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Writing complex computer programs to study scientific problems requires careful planning and an in-depth knowledge of programming languages and tools. In this chapter the importance of using the right tool for the right problem is…

In the last couple of years we have witnessed an enormous increase of machine learning (ML) applications. More and more program functions are no longer written in code, but learnt from a huge amount of data samples using an ML algorithm.…

We introduce the notion of a robust parameterized arithmetic circuit for the evaluation of algebraic families of multivariate polynomials. Based on this notion, we present a computation model, adapted to Scientific Computing, which captures…

Large Language Models (LLMs) have significantly advanced tool-augmented agents, enabling autonomous reasoning via API interactions. However, executing multi-step tasks within massive tool libraries remains challenging due to two critical…

Mathematical programming -- the task of expressing operations and decision-making problems in precise mathematical language -- is fundamental across domains, yet remains a skill-intensive process requiring operations research expertise.…

Linear algebra operations are widely used in scientific computing and machine learning applications. However, it is challenging for scientists and data analysts to run linear algebra at scales beyond a single machine. Traditional approaches…

The increasing complexity of software systems has driven significant advancements in program analysis, as traditional methods unable to meet the demands of modern software development. To address these limitations, deep learning techniques,…

Graph algorithms can be expressed in terms of linear algebra. GraphBLAS is a library of low-level building blocks for such algorithms that targets algorithm developers. LAGraph builds on top of the GraphBLAS to target users of graph…

Many fields use search algorithms, which automatically explore a search space to find high-performing solutions: chemists search through the space of molecules to discover new drugs; engineers search for stronger, cheaper, safer designs,…

This paper studies a strategy for data-driven algorithm design for large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general purpose ways. The goal is to arrive at new approaches that can…

Deep learning technologies have demonstrated remarkable effectiveness in a wide range of tasks, and deep learning holds the potential to advance a multitude of applications, including in edge computing, where deep models are deployed on…

In this paper we propose a set of guidelines to select a solver for the solution of nonlinear programming problems. With this in mind, we present a comparison of the convergence performances of commonly used solvers for both unconstrained…

Linear systems are the bedrock of virtually all numerical computation. Machine learning poses specific challenges for the solution of such systems due to their scale, characteristic structure, stochasticity and the central role of…

To bridge the digital skills gap, we need to train more people in Software Engineering techniques. This paper reports on a project exploring the way students solve tasks using collaborative development platforms and version control systems,…

We present a complete reimplementation of the LinearSystem package of Magma, with substantial improvements in design and performance. The resulting efficiency enables computations that were previously out of reach. We briefly describe the…

Enhancing the mathematical reasoning of large language models (LLMs) demands high-quality training data, yet conventional methods face critical challenges in scalability, cost, and data reliability. To address these limitations, we propose…

Integer linear programming (ILP) encompasses a very important class of optimization problems that are of great interest to both academia and industry. Several algorithms are available that attempt to explore the solution space of this class…

Large language models (LLMs) have revolutionized natural language processing with their exceptional understanding, synthesizing, and reasoning capabilities. However, deploying LLMs on resource-constrained edge devices presents significant…

As large language models (LLMs) continue to advance, the need for up-to-date and well-organized benchmarks becomes increasingly critical. However, many existing datasets are scattered, difficult to manage, and make it challenging to perform…

Deep learning holds immense promise for spectroscopy, yet research and evaluation in this emerging field often lack standardized formulations. To address this issue, we introduce SpectrumLab, a pioneering unified platform designed to…