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We present a high-performance budgeted multi-level Monte Carlo method for estimates on the entire spatial domain of multi-PDE problems with random input data. The method is designed to operate optimally within memory and CPU-time…

Numerical Analysis · Mathematics 2025-06-10 Niklas Baumgarten , Robert Kutri , Robert Scheichl

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-28 Johannes Pekkilä , Oskar Lappi , Fredrik Robertsén , Maarit J. Korpi-Lagg

Financial derivatives are contracts that can have a complex payoff dependent upon underlying benchmark assets. In this work, we present a quantum algorithm for the Monte Carlo pricing of financial derivatives. We show how the relevant…

Quantum Physics · Physics 2018-08-23 Patrick Rebentrost , Brajesh Gupt , Thomas R. Bromley

We present how we ported the Hybrid Monte Carlo implementation in the tmLQCD software suite to GPUs through offloading its most expensive parts to the QUDA library. We discuss our motivations and some of the technical challenges that we…

High Energy Physics - Lattice · Physics 2022-12-14 Bartosz Kostrzewa , Simone Bacchio , Jacob Finkenrath , Marco Garofalo , Ferenc Pittler , Simone Romiti , Carsten Urbach

Monte Carlo simulations of physics processes at particle colliders like the Large Hadron Collider at CERN take up a major fraction of the computational budget. For some simulations, a single data point takes seconds, minutes, or even hours…

Computational Physics · Physics 2023-02-03 Fady Bishara , Ayan Paul , Jennifer Dy

Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study quantum algorithms for stochastic differential equations (SDEs). Firstly we provide a quantum algorithm that gives a quadratic…

Quantum Physics · Physics 2021-06-30 Dong An , Noah Linden , Jin-Peng Liu , Ashley Montanaro , Changpeng Shao , Jiasu Wang

We develop a novel Monte Carlo algorithm for the vector consisting of the supremum, the time at which the supremum is attained and the position at a given (constant) time of an exponentially tempered L\'evy process. The algorithm, based on…

Mathematical Finance · Quantitative Finance 2023-11-20 Jorge Ignacio González Cázares , Aleksandar Mijatović

In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithm, in the paradigm of applications in financial engineering. We specifically focus on the recent studies conducted in two…

Computational Finance · Quantitative Finance 2022-09-30 Devang Sinha , Siddhartha P. Chakrabarty

Graphics Processing Units (GPUs) are now powerful and flexible systems adapted and used for other purposes than graphics calculations (General Purpose computation on GPU -- GPGPU). We present here a prototype to be integrated into…

Distributed, Parallel, and Cluster Computing · Computer Science 2007-06-13 Sylvain Collange , Marc Daumas , David Defour

Particle-in-cell (PIC) simulations with Monte-Carlo collisions are used in plasma science to explore a variety of kinetic effects. One major problem is the long run-time of such simulations. Even on modern computer systems, PIC codes take a…

This paper explores advancements in quantum algorithms for derivative pricing of exotics, a computational pipeline of fundamental importance in quantitative finance. For such cases, the classical Monte Carlo integration procedure provides…

We present MadFlow, a first general multi-purpose framework for Monte Carlo (MC) event simulation of particle physics processes designed to take full advantage of hardware accelerators, in particular, graphics processing units (GPUs). The…

Computational Physics · Physics 2021-08-18 Stefano Carrazza , Juan Cruz-Martinez , Marco Rossi , Marco Zaro

Multilevel Monte Carlo (MLMC) reduces the total computational cost of financial option pricing by combining SDE approximations with multiple resolutions. This paper explores a further avenue for reducing cost and improving power efficiency…

Computational Finance · Quantitative Finance 2025-02-12 Irina-Beatrice Haas , Michael B. Giles

Precise hardware performance models play a crucial role in code optimizations. They can assist compilers in making heuristic decisions or aid autotuners in identifying the optimal configuration for a given program. For example, the…

Recent advances in high-resolution CT-imaging technology are creating a new class of ultra-high resolved micro-structural datasets that challenge the limits of traditional homogenization approaches. While state-of-the-art FFT-based…

Materials Science · Physics 2025-12-10 Sascha H. Hauck , Matthias Kabel , Nicolas R. Gauger

Modern parallel computing devices, such as the graphics processing unit (GPU), have gained significant traction in scientific and statistical computing. They are particularly well-suited to data-parallel algorithms such as the particle…

Computation · Statistics 2015-06-12 Lawrence M. Murray , Anthony Lee , Pierre E. Jacob

The recently-introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement…

Strongly Correlated Electrons · Physics 2017-10-11 Yuki Nagai , Huitao Shen , Yang Qi , Junwei Liu , Liang Fu

The computational cost of traditional first-principles method quickly becomes prohibitively expensive as the number of atoms increases. This challenge is further amplified by the need to evaluate finite-temperature properties with Monte…

Materials Science · Physics 2025-08-13 Xianglin Liu , Kai Yang , Yongxiang Liu , Fanli Zhou , Dengdong Fan , Zongrui Pei , Pengxiang Xu , Yonghong Tian

The recent trend of using Graphics Processing Units (GPU's) for high performance computations is driven by the high ratio of price performance for these units, complemented by their cost effectiveness. At first glance, computational fluid…

Computational Engineering, Finance, and Science · Computer Science 2018-02-13 Kiril S. Shterev

The exponential emergence of Field Programmable Gate Array (FPGA) has accelerated the research of hardware implementation of Deep Neural Network (DNN). Among all DNN processors, domain specific architectures, such as, Google's Tensor…

Hardware Architecture · Computer Science 2022-02-15 Rourab Paul , Sreetama Sarkar , Suman Sau , Koushik Chakraborty , Sanghamitra Roy , Amlan Chakrabarti