Welcome Session

• Stefan Roiser (CERN)

Room: 40/S2-A01 – Salle Anderson

Problem statement from experiments and SFT Room: 40/S2-A01 – Salle Anderson

Problem statement from Theory Department

• Jacob Finkenrath

Room: 40/S2-A01 – Salle Anderson

Problem statement from Beams

• Riccardo di Maria

Room: 40/S2-A01 – Salle Anderson

NVidia - Floating point for future GPU hardware

• Samuel Rodriguez

Room: 40/S2-A01 – Salle Anderson

AMD - Floating point for future GPU hardware Room: 40/S2-A01 – Salle Anderson

Extended Precision in Convex Optimisation

• David Herrera-Marti
• Eric Guthmuller
• Jerome Fereyre

Room: 40/S2-A01 – Salle Anderson Semidefinite Programming is a matrix-form generalisation of linear programming, and is typically tackled using Interior Point Methods. These methods are of iterative nature and at each step, a matrix inversion needs to be performed. For small or sparse matrices, direct methods like sparse Cholesky factorisation are used. For dense matrices of larger size, like the ones that arise in convex relaxations of combinatorial problems, Krylov methods like Conjugate Gradient seem a better approach. We show how, as the dual-primal central trajectory approaches the feasible set and the tentative solution becomes rank-deficient, increasing the precision accelerates the convergence (in terms of number of CG iterations).

Discussion - Questions Room: 40/S2-A01 – Salle Anderson

Using physics knowledge to improve numerical stability

• Enrico Bothmann

Room: 40/S2-B01 - Salle Bohr The numerically stable evaluation of scattering matrix elements near the infrared limit of gauge theories is of great importance for the success of collider physics experiments. We present a novel algorithm that utilizes double precision arithmetic and reaches higher precision than a naive quadruple precision implementation at smaller computational cost. The method is based on physics-driven modifications to propagators, vertices and external polarizations. [https://arxiv.org/abs/2406.07671] Authors: E. Bothmann (speaker), J. M. Campbell, S. Höche, M. Knobbe

KIT - Double-double for pySecDec on GPU

• Vitaly Magery

Room: 40/S2-B01 - Salle Bohr

An overview of mixed precision strategies for scientific computing

• Theo Mary

Room: 40/S2-B01 - Salle Bohr The increasing support of lower precision arithmetics in hardware provides new opportunities for high performance scientific computing. However, even though low precision arithmetics can provide significant speed, communication, and energy benefits, their use in scientific computing poses the challenge of preserving the accuracy and stability of the computation. To address this issue, a variety of mixed precision algorithms that combine low and high precisions have emerged. In this talk I will give an overview of mixed precision algorithms in numerical linear algebra, with a focus on recent advances to accelerate the solution of linear systems.

Nicolo's talk

• Nicolo Ghielmetti (CERN)

Room: 40/S2-A01 – Salle Anderson

Discussion - Questions Room: 40/S2-B01 - Salle Bohr

University of Budapest - Tensor networks, FP64 emulation Room: 40/S2-B01 - Salle Bohr

TNL: Numerical Library for Modern Parallel Architectures

• Thomas Oberhuber

Room: 40/S2-B01 - Salle Bohr TNL (www.tnl-project.org) is a collection of building blocks that facilitate the development of efficient numerical solvers and HPC algorithms. It is implemented in C++ using modern programming paradigms in order to provide a flexible and user-friendly interface similar to, for example, the C++ Standard Template Library. TNL provides native support for modern hardware architectures such as multicore CPUs, GPUs, and distributed systems, which can be managed via a unified interface. In our presentation, we will demonstrate the main features of the library together with efficiency of the implemented algorithms and data structures.

Float32 Expansions – A Possible Answer for Scientific Computing in the Era of AI-Driven GPU Development

• František Stloukal

Room: 40/S2-A01 – Salle Anderson In recent years, the emergence of large language models has led GPU vendors to prioritize performance improvements for lower-precision arithmetic, often at the expense of continued development for Float64. Meanwhile, scientific computing has increasingly relied on GPGPU acceleration, where double precision is still essential. Multi-word expansions for single-precision floating point numbers may offer a viable alternative—providing comparable or even superior precision while achieving better performance than native double precision. In this talk, we will present results using a CUDA-enabled, templated, and ported version of the QD library within the TNL framework, applied to existing numerical algorithms.

Discussion - Questions Room: 40/S2-B01 - Salle Bohr

LBNL - Differential programming / algo need for precision

• Garima Singh

Room: 40/S2-B01 - Salle Bohr

Precision auto-tuning and control of accuracy in high performance simulations

• Fabienne Jézéquel (LIP6, Sorbonne Université)

Room: 40/S2-B01 - Salle Bohr In the context of high performance computing, new architectures, becoming more and more parallel, offer higher floating-point computing power. Thus, the size of the problems considered (and with it, the number of operations) increases, becoming a possible cause for increased uncertainty. As such, estimating the reliability of a result at a reasonable cost is of major importance for numerical software. In this talk we present an overview of different approaches for accuracy analysis (guaranteed or probabilistic ones) and the related software. We also describe methods to improve the results accuracy. We present the principles of Discrete Stochastic Arithmetic (DSA) that enables one to estimate rounding errors in simulation codes. DSA can be used to control the accuracy of programs in half, single, or double precision via the CADNA library, and also in arbitrary precision via the SAM library. Thanks to DSA, the accuracy estimation and the detection of numerical instabilities can be performed in parallel codes on CPU and on GPU. Most numerical simulations are performed in double precision, and this can be costly in terms of computing time, memory transfer and energy consumption. We present tools for floating-point auto-tuning that aim at reducing the numerical formats used in simulation programs.

Experiences with CADNA and the Madgraph5 Event Generator

• Stephan Hageboeck

Room: 40/S2-B01 - Salle Bohr This talk presents a summer student project that explored the numerical stability of MadGraph5 using CADNA. It focuses on how CADNA’s warning system and its ability to quantify floating-point precision were used to assess whether MadGraph5 can operate reliably with single-precision floating-point numbers.

Emulating Matrix Multiplication Using Mixed-Precision Computation

• Katsuhisa Ozaki

Room: 40/S2-B01 - Salle Bohr This talk introduces a method for emulating matrix multiplication through mixed-precision computation. As exemplified by the Matrix Engine on GPUs, low-precision arithmetic can be performed significantly faster than conventional FP32 or FP64 operations. We present Ozaki Scheme I and II, which leverage low-precision arithmetic to achieve accuracy comparable to standard FP64, and discuss their numerical performance.

Discussion - Questions Room: 40/S2-B01 - Salle Bohr

Closing Session Room: 40/S2-B01 - Salle Bohr