Comparison of neural closure models for discretised PDEs

DOI10.1016/j.camwa.2023.04.030arXiv2210.14675OpenAlexW4376958741MaRDI QIDQ6104834

Daan Crommelin, Barry Koren, Vlado Menkovski, B. Sanderse, Hugo Melchers

Publication date: 28 June 2023

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2210.14675

zbMATH Keywords

neural networksordinary differential equationspartial differential equationsmultiscale modellingclosure modelneural ODE

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Fluid mechanics (76-XX)

Related Items (1)

Neural integration for constitutive equations using small data

Cites Work

• Unnamed Item
• Unnamed Item
• Runge-Kutta pairs of order \(5(4)\) satisfying only the first column simplifying assumption
• Exponential time differencing for stiff systems
• Higher-order additive Runge-Kutta schemes for ordinary differential equations
• Neural network closures for nonlinear model order reduction
• DPM: a deep learning PDE augmentation method with application to large-eddy simulation
• Stable \textit{a posteriori} LES of 2D turbulence using convolutional neural networks: backscattering analysis and generalization to higher \(Re\) via transfer learning
• Collocation based training of neural ordinary differential equations
• Solving Ordinary Differential Equations I
• Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
• Data-Driven Discovery of Closure Models
• Learned turbulence modelling with differentiable fluid solvers: physics-based loss functions and optimisation horizons
• LYAPUNOV EXPONENTS OF THE KURAMOTO–SIVASHINSKY PDE
• Fourth-Order Time-Stepping for Stiff PDEs
• Large Eddy Simulation for Incompressible Flows
• Toward neural-network-based large eddy simulation: application to turbulent channel flow

This page was built for publication: Comparison of neural closure models for discretised PDEs