Learning proper orthogonal decomposition of complex dynamics using heavy-ball neural ODEs

DOI10.1007/s10915-023-02176-8zbMath1515.65255arXiv2202.12373OpenAlexW4362560979MaRDI QIDQ6101554

Akil C. Narayan, Bao Wang, Justin Baker, Elena Cherkaev

Publication date: 20 June 2023

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.12373

zbMATH Keywords

momentumreduced-order modelingdeep learningneural ODE

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical problems in dynamical systems (65P99)

Cites Work

• Unnamed Item
• A family of embedded Runge-Kutta formulae
• Neural network closures for nonlinear model order reduction
• How does momentum benefit deep neural networks architecture design? A few case studies
• An artificial neural network framework for reduced order modeling of transient flows
• Machine learning closures for model order reduction of thermal fluids
• A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
• PROPER ORTHOGONAL DECOMPOSITION AND ITS APPLICATIONS—PART I: THEORY
• Dynamic mode decomposition of numerical and experimental data
• Interpolatory Model Reduction of Large-Scale Dynamical Systems
• Absolute stability of global pattern formation and parallel memory storage by competitive neural networks
• Adaptive Semidiscrete Central-Upwind Schemes for Nonconvex Hyperbolic Conservation Laws
• On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
• Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
• On Flame Propagation Under Conditions of Stoichiometry
• A dynamic subgrid-scale eddy viscosity model
• A Survey of Model Reduction by Balanced Truncation and Some New Results
• DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research
• Data-driven correction reduced order models for the quasi-geostrophic equations: a numerical investigation
• Scheduled Restart Momentum for Accelerated Stochastic Gradient Descent
• A dynamic global-coefficient subgrid-scale eddy-viscosity model for large-eddy simulation in complex geometries
• Construction of reduced-order models for fluid flows using deep feedforward neural networks
• Nonlinear mode decomposition with convolutional neural networks for fluid dynamics
• Some methods of speeding up the convergence of iteration methods
• Approximation of Large-Scale Dynamical Systems

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