Related papers: OPESCI-FD: Automatic Code Generation Package for F…
Partial differential equations (PDEs) are crucial in modeling diverse phenomena across scientific disciplines, including seismic and medical imaging, computational fluid dynamics, image processing, and neural networks. Solving these PDEs at…
This paper presents a new finite difference method, called {\varphi}-FD, inspired by the {\phi}-FEM approach for solving elliptic partial differential equations (PDEs) on general geometries. The proposed method uses Cartesian grids,…
Domain-specific high-productivity environments are playing an increasingly important role in scientific computing due to the levels of abstraction and automation they provide. In this paper we introduce Devito, an open-source…
OpenSBLI is an open-source code-generation system for compressible fluid dynamics (CFD) on heterogeneous computing architectures. Written in Python, OpenSBLI is an explicit high-order finite-difference solver on structured curvilinear…
This paper introduces the FEDM (Finite Element Discharge Modelling) code, which was developed using the open-source computing platform FEniCS (https://fenicsproject.org). Building on FEniCS, the FEDM code utilises the finite element method…
In this paper we discuss three symbolic approaches for the generation of a finite difference scheme of a partial differential equation (PDE). We prove, that for a linear PDE with constant coefficients these three approaches are equivalent…
We present spd-metrics-id, a Python package for computing distances and divergences between symmetric positive-definite (SPD) matrices. Unlike traditional toolkits that focus on specific applications, spd-metrics-id provides a unified,…
PySCF is a general-purpose electronic structure platform designed from the ground up to emphasize code simplicity, both to aid new method development, as well as for flexibility in computational workflow. The package provides a wide range…
Finite difference (FD) approximation is a classic approach to stochastic gradient estimation when only noisy function realizations are available. In this paper, we first provide a sample-driven method via the bootstrap technique to estimate…
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…
We introduce an efficient open-source python package for the inverse design of three-dimensional photonic nanostructures using the Finite-Difference Time-Domain (FDTD) method. Leveraging a flexible reverse-mode automatic differentiation…
We present gradiend, an open-source Python package that operationalizes the GRADIEND method for learning feature directions from factual-counterfactual MLM and CLM gradients in language models. The package provides a unified workflow for…
The dynamic mode decomposition (DMD) is a simple and powerful data-driven modeling technique that is capable of revealing coherent spatiotemporal patterns from data. The method's linear algebra-based formulation additionally allows for a…
Simflowny is an open platform which automatically generates efficient parallel code of scientific dynamical models for different simulation frameworks. Here we present major upgrades on this software to support simultaneously a quite…
A complete and rigorously validated open-source Python framework to automate point defect calculations using density functional theory has been developed. The framework provides an effective and efficient method for defect structure…
Spatially-coupled (SC) codes are a class of low-density parity-check (LDPC) codes that is gaining increasing attention. Multi-dimensional (MD) SC codes are constructed by connecting copies of an SC code via relocations in order to mitigate…
Solving partial differential equations (PDEs) with highly oscillatory solutions on complex domains remains a challenging and important problem. High-frequency oscillations and intricate geometries often result in prohibitively expensive…
Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community. PySINDy is a Python package that provides tools for applying the…
We introduce Devito, a new domain-specific language for implementing high-performance finite difference partial differential equation solvers. The motivating application is exploration seismology where methods such as Full-Waveform…
Derivative boundary conditions introduce challenges for mesh-free discretizations of PDEs on surfaces, especially when the domain is represented by randomly sampled point clouds. The recently developed two-step tangent-space RBF-generated…