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This paper describes the algorithms, features and implementation of PyDEC, a Python library for computations related to the discretization of exterior calculus. PyDEC facilitates inquiry into both physical problems on manifolds as well as…
Artificial intelligence (AI) is revolutionizing numerous fields, with increasing applications in Global Navigation Satellite Systems (GNSS) positioning algorithms in intelligent transportation systems (ITS) via deep learning. However, a…
Translating statistical methods into reliable software is a persistent bottleneck in quantitative research. Existing AI code-generation tools produce code quickly but cannot guarantee faithful implementation -- a critical requirement for…
Mathematical models allow us to gain a deeper understanding of real-world dynamical systems. One of the most powerful mathematical frameworks for modeling real-world phenomena are systems of differential equations. In the majority of fields…
With recent advancements in machine learning for interatomic potentials, Python has become the go-to programming language for exploring new ideas. While machine-learning potentials are often developed in Python-based frameworks, existing…
High-level synthesis (HLS) tools have brought FPGA development into the mainstream, by allowing programmers to design architectures using familiar languages such as C, C++, and OpenCL. While the move to these languages has brought…
PyFR is an open-source high-order accurate computational fluid dynamics solver for mixed unstructured grids that can target a range of hardware platforms from a single codebase. In this paper we demonstrate the ability of PyFR to perform…
The recomputability and reproducibility of results from scientific software requires access to both the source code and all associated input and output data. However, the full collection of these resources often does not accompany the key…
In spite of showing unreasonable effectiveness in modalities like Text and Image, Deep Learning has always lagged Gradient Boosting in tabular data - both in popularity and performance. But recently there have been newer models created…
The demand for substantial increases in the spatial resolution of global weather- and climate- prediction models makes it necessary to use numerically efficient and highly scalable algorithms to solve the equations of large scale…
This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…
This paper presents HDGlab, an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of both the HDG method for elliptic problems and its implementation…
Pyqcm is a Python/C++ library that implements a few quantum cluster methods with an exact diagonalization impurity solver. Quantum cluster methods are used in the study of strongly correlated electrons to provide an approximate solution to…
A scalable algorithm for solving compact banded linear systems on distributed memory architectures is presented. The proposed method factorizes the original system into two levels of memory hierarchies, and solves it using parallel cyclic…
Data gridding is a common task in astronomy and many other science disciplines. It refers to the resampling of irregularly sampled data to a regular grid. We present cygrid, a library module for the general purpose programming language…
In the Exa-Dune project we have developed, implemented and optimised numerical algorithms and software for the scalable solution of partial differential equations (PDEs) on future exascale systems exhibiting a heterogeneous massively…
Scientific simulation leveraging high-performance computing (HPC) systems is crucial for modeling complex systems and phenomena in fields such as astrophysics, climate science, and fluid dynamics, generating massive datasets that often…
The data engineering and data science community has embraced the idea of using Python & R dataframes for regular applications. Driven by the big data revolution and artificial intelligence, these applications are now essential in order to…
The combination of machine learning and physical laws has shown immense potential for solving scientific problems driven by partial differential equations (PDEs) with the promise of fast inference, zero-shot generalisation, and the ability…
The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations…