Related papers: Quantifying the Computational Advantage of Forward…

In many industries, including aerospace and defense, waveform analysis is commonly conducted to compute the resonance of physical objects, with the Finite Element Method (FEM) being the standard approach. The Finite Difference Method (FDM)…

This paper studies the numerical approximation of parametric time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Although many papers in the literature consider reduced…

Gradient temporal difference (Gradient TD) algorithms are a popular class of stochastic approximation (SA) algorithms used for policy evaluation in reinforcement learning. Here, we consider Gradient TD algorithms with an additional heavy…

Modal decomposition techniques are showing a fast growth in popularity for their good properties as data-driven tools. There are several modal decomposition techniques, yet Proper Orthogonal Decomposition (POD) and Dynamic Mode…

In the past few years considerable progress has been made in Monte Carlo simulations of first-order phase transitions and in the analysis of the resulting finite-size data. In this paper special emphasis will be placed on multicanonical…

Modern GPUs are equipped with large amounts of high-bandwidth memory, enabling them to support mini-batch sizes of up to tens of thousands of training samples. However, most existing optimizers struggle to perform effectively at such a…

We present a toy model for extending the Friedmann equations of relativistic cosmology using fractional derivatives. We do this by replacing the integer derivatives, in a few well-known cosmological results with fractional derivatives…

We present a method which extends Monte Carlo studies to situations that require a large dynamic range in particle number. The underlying idea is that, in order to calculate the collisional evolution of a system, some particle interactions…

Thul et al. (2020) called attention to problems that arise when chronometric experiments implementing specific factorial designs are analysed with the generalized additive mixed model (GAMM), using factor smooths to capture trial-to-trial…

The recovery of an unknown density matrix of large size requires huge computational resources. The recent Factored Gradient Descent (FGD) algorithm and its variants achieved state-of-the-art performance since they could mitigate the…

Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…

Forward uncertainty quantification (UQ) for partial differential equations is a many-query task that requires a significant number of model evaluations. The objective of this work is to mitigate the computational cost of UQ for a 3D-1D…

The period of a Morse oscillator and mathematical pendulum system are obtained, accurate to 100 significant digits, by forward period analysis (FPA). From these results, the long-term [0, 10^60] (time unit) solutions, which overlap from the…

Modern graphics processing units (GPUs) provide impressive computing resources, which can be accessed conveniently through the CUDA programming interface. We describe how GPUs can be used to considerably speed up molecular dynamics (MD)…

Quantifying degrees of fusion and separability between data groups in representation space is a fundamental problem in representation learning, particularly under domain shift. A meaningful metric should capture fusion-altering factors like…

The Lagrangian vortex method offers an alternative numerical approach for direct numerical simulation of turbulence. The fact that it uses the fast multipole method (FMM)--a hierarchical algorithm for N-body problems with highly scalable…

The fundamental concepts and challenges of orthogonal time frequency space (OTFS) modulation have been reviewed in Part I of this three-part tutorial. In this second part, we provide an overview of the state-of-the-art transceiver designs…

Since numerical computing with MATLAB offers a wide variety of advantages, such as easier developing and debugging of computational codes rather than lower-level languages, the popularity of this tool is significantly increased in the past…

This paper introduces Tempered Fractional Gradient Descent (TFGD), a novel optimization framework that synergizes fractional calculus with exponential tempering to enhance gradient-based learning. Traditional gradient descent methods often…

Many domains, from deep learning to finance, require compounding real numbers over long sequences, often leading to catastrophic numerical underflow or overflow. We introduce generalized orders of magnitude (GOOMs), a principled extension…