Related papers: Optimising finite-difference methods for PDEs thro…

Monotone finite difference methods provide stable convergent discretizations of a class of degenerate elliptic and parabolic Partial Differential Equations (PDEs). These methods are best suited to regular rectangular grids, which leads to…

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…

We present a Pseudo-Transient Topology Optimization (PeTTO) approach that can leverage graphics processing units (GPUs) to efficiently solve single-material and multi-material topology optimization problems. By integrating PeTTO with phase…

Physics-informed neural networks (PINNs) provide a promising machine learning framework for solving partial differential equations, but their training often breaks down on challenging problems, sometimes converging to physically incorrect…

We present a new deep learning-based approach for dense stereo matching. Compared to previous works, our approach does not use deep learning of pixel appearance descriptors, employing very fast classical matching scores instead. At the same…

Neural network-based solvers for partial differential equations (PDEs) have attracted considerable attention, yet they often face challenges in accuracy and computational efficiency. In this work, we focus on time-dependent PDEs and observe…

Dynamical systems are essential to model various phenomena in physics, finance, economics, and are also of current interest in machine learning. A central modeling task is investigating parameter sensitivity, whether tuning atmospheric…

This paper presents a novel approach for numerical solution of a class of fourth order time fractional partial differential equations (PDE's). The finite difference formulation has been used for temporal discretization, whereas, the space…

This paper develops and analyzes an optimal-order semi-discrete scheme and its fully discrete finite element approximation for nonlinear stochastic elastic wave equations with multiplicative noise. A non-standard time-stepping scheme is…

We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…

Stencil computation is one of the most important kernels in various scientific and engineering applications. A variety of work has focused on vectorization and tiling techniques, aiming at exploiting the in-core data parallelism and data…

Stencil computation is one of the most important kernels in various scientific and engineering applications. A variety of work has focused on vectorization techniques, aiming at exploiting the in-core data parallelism. Briefly, they either…

Iterative stencils are used widely across the spectrum of High Performance Computing (HPC) applications. Many efforts have been put into optimizing stencil GPU kernels, given the prevalence of GPU-accelerated supercomputers. To improve the…

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…

Multidimensional Retiming is one of the most important optimization techniques to improve timing parameters of nested loops. It consists in exploring the iterative and recursive structures of loops to redistribute computation nodes on cycle…

This is a study of certain finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, we analyze high order space-time tensor product finite element discretizations, used in a…

Matrix-free finite element implementations for large applications provide an attractive alternative to standard sparse matrix data formats due to the significantly reduced memory consumption. Here, we show that they are also competitive…

This work aims to construct an efficient and highly accurate numerical method to address the time singularity at $t=0$ involved in a class of time-fractional parabolic integro-partial differential equations in one and two dimensions. The…

Neural Stochastic Differential Equations (Neural SDEs) have emerged as powerful mesh-free generative models for continuous stochastic processes, with critical applications in fields such as finance, physics, and biology. Previous…

While fine-tuning of pre-trained language models generally helps to overcome the lack of labelled training samples, it also displays model performance instability. This instability mainly originates from randomness in initialisation or data…