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We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-06-24 Ioannis Sakiotis , Kamesh Arumugam , Marc Paterno , Desh Ranjan , Balša Terzić , Mohammad Zubair

We present an adaptive algorithm for effectively solving rough differential equations (RDEs) using the log-ODE method. The algorithm is based on an error representation formula that accurately describes the contribution of local errors to…

Numerical Analysis · Mathematics 2023-07-25 Christian Bayer , Simon Breneis , Terry Lyons

Neural ordinary differential equations (neural ODEs) have emerged as a novel network architecture that bridges dynamical systems and deep learning. However, the gradient obtained with the continuous adjoint method in the vanilla neural ODE…

Machine Learning · Computer Science 2023-06-12 Hong Zhang , Wenjun Zhao

In recent years, GPU-accelerated optimization solvers based on second-order methods (e.g., interior-point methods) have gained momentum with the advent of mature and efficient GPU-accelerated direct sparse linear solvers, such as cuDSS.…

Optimization and Control · Mathematics 2025-11-25 Alexis Montoison , François Pacaud , Sungho Shin , Mihai Anitescu

Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present…

Machine Learning · Computer Science 2024-12-17 Hong Zhang , Ying Liu , Romit Maulik

We focus on implementing and optimizing a sixth-order finite-difference solver for simulating compressible fluids on a GPU using third-order Runge-Kutta integration. Since graphics processing units perform well in data-parallel tasks, this…

Computational Physics · Physics 2017-07-28 Johannes Pekkilä , Miikka S. Väisälä , Maarit J. Käpylä , Petri J. Käpylä , Omer Anjum

Many emerging cyber-physical systems, such as autonomous vehicles and robots, rely heavily on artificial intelligence and machine learning algorithms to perform important system operations. Since these highly parallel applications are…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-02-07 An Zou , Jing Li , Christopher D. Gill , Xuan Zhang

Errors due to hardware or low level software problems, if detected, can be fixed by various schemes, such as recomputation from a checkpoint. Silent errors are errors in application state that have escaped low-level error detection. At…

Numerical Analysis · Computer Science 2018-01-08 Austin R. Benson , Sven Schmit , Robert Schreiber

A high fidelity flow simulation for complex geometries for high Reynolds number ($Re$) flow is still very challenging, which requires more powerful computational capability of HPC system. However, the development of HPC with traditional CPU…

Computational Physics · Physics 2022-03-03 Chuangchao Ye , Pengjunyi Zhang , Rui Yan , Dejun Sun , Zhenhua Wan

We introduce an ODE solver for the PyTorch ecosystem that can solve multiple ODEs in parallel independently from each other while achieving significant performance gains. Our implementation tracks each ODE's progress separately and is…

Machine Learning · Computer Science 2023-01-18 Marten Lienen , Stephan Günnemann

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-11-04 Dániel Nagy , Lambert Plavecz , Ferenc Hegedűs

Machine learning based on neural networks has advanced rapidly, but the high energy consumption required for training and inference remains a major challenge. Hyperdimensional Computing (HDC) offers a lightweight, brain-inspired alternative…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-11-10 Wakuto Matsumi , Riaz-Ul-Haque Mian

Dynamic programming (DP) is a cornerstone of combinatorial optimization, yet its inherently sequential structure has long limited its scalability in scenario-based stochastic programming (SP). This paper introduces a GPU-accelerated…

Optimization and Control · Mathematics 2025-11-25 Jingyi Zhao , Linxin Yang , Haohua Zhang , Tian Ding

Open Computing Language (OpenCL) is a parallel processing language that is ideally suited for running parallel algorithms on Graphical Processing Units (GPUs). In the present work we report on the development of a generic parallel…

Computational Physics · Physics 2012-05-31 Cathal Ó Broin , L. A. A. Nikolopoulos

We study the connections between ordinary differential equations and optimization algorithms in a non-Euclidean setting. We propose a novel accelerated algorithm for minimising convex functions over a convex constrained set. This algorithm…

Optimization and Control · Mathematics 2026-03-30 Paul Dobson , Jesus María Sanz-Serna , Konstantinos C. Zygalakis

GPU computing is expected to play an integral part in all modern Exascale supercomputers. It is also expected that higher order Godunov schemes will make up about a significant fraction of the application mix on such supercomputers. It is,…

Numerical Analysis · Mathematics 2023-04-06 Sethupathy Subramanian , Dinshaw S. Balsara , Deepak Bhoriya , Harish Kumar

In this paper, we propose a hybrid parallel programming approach for a numerical solution of a two-dimensional acoustic wave equation using an implicit difference scheme for a single computer. The calculations are carried out in an implicit…

Computational Physics · Physics 2020-06-19 Arshyn Altybay , Michael Ruzhansky , Niyaz Tokmagambetov

Learning neural ODEs often requires solving very stiff ODE systems, primarily using explicit adaptive step size ODE solvers. These solvers are computationally expensive, requiring the use of tiny step sizes for numerical stability and…

The electrical and electronic engineering has used parallel programming to solve its large scale complex problems for performance reasons. However, as parallel programming requires a non-trivial distribution of tasks and data, developers…

Distributed, Parallel, and Cluster Computing · Computer Science 2011-07-05 Antonio Wendell De Oliveira Rodrigues , Frédéric Guyomarc'H , Jean-Luc Dekeyser , Yvonnick Le Menach

The performance of graph programs depends highly on the algorithm, the size and structure of the input graphs, as well as the features of the underlying hardware. No single set of optimizations or one hardware platform works well across all…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-01-11 Ajay Brahmakshatriya , Yunming Zhang , Changwan Hong , Shoaib Kamil , Julian Shun , Saman Amarasinghe