Related papers: Confederated Modular Differential Equation APIs fo…

We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…

Simulating physical systems is a core component of scientific computing, encompassing a wide range of physical domains and applications. Recently, there has been a surge in data-driven methods to complement traditional numerical simulations…

Quantum computers have been proposed as a solution for efficiently solving non-linear differential equations (DEs), a fundamental task across diverse technological and scientific domains. However, a crucial milestone in this regard is to…

Sequence-based specification and usage-driven statistical testing are designed for rigorous and cost-effective software development, offering a semi-formal approach to assessing the behavior of complex systems and interactions between…

Proving correctness of distributed or concurrent algorithms is a mind-challenging and complex process. Slight errors in the reasoning are difficult to find, calling for computer-checked proof systems. In order to build computer-checked…

Mathematical models are increasingly used in both academia and the pharmaceutical industry to understand how phenotypes emerge from systems of molecular interactions. However, their current construction as monolithic sets of equations…

This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to…

In computational biology and other sciences, researchers are frequently faced with a choice between several computational methods for performing data analyses. Benchmarking studies aim to rigorously compare the performance of different…

Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and non-measurable parameters, which have to be…

Large Language Models (LLM) are increasingly used for software development, yet existing benchmarks for LLM-based coding assistance do not reflect the constraints of High Energy Physics (HEP) and High Performance Computing (HPC) software.…

Comparative evaluation of several systems is a recurrent task in researching. It is a key step before deciding which system to use for our work, or, once our research has been conducted, to demonstrate the potential of the resulting model.…

Domain-specific software and hardware co-design is encouraging as it is much easier to achieve efficiency for fewer tasks. Agile domain-specific benchmarking speeds up the process as it provides not only relevant design inputs but also…

Large language models (LLMs) have achieved strong performance on reasoning benchmarks, yet their ability to solve real-world problems requiring end-to-end workflows remains unclear. Mathematical modeling competitions provide a stringent…

For scientific software, especially those used for large-scale simulations, achieving good performance and efficiently using the available hardware resources is essential. It is important to regularly perform benchmarks to ensure the…

Scientists construct and analyze computational models to understand the world. That understanding comes from efforts to augment, combine, and compare models of related phenomena. We propose SemanticModels.jl, a system that leverages…

Numerical solutions of partial differential equations enable a broad range of scientific research. The Dedalus Project is a flexible, open-source, parallelized computational framework for solving general partial differential equations using…

Ordinary differential equation models facilitate the understanding of cellular signal transduction and other biological processes. However, for large and comprehensive models, the computational cost of simulating or calibrating can be…

Machine learning-based modeling of physical systems has experienced increased interest in recent years. Despite some impressive progress, there is still a lack of benchmarks for Scientific ML that are easy to use but still challenging and…

The massive trend of integrating data-driven AI capabilities into traditional software systems is rising new intriguing challenges. One of such challenges is achieving a smooth transition from the explorative phase of Machine Learning…

Differentiable optimization has attracted significant research interest, particularly for quadratic programming (QP). Existing approaches for differentiating the solution of a QP with respect to its defining parameters often rely on…