☆ 4.7 Article

Fast and scalable computation of shape-morphing nonlinear solutions with application to evolutional neural networks

JOURNAL OF COMPUTATIONAL PHYSICS (2024)

相关参考文献

注意：仅列出部分参考文献，下载原文获取全部文献信息。

Article Mathematics, Applied

EVOLUTION OF NONLINEAR REDUCED-ORDER SOLUTIONS FOR PDEs WITH CONSERVED QUANTITIES

William Anderson et al.

Summary: Reduced order nonlinear solutions (RONS) is a unified framework for deriving reduced-order models that depend nonlinearly on a set of time-dependent parameters. By minimizing the discrepancy between reduced dynamics and full PDE dynamics, explicit ordinary differential equations on the tangent bundle of the manifold can be obtained.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2022)

添加到收藏夹

Article Mathematics, Applied

COMPUTING SENSITIVITIES IN EVOLUTIONARY SYSTEMS: A REAL-TIME REDUCED ORDER MODELING STRATEGY

Michael Donello et al.

Summary: We propose a model-driven low-rank approximation method for computing sensitivities in evolutionary systems. This approach allows for accurate and tractable computation of sensitivities with respect to a large number of parameters by extracting correlations between different sensitivities.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2022)

添加到收藏夹

Article Engineering, Mechanical

Shape-morphing reduced-order models for nonlinear Schrodinger equations

William Anderson et al.

Summary: This study investigates the reduced-order modeling of nonlinear dispersive waves described by nonlinear Schrodinger (NLS) equations. Two nonlinear reduced-order modeling methods are compared: the reduced Lagrangian approach based on the variational formulation of NLS, and the recently developed method of reduced-order nonlinear solutions (RONS). The surprising result is that, despite their apparent differences, these two methods can be obtained from the real and imaginary parts of a single complex-valued master equation. The study also reveals that the reduced Lagrangian method fails to predict the correct group velocity of waves in the NLS equation, while RONS accurately predicts the correct group velocity.

NONLINEAR DYNAMICS (2022)

添加到收藏夹

Article Physics, Fluids & Plasmas

Casimir preserving spectrum of two-dimensional turbulence

Paolo Cifani et al.

Summary: This study presents predictions of the energy spectrum of forced two-dimensional turbulence and constructs a finite-mode approximation of the Navier-Stokes equations. It provides robust evidence for the existence of double energy cascade.

PHYSICAL REVIEW FLUIDS (2022)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks

Suchuan Dong et al.

Summary: The proposed method effectively enforces periodic boundary conditions for solving differential equations with deep neural networks by composing DNN-represented functions with independent periodic functions. Different levels of periodicity requirements can be satisfied through imposing periodicity on functions and their derivatives.

JOURNAL OF COMPUTATIONAL PHYSICS (2021)

添加到收藏夹

Article Physics, Fluids & Plasmas

Evolutional deep neural network

Yifan Du et al.

Summary: The concept of an Evolutional Deep Neural Network (EDNN) is introduced for solving partial differential equations (PDE). The network parameters are trained to represent the initial state of the system and are dynamically updated to accurately predict the system's evolution. This framework treats network parameters as functions with respect to appropriate coordinates and ensures precise satisfying of hard constraints.

PHYSICAL REVIEW E (2021)

添加到收藏夹

Article Biochemical Research Methods

Systems biology informed deep learning for inferring parameters and hidden dynamics

Alireza Yazdani et al.

PLOS COMPUTATIONAL BIOLOGY (2020)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Conservative model reduction for finite-volume models

Kevin Carlberg et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2018)

添加到收藏夹

Article Physics, Multidisciplinary

Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach

Jaideep Pathak et al.

PHYSICAL REVIEW LETTERS (2018)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

DGM: A deep learning algorithm for solving partial differential equations

Justin Sirignano et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2018)

添加到收藏夹

Article Multidisciplinary Sciences

Solving high-dimensional partial differential equations using deep learning

Jiequn Han et al.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2018)

添加到收藏夹

Article Mathematics, Applied

Reduced-order description of transient instabilities and computation of finite-time Lyapunov exponents

Hessam Babaee et al.

CHAOS (2017)

添加到收藏夹

Article Mechanics

An adjoint-based approach for finding invariant solutions of Navier-Stokes equations

M. Farazmand

JOURNAL OF FLUID MECHANICS (2016)

添加到收藏夹

Article Multidisciplinary Sciences

A minimization principle for the description of modes associated with finite-time instabilities

H. Babaee et al.

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2016)

添加到收藏夹

Article Mathematics, Applied

SYMPLECTIC MODEL REDUCTION OF HAMILTONIAN SYSTEMS

Liqian Peng et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2016)

添加到收藏夹

Article Physics, Fluids & Plasmas

Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems

Mohammad Farazmand et al.

PHYSICAL REVIEW E (2016)

添加到收藏夹

Article Physics, Multidisciplinary

Anomalous wave as a result of the collision of two wave groups on the sea surface

V. P. Ruban

JETP LETTERS (2015)

添加到收藏夹

Article Physics, Multidisciplinary

Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation

V. P. Ruban

JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS (2015)

添加到收藏夹

Article Physics, Fluids & Plasmas

Unsteady evolution of localized unidirectional deep-water wave groups

Will Cousins et al.

PHYSICAL REVIEW E (2015)

添加到收藏夹

Review Mathematics, Applied

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

Peter Benner et al.

SIAM REVIEW (2015)

添加到收藏夹

Article Multidisciplinary Sciences

The nonlinear evolution and approximate scaling of directionally spread wave groups on deep water

Thomas A. A. Adcock et al.

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2012)

添加到收藏夹

Article Mathematics, Applied

A REGULARIZATION PARAMETER FOR NONSMOOTH TIKHONOV REGULARIZATION

Kazufumi Ito et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2011)

添加到收藏夹

Article Mathematics, Applied

On the State Space Geometry of the Kuramoto-Sivashinsky Flow in a Periodic Domain

Predrag Cvitanovic et al.

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2010)

添加到收藏夹

Article Multidisciplinary Sciences

Focusing of unidirectional wave groups on deep water: an approximate nonlinear Schrodinger equation-based model

T. A. A. Adcock et al.

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2009)

添加到收藏夹

Article Mathematics, Applied

The quasi-optimality criterion for classical inverse problems

Frank Bauer et al.

INVERSE PROBLEMS (2008)

添加到收藏夹

Article Mathematics, Applied

Regularization independent of the noise level: an analysis of quasi-optimality

Frank Bauer et al.

INVERSE PROBLEMS (2008)

添加到收藏夹

Review Physics, Multidisciplinary

Numerical methods for Hamiltonian PDEs

Thomas J. Bridges et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL (2006)

添加到收藏夹

Review Physics, Multidisciplinary

Geometric integrators for ODEs

Robert I. McLachlan et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL (2006)

添加到收藏夹

Article Mathematics, Applied

Tikhonov regularization and the L-curve for large discrete ill-posed problems

D Calvetti et al.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2000)

添加到收藏夹

© Peeref 2019-2024. All rights reserved.