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Partial differential equations (PDEs) are crucial for modeling various physical phenomena such as heat transfer, fluid flow, and electromagnetic waves. In computer-aided engineering (CAE), the ability to handle fine resolutions and large…
Neural network-based approaches for solving partial differential equations (PDEs) have recently received special attention. However, the large majority of neural PDE solvers only apply to rectilinear domains, and do not systematically…
Numerically solving high-dimensional partial differential equations (PDEs) is a major challenge. Conventional methods, such as finite difference methods, are unable to solve high-dimensional PDEs due to the curse-of-dimensionality. A…
The past decade has witnessed a dramatic acceleration of lattice quantum chromodynamics calculations in nuclear and particle physics. This has been due to both significant progress in accelerating the iterative linear solvers using…
Differential Evolution (DE) is a highly successful population based global optimisation algorithm, commonly used for solving numerical optimisation problems. However, as the complexity of the objective function increases, the wall-clock…
Many problems in geophysical and atmospheric modelling require the fast solution of elliptic partial differential equations (PDEs) in "flat" three dimensional geometries. In particular, an anisotropic elliptic PDE for the pressure…
Deep neural networks are powerful tools for approximating functions, and they are applied to successfully solve various problems in many fields. In this paper, we propose a neural network-based numerical method to solve partial differential…
Applications that exploit the architectural details of high-performance computing (HPC) systems have become increasingly invaluable in academia and industry over the past two decades. The most important hardware development of the last…
Stencil computations are widely used in HPC applications. Today, many HPC platforms use GPUs as accelerators. As a result, understanding how to perform stencil computations fast on GPUs is important. While implementation strategies for…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
The paper considers the problem of implementation on graphics processors of numerical integration routines for higher order finite element approximations. The design of suitable GPU kernels is investigated in the context of general purpose…
High-dimensional partial differential equations (PDEs) pose significant challenges for numerical computation due to the curse of dimensionality, which limits the applicability of traditional mesh-based methods. Since 2017, the Deep BSDE…
Over the last ten years, graphics processors have become the de facto accelerator for data-parallel tasks in various branches of high-performance computing, including machine learning and computational sciences. However, with the recent…
Solving large complex partial differential equations (PDEs), such as those that arise in computational fluid dynamics (CFD), is a computationally expensive process. This has motivated the use of deep learning approaches to approximate the…
Physics-Informed Neural Networks (PINNs) have been widely used for solving partial differential equations (PDEs) of different types, including fractional PDEs (fPDES) [29]. Herein, we propose a new general (quasi) Monte Carlo PINN for…
Numerical integration of stochastic differential equations is commonly used in many branches of science. In this paper we present how to accelerate this kind of numerical calculations with popular NVIDIA Graphics Processing Units using the…
We introduce and study a new class of partial differential equations (PDEs) with hybrid fuzzy-stochastic parameters, coined fuzzy-stochastic PDEs. Compared to purely stochastic PDEs or purely fuzzy PDEs, fuzzy-stochastic PDEs offer powerful…
The numerical solution of the Kadanoff-Baym nonlinear integro-differential equations, which yields the non-equilibrium Green's functions (NEGFs) of quantum many-body systems, poses significant computational challenges due to its high…
In this paper, the performance characteristics of different solution techniques and program packages to solve a large number of independent ordinary differential equation systems is examined. The employed hardware are an Intel Core i7-4820K…
Partial differential equations have a wide range of applications in modeling multiple physical, biological, or social phenomena. Therefore, we need to approximate the solutions of these equations in computationally feasible terms. Nowadays,…