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Ordinary Differential Equations (ODE) are used throughout science where the capture of rates of change in states is sought. While both pieces of commercial and open software exist to study such systems, their efficient and accurate usage…
$\textit{Pymc-learn}$ is a Python package providing a variety of state-of-the-art probabilistic models for supervised and unsupervised machine learning. It is inspired by $\textit{scikit-learn}$ and focuses on bringing probabilistic machine…
SfePy (Simple finite elements in Python) is a software for solving various kinds of problems described by partial differential equations in one, two or three spatial dimensions by the finite element method. Its source code is mostly (85\%)…
\textsc{Pykat} is a Python package which extends the popular optical interferometer modelling software \textsc{Finesse}. It provides a more modern and efficient user interface for conducting complex numerical simulations, as well as…
In this project, we introduce OPESCI-FD, a Python package built on symbolic mathematics to automatically generate Finite Difference models from a high-level description of the model equations. We investigate applying this framework to…
The use of machine learning (ML) techniques to solve complex physical problems has been considered recently as a promising approach. However, the evaluation of such learned physical models remains an important issue for industrial use. The…
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…
Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of…
In non-linear systems, where explicit analytic solutions usually can't be found, visualisation is a powerful approach which can give insights into the dynamical behaviour of models; it is also crucial for teaching this area of mathematics.…
In this paper, we develop a framework for solving inverse deformation problems using the FEniCS Project finite element software. We validate our approach with experimental imaging data acquired from a soft silicone beam under gravity. In…
This study introduces Pedophysics, an open-source Python package designed to facilitate solutions for users who work in the field of soil assessment using near-surface geophysical electromagnetic techniques. At the core of this software is…
PYSCF is a Python-based general-purpose electronic structure platform that both supports first-principles simulations of molecules and solids, as well as accelerates the development of new methodology and complex computational workflows.…
We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…
In this paper we present FeynRules, a new Mathematica package that facilitates the implementation of new particle physics models. After the user implements the basic model information (e.g. particle content, parameters and Lagrangian),…
Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. Compared to classical numerical methods PINNs have several advantages, for example their…
MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods…
The fast simulation of dynamical systems is a key challenge in many scientific and engineering applications, such as weather forecasting, disease control, and drug discovery. With the recent success of deep learning, there is increasing…
Scikit-learn is a Python module integrating a wide range of state-of-the-art machine learning algorithms for medium-scale supervised and unsupervised problems. This package focuses on bringing machine learning to non-specialists using a…
Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…
In this article we introduce the supervised machine learning tool called Feyn. The simulation engine that powers this tool is called the QLattice. The QLattice is a supervised machine learning tool inspired by Richard Feynman's path…