Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps

C Lu, Y Zhou, F Bao, J Chen, C Li… - Advances in Neural …, 2022‏ - proceedings.neurips.cc
Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite
their high-quality generation performance, DPMs still suffer from their slow sampling as they …

High-order implicit time integration scheme based on Padé expansions

C Song, S Eisenträger, X Zhang - Computer Methods in Applied Mechanics …, 2022‏ - Elsevier
A single-step high-order implicit time integration scheme for the solution of transient as well
as wave propagation problems is presented. It is constructed from the Padé expansion of the …

[HTML][HTML] Time-accurate and highly-stable explicit peer methods for stiff differential problems

D Conte, G Pagano, B Paternoster - Communications in Nonlinear Science …, 2023‏ - Elsevier
We derive a new class of parallelizable two-step peer methods for the numerical solution of
stiff systems of Ordinary Differential Equations (ODEs), inspired by a technique introduced in …

BAMPHI: Matrix-free and transpose-free action of linear combinations of φ-functions from exponential integrators

M Caliari, F Cassini, F Zivcovich - Journal of Computational and Applied …, 2023‏ - Elsevier
The time integration of stiff systems of Ordinary Differential Equations (ODEs), usually arising
from the spatial discretization of Partial Differential Equations (PDEs), constitutes a hot topic …

Develo** an artificial intelligence-based method for predicting the trajectory of surface drifting buoys using a hybrid multi-layer neural network model

M Song, W Hu, S Liu, S Chen, X Fu, J Zhang… - Journal of Marine …, 2024‏ - mdpi.com
Accurately predicting the long-term trajectory of a surface drifting buoy (SDB) is challenging.
This paper proposes a promising solution to the SDB trajectory prediction based on artificial …

Leveraging mixed precision in exponential time integration methods

CJ Balos, S Roberts, DJ Gardner - 2023 IEEE High …, 2023‏ - ieeexplore.ieee.org
The machine learning explosion has created a prominent trend in modern computer
hardware towards low precision floating-point operations. In response, there have been …

Exponential Runge-Kutta methods for delay equations in the sun-star abstract framework

A Ando, R Vermiglio - arxiv preprint arxiv:2410.00498, 2024‏ - arxiv.org
Exponential Runge-Kutta methods for semilinear ordinary differential equations can be
extended to abstract differential equations, defined on Banach spaces. Thanks to the sun …

A -mode approach for exponential integrators: actions of -functions of Kronecker sums

M Caliari, F Cassini, F Zivcovich - Calcolo, 2024‏ - Springer
We present a method for computing actions of the exponential-like φ-functions for a
Kronecker sum K of d arbitrary matrices A μ. It is based on the approximation of the integral …

On the stability of exponential integrators for non-diffusive equations

T Buvoli, ML Minion - Journal of Computational and Applied Mathematics, 2022‏ - Elsevier
Exponential integrators are a well-known class of time integration methods that have been
the subject of many studies and developments in the past two decades. Surprisingly, there …

[HTML][HTML] Exploratory Study of a Green Function Based Solver for Nonlinear Partial Differential Equations

P Solano-López, J Saavedra, R Molina - Algorithms, 2024‏ - mdpi.com
This work explores the numerical translation of the weak or integral solution of nonlinear
partial differential equations into a numerically efficient, time-evolving scheme. Specifically …