Related papers: Optimised finite difference computation from symbo…
Domain specific languages have successfully been used in a variety of fields to cleanly express scientific problems as well as to simplify implementation and performance opti- mization on different computer architectures. Although a large…
Domain specific languages (DSL) have been used in a variety of fields to express complex scientific problems in a concise manner and provide automated performance optimization for a range of computational architectures. As such DSLs provide…
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…
Stencil computations are a key part of many high-performance computing applications, such as image processing, convolutional neural networks, and finite-difference solvers for partial differential equations. Devito is a framework capable of…
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…
Finite-difference methods are widely used in solving partial differential equations. In a large problem set, approximations can take days or weeks to evaluate, yet the bulk of computation may occur within a single loop nest. The modelling…
Stencil kernels dominate a range of scientific applications, including seismic and medical imaging, image processing, and neural networks. Temporal blocking is a performance optimization that aims to reduce the required memory bandwidth of…
The growth of data to be processed in the Oil & Gas industry matches the requirements imposed by evolving algorithms based on stencil computations, such as Full Waveform Inversion and Reverse Time Migration. Graphical processing units…
The Devito DSL is a code generation tool for the solution of partial differential equations using the finite difference method specifically aimed at seismic inversion problems. In this work we investigate the integration of OPS, an API to…
[Devito] is an open-source Python project based on domain-specific language and compiler technology. Driven by the requirements of rapid HPC applications development in exploration seismology, the language and compiler have evolved…
This work presents a brief discussion and a plan towards the analytical solving of Partial Differential Equations (PDEs) using symbolic computing, as well as an implementation of part of this plan as the PDEtools software-package of…
The run time of many scientific computation applications for numerical methods is heavily dependent on just a few multi-dimensional loop nests. Since these applications are often limited by memory bandwidth rather than computational…
We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…
Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…
Using exhaustion method and finite differences a new method to solve system of partial differential equations and is presented. This method allows design algorithm to solve linear and nonlinear systems in irregular domains. Applying this…
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 describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…
The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations,…
Computational Fluid Dynamics (CFD) is an important approach for analyzing flow phenomena and predicting engineering-relevant quantities. The governing physics is formulated as partial differential equations(PDEs) and solved numerically on…
Neural operator models for solving partial differential equations (PDEs) often rely on global mixing mechanisms-such as spectral convolutions or attention-which tend to oversmooth sharp local dynamics and introduce high computational cost.…