Related papers: Optimizing Large-Scale ODE Simulations

With the decline of Moore's law, optimizing program performance has become a major focus of software research. However, high-level optimizations such as API and algorithm changes remain elusive due to the difficulty of understanding the…

Deep learning implementations on CPUs (Central Processing Units) are gaining more traction. Enhanced AI capabilities on commodity x86 architectures are commercially appealing due to the reuse of existing hardware and virtualization ease. A…

The Quantum Approximate Optimization Algorithm (QAOA) is a prominent quantum algorithm designed to find approximate solutions to combinatorial optimization problems, which are challenging for classical computers. In the current era, where…

Parallel computing can offer an enormous advantage regarding the performance for very large applications in almost any field: scientific computing, computer vision, databases, data mining, and economics. GPUs are high performance many-core…

Many computer systems for calculating the proper organization of memory are among the most critical issues. Using a tier cache memory (along with branching prediction) is an effective means of increasing modern multi-core processors'…

We present a software implementation integrating the time-integration library Odeint from Boost with the OpenFPM framework for scalable scientific computing. This enables compact and scalable codes for multi-stage, multi-step, and adaptive…

Interconnecting clusters of qubits will be an essential element of scaling up future quantum computers. Operations between quantum processing units (QPUs) are usually significantly slower and costlier than those within a single QPU, so…

Training large language models (LLMs) is known to be challenging because of the huge computational and memory capacity requirements. To address these issues, it is common to use a cluster of GPUs with 3D parallelism, which splits a model…

This work focuses on the numerical study of a recently published class of Runge-Kutta methods designed for mixed-precision arithmetic. We employ the methods in solving partial differential equations on modern hardware. In particular we…

Discrete optimization is a central problem in artificial intelligence. The optimization of the aggregated cost of a network of cost functions arises in a variety of problems including (W)CSP, DCOP, as well as optimization in stochastic…

Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…

Large language models (LLMs) have shown exceptional performance and vast potential across diverse tasks. However, the deployment of LLMs with high performance in low-resource environments has garnered significant attention in the industry.…

We deal with optimal approximation of solutions of ODEs under local Lipschitz condition and inexact discrete information about the right-hand side functions. We show that the randomized two-stage Runge-Kutta scheme is the optimal method…

Unbalanced optimal transport (UOT) has been widely used as a fundamental tool in many application domains, where it often dominates the application running time. While many researchers have proposed various optimizations for UOT, few have…

For computational fluid dynamics (CFD) applications with a large number of grid points/cells, parallel computing is a common efficient strategy to reduce the computational time. How to achieve the best performance in the modern…

This paper proposes a novel set of trigonometric implementations which are 5x faster than the inbuilt C++ functions. The proposed implementation is also highly memory efficient requiring no precomputations of any kind. Benchmark comparisons…

With the development of quantum computing, quantum processor demonstrates the potential supremacy in specific applications, such as Grovers database search and popular quantum neural networks (QNNs). For better calibrating the quantum…

Modern GPUs are able to perform significantly more arithmetic operations than transfers of a single word to or from global memory. Hence, many GPU kernels are limited by memory bandwidth and cannot exploit the arithmetic power of GPUs.…

With the advent of high-performance computing techniques, the data for analysis has grown significantly. Here, graphic processing unit (GPU) based program kernels are discussed to exploit parallelism in the analysis codes specific to…

Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it…