shaping the future of computing innovation and maintaining global competitiveness.

Ootomo, Ozaki, and Yokota [Int. J. High Perform. Comput. Appl., 38 (2024), p. 297-313] have proposed a strategy to recast a floating-point matrix multiplication in terms of integer matrix products. The factors A and B are split into integer slices, the product of these slices is computed exactly, and AB is approximated by accumulating these integer products in floating-point arithmetic. This technique is particularly well suited to mixed-precision matrix multiply-accumulate units with integer support, such as the NVIDIA tensor cores or the AMD matrix cores. The number of slices allows for performance-accuracy tradeoffs: more slices yield better accuracy but require more multiplications, which in turn reduce performance. We propose an inexpensive way to estimate the minimum number of multiplications needed to achieve a prescribed level of accuracy. Our error analysis shows that the algorithm may become inaccurate (or inefficient) if rows of A or columns of B are badly scaled. We perform a range of numerical experiments, both in simulation and on the latest NVIDIA GPUs, that confirm the analysis and illustrate strengths and weaknesses of the algorithm.

We present a mixed-precision benchmark called HPL-MxP that uses both a lower-precision LU factorization with a non-stationary iterative refinement based on GMRES. We evaluate the numerical stability of one of the methods of generating the input matrix in a scalable fashion and show how the diagonal scaling affects the solution quality in terms of the backward-error. Some of the performance results at large scale supercomputing installations produced Exascale-level compute throughput numbers thus proving the viability of the proposed benchmark for evaluating such machines. We also present the potential of the benchmark to continue increasing its use with proliferation of hardware accelerators for AI workloads whose reliable evaluation continues to pose a particular challenge for the users.

Long-term plans and comprehensive vision are needed.

Hardware performance events are at the center of application performance analysis. However, the sheer volume of low-level hardware events in modern HPC systems is overwhelming, making them difficult for users to comprehend. Understanding which concepts are monitored by performance events can be achieved using a two-step process. The first step is the execution of benchmarks designed to stress different hardware attributes in isolation. For every hardware event we wish to understand, we execute the benchmarks while measuring the event. In the second step, the data produced by executing the benchmarks is analyzed to identify what each event actually measures. In this paper, we present the methodology for analyzing the data from four previously developed benchmarks that stress key hardware attributes-CPU and GPU floating-point units, branching units, and data caches-to map low-level hardware events to high-level programming concepts. We present an automated methodology to express the event data in a well-understood, conceptual basis. We implement a specialized pivoting scheme for QR factorization to identify events that provide distinct information from each other, and techniques for addressing noise in event measurements. Lastly, we utilize least-squares regression to combine the chosen events to define particular metrics of interest.

HPC and Cloud have evolved independently, specializing their innovations into performance or productivity. Acceleration as a Service (XaaS) is a recipe to empower both fields with a shared execution platform that provides transparent access to computing resources, regardless of the underlying cloud or HPC service provider. Bridging HPC and cloud advancements, XaaS presents a unified architecture built on performance-portable containers. Our converged model concentrates on low-overhead, high-performance communication and computing, targeting resource-intensive workloads from climate simulations to machine learning. XaaS lifts the restricted allocation model of Function-as-a-Service (FaaS), allowing users to benefit from the flexibility and efficient resource utilization of serverless while supporting long-running and performance-sensitive workloads from HPC.

The evolution of floating-point computation has been shaped by algorithmic advancements, architectural innovations, and the increasing computational demands of modern technologies, such as artificial intelligence (AI) and high-performance computing (HPC). This paper examines the historical progression of floating-point computation in scientific applications and contextualizes recent trends driven by AI, particularly the adoption of reduced-precision floating-point types. The challenges posed by these trends, including the trade-offs between performance, efficiency, and precision, are discussed, as are innovations in mixed-precision computing and emulation algorithms that offer solutions to these challenges. This paper also explores architectural shifts, including the role of specialized and general-purpose hardware, and how these trends will influence future advancements in scientific computing, energy efficiency, and system design.

We analyze 7826 publications from the International Conference on Computational Science (ICCS) between 2001 and 2023 using natural language processing and network analysis. We categorize computer science into 13 main disciplines and 102 sub-disciplines sourced from Wikipedia. After lemmatizing full texts of these papers, we calculate the similarity scores between the papers and each sub-discipline using vectors built with TF-IDF evaluation. Among the 13 main disciplines, machine learning & AI have become the most popular topics since 2019, surpassing parallel & distributed computing, which peaked in the early 2010 s. Modeling & simulation, and algorithms & data structure have always been popular disciplines in ICCS over the past 23 years. The most frequently researched sub-disciplines, on average, are algorithms, numerical analysis, and machine learning. Deep learning shows the most rapid growth, while parallel computing has declined over the past 23 years in ICCS publications. The network of sub-disciplines exhibits a scale-free distribution, indicating certain disciplines are more connected than others. We also present correlation analysis of sub-disciplines, both within the same main disciplines and between different main disciplines.

Performing a variety of numerical computations efficiently and, at the same time, in a portable fashion requires both an overarching design followed by a number of implementation strategies. All of these are exemplified below as we present transitioning the PLASMA numerical library from relying on dependence-driven large tasks to achieving utilization of fine grain tasking and offload to hardware accelerators while keeping its core dependence sets: OpenMP source code pragmas and runtime for most system-level functionality and basic low-level numerical kernels provided directly by hardware vendors or open source projects with vendor contributions. We also present new algorithmic methods and their efficient parallel implementations including fine grained tasking for eigen-spectrum slicing and offload for mixed-precision eigenvalue refinement. We provide performance, scaling, and numerical results showing sizable gains over the available solutions from either the open source and vendor-provided packages.

Parker and Lê introduced random butterfly transforms (RBTs) as a preprocessing technique to replace pivoting in dense LU factorization. Unfortunately, their FFT-like recursive structure restricts the dimensions of the matrix. Furthermore, on multi-node systems, efficient management of the communication overheads restricts the matrix’s distribution even more. To remove these limitations, we have generalized the RBT to arbitrary matrix sizes by truncating the dimensions of each layer in the transform. We expanded Parker’s theoretical analysis to generalized RBT, specifically that in exact arithmetic, Gaussian elimination with no pivoting will succeed with probability 1 after transforming a matrix with full-depth RBTs. Furthermore, we experimentally show that these generalized transforms improve performance over Parker’s formulation by up to 62 % while retaining the ability to replace pivoting. This generalized RBT is available in the SLATE numerical software library.