Fast and scalable computation of shape-morphing nonlinear solutions with application to evolutional neural networks
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Publication:6187618
DOI10.1016/j.jcp.2023.112649arXiv2207.13828OpenAlexW4388907182MaRDI QIDQ6187618
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Publication date: 31 January 2024
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2207.13828
Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Partial differential equations of mathematical physics and other areas of application (35Qxx) Numerical analysis in abstract spaces (65Jxx)
Cites Work
- Unnamed Item
- Fundamental limitations of ad hoc linear and quadratic multi-level regression models for physical systems
- High order accurate vortex methods with explicit velocity kernels
- The Kuramoto-Sivashinsky equation: a bridge between PDE's and dynamical systems
- A family of embedded Runge-Kutta formulae
- Chaotic behavior of Newton's method
- Tikhonov regularization and the L-curve for large discrete ill-posed problems
- DGM: a deep learning algorithm for solving partial differential equations
- A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks
- Conservative model reduction for finite-volume models
- A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
- An adjoint-based approach for finding invariant solutions of Navier–Stokes equations
- Model Reduction for Flow Analysis and Control
- A Regularization Parameter for Nonsmooth Tikhonov Regularization
- The MATLAB ODE Suite
- Back in the Saddle Again: A Computer Assisted Study of the Kuramoto–Sivashinsky Equation
- Symplectic Model Reduction of Hamiltonian Systems
- The quasi-optimality criterion for classical inverse problems
- Regularization independent of the noise level: an analysis of quasi-optimality
- Focusing of unidirectional wave groups on deep water: an approximate nonlinear Schrödinger equation-based model
- Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
- Reduced-order description of transient instabilities and computation of finite-time Lyapunov exponents
- Tikhonov Regularization and Total Least Squares
- Computational Methods for Inverse Problems
- Solving high-dimensional partial differential equations using deep learning
- Computing Sensitivities in Evolutionary Systems: A Real-Time Reduced Order Modeling Strategy
- Evolution of Nonlinear Reduced-Order Solutions for PDEs with Conserved Quantities
- Numerical Linear Algebra and Optimization
- The nonlinear evolution and approximate scaling of directionally spread wave groups on deep water
- A minimization principle for the description of modes associated with finite-time instabilities
- Numerical methods for Hamiltonian PDEs
- Use of the regularization method in non-linear problems
- Spectral/hp Element Methods for Computational Fluid Dynamics
- On the State Space Geometry of the Kuramoto–Sivashinsky Flow in a Periodic Domain
- Approximation by superpositions of a sigmoidal function
- The \(N\)-vortex problem. Analytical techniques