English
Related papers

Related papers: Relaxation Deferred Correction Methods and their A…

200 papers

Deep Equilibrium Models (DEQs) are an established framework for image restoration that learn a problem-adapted regularization by solving a fixed-point (i.e. equilibrium) problem. While flexible and expressive, DEQs are often hindered by…

Optimization and Control · Mathematics 2026-05-20 Antonin Clerc , Marien Renaud , Baudouin Denis De Seneville , Nicolas Papadakis

We present a robust computational framework for the numerical solution of a hyperbolic 6-equation single-velocity two-phase system. The system's main interest is that, when combined with instantaneous mechanical relaxation, it recovers the…

Numerical Analysis · Mathematics 2026-02-12 Giuseppe Orlando , Ward Haegeman , Marica Pelanti , Marc Massot

We present a novel enhanced cyclic coordinate descent (ECCD) framework for solving generalized linear models with elastic net constraints that reduces training time in comparison to existing state-of-the-art methods. We redesign the CD…

Machine Learning · Statistics 2025-10-24 Yixiao Wang , Zishan Shao , Ting Jiang , Aditya Devarakonda

This work proposes a systematic model reduction approach based on rank adaptive tensor recovery for partial differential equation (PDE) models with high-dimensional random parameters. Since the standard outputs of interest of these models…

Numerical Analysis · Mathematics 2019-02-15 Kejun Tang , Qifeng Liao

We show how to combine in a natural way (i.e. without any test nor switch) the conservative and non conservative formulations of an hyperbolic system that has a conservative form. This is inspired from two different class of schemes: the…

Numerical Analysis · Mathematics 2021-10-27 Rémi Abgrall

This paper proposes a hierarchical decentralized reference governor for constrained cascade systems. The reference governor (RG) approach is reformulated in terms of receding horizon strategy such that a locally receding horizon…

Optimization and Control · Mathematics 2020-12-21 Shahram Aghaei , Abolghasem Daeichian , Vicenç Puig

A delayed feedback reservoir (DFR) is a reservoir computing system well-suited for hardware implementations. However, achieving high accuracy in DFRs depends heavily on selecting appropriate hyperparameters. Conventionally, due to the…

Hardware Architecture · Computer Science 2025-04-18 Sosei Ikeda , Hiromitsu Awano , Takashi Sato

This article considers the application of Smoothness-Increasing Accuracy-Conserving (SIAC) filtering for the non-linear stabilization of discontinuous Galerkin (DG) discretizations via entropy correction. Upon constructing discrete filters…

Numerical Analysis · Mathematics 2023-12-11 Matthew J. Picklo , Ayaboe K. Edoh

We consider new implicit-explicit (IMEX) Runge-Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability-preserving (SSP) scheme, and the implicit part is…

Numerical Analysis · Mathematics 2010-09-16 L. Pareschi , G. Russo

Reinforcement learning (RL) is highly suitable for devising control strategies in the context of dynamical systems. A prominent instance of such a dynamical system is the system of equations governing fluid dynamics. Recent research results…

Machine Learning · Computer Science 2022-11-21 Marius Kurz , Philipp Offenhäuser , Dominic Viola , Oleksandr Shcherbakov , Michael Resch , Andrea Beck

In this work, we further investigate the application of the well-known Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for numerically solving initial-value…

Numerical Analysis · Mathematics 2025-02-25 Imre Fekete , Lajos Lóczi

Partial differential equation (PDE)-governed inverse problems are fundamental across various scientific and engineering applications; yet they face significant challenges due to nonlinearity, ill-posedness, and sensitivity to noise. Here,…

Machine Learning · Computer Science 2026-03-03 Siming Shan , Min Zhu , Youzuo Lin , Lu Lu

We develop two new sets of stable, rank-adaptive Dynamically Orthogonal Runge-Kutta (DORK) schemes that capture the high-order curvature of the nonlinear low-rank manifold. The DORK schemes asymptotically approximate the truncated singular…

Numerical Analysis · Mathematics 2023-08-08 Aaron Charous , Pierre F. J. Lermusiaux

In the case of hyperbolic conservation laws, high-order methods, such as the classical DG method, experience the phenomenon of unwanted high-frequency oscillations in the vicinity of a shock. Shock-capturing methods such as artificial…

Numerical Analysis · Mathematics 2025-11-04 Sai Shruthi Srinivasan , Siva Nadarajah

The Scheduled Relaxation Jacobi (SRJ) method is a linear solver algorithm which greatly improves the convergence of the Jacobi iteration through the use of judiciously chosen relaxation factors (an SRJ scheme) which attenuate the solution…

Numerical Analysis · Mathematics 2021-12-14 Mohammad Shafaet Islam , Qiqi Wang

Recently, relaxation methods have been developed to guarantee the preservation of a single global functional of the solution of an ordinary differential equation. Here, we generalize this approach to guarantee local entropy inequalities for…

Numerical Analysis · Mathematics 2020-07-14 Hendrik Ranocha , Lisandro Dalcin , Matteo Parsani

In this paper a new semi-implicit relaxation scheme for the simulation of multi-scale hyperbolic conservation laws based on a Jin-Xin relaxation approach is presented. It is based on the splitting of the flux function into two or more…

Numerical Analysis · Mathematics 2025-02-24 Andrea Thomann

Mixed-precision algorithms combine low- and high-precision computations in order to benefit from the performance gains of reduced-precision without sacrificing accuracy. In this work, we design mixed-precision Runge-Kutta-Chebyshev (RKC)…

Numerical Analysis · Mathematics 2023-01-10 Matteo Croci , Giacomo Rosilho de Souza

Benders decomposition with adaptive oracles was proposed to solve large-scale optimisation problems with a column bounded block-diagonal structure, where subproblems differ on the right-hand side and cost coefficients. Adaptive Benders…

Optimization and Control · Mathematics 2022-09-09 Hongyu Zhang , Nicolò Mazzi , Ken McKinnon , Rodrigo Garcia Nava , Asgeir Tomasgard

This paper develops the high-order entropy stable (ES) finite difference schemes for multi-dimensional compressible Euler equations with the van der Waals equation of state (EOS) on adaptive moving meshes. Semi-discrete schemes are first…

Numerical Analysis · Mathematics 2024-07-09 Shangting Li , Huazhong Tang