Louise Huot | Searcharxiv

arXiv2025

Aurora: Architecting Argonne's First Exascale Supercomputer for Accelerated Scientific Discovery

Aurora is Argonne National Laboratory's pioneering Exascale supercomputer, designed to accelerate scientific discovery with cutting-edge architectural innovations. Key new technologies include the Intel(TM) Xeon(TM) Data Center GPU Max Series (code-named Sapphire Rapids) with support for High Bandwidth Memory (HBM), alongside the Intel(TM) Data Center GPU Max Series (code-named Ponte Vecchio) on each compute node. Aurora also integrates the Distributed Asynchronous Object Storage (DAOS), a novel exascale storage solution, and leverages Intel's oneAPI programming environment. This paper presents an in-depth exploration of Aurora's node architecture, the HPE Slingshot interconnect, the supporting software ecosystem, and DAOS. We provide insights into standard benchmark performance and applications readiness efforts via Aurora's Early Science Program and the Exascale Computing Project.

cs.DC↗

arXiv2013

Polynomial Systems Solving by Fast Linear Algebra

Polynomial system solving is a classical problem in mathematics with a wide range of applications. This makes its complexity a fundamental problem in computer science. Depending on the context, solving has different meanings. In order to stick to the most general case, we consider a representation of the solutions from which one can easily recover the exact solutions or a certified approximation of them. Under generic assumption, such a representation is given by the lexicographical Gröbner basis of the system and consists of a set of univariate polynomials. The best known algorithm for computing the lexicographical Gröbner basis is in $\widetilde{O}(d^{3n})$ arithmetic operations where $n$ is the number of variables and $d$ is the maximal degree of the equations in the input system. The notation $\widetilde{O}$ means that we neglect polynomial factors in $n$. We show that this complexity can be decreased to $\widetilde{O}(d^{ωn})$ where $2 \leq ω< 2.3727$ is the exponent in the complexity of multiplying two dense matrices. Consequently, when the input polynomial system is either generic or reaches the Bézout bound, the complexity of solving a polynomial system is decreased from $\widetilde{O}(D^3)$ to $\widetilde{O}(D^ω)$ where $D$ is the number of solutions of the system. To achieve this result we propose new algorithms which rely on fast linear algebra. When the degree of the equations are bounded uniformly by a constant we propose a deterministic algorithm. In the unbounded case we present a Las Vegas algorithm.

cs.SC↗