Learning the flux and diffusion function for degenerate convection-diffusion equations using different types of observations

DOI10.1007/S10543-024-01018-9MaRDI QIDQ6492247

Steinar Evje, Qing Li

Publication date: 24 April 2024

Published in: BIT (Search for Journal in Brave)

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Inverse problems for PDEs (35R30) Hyperbolic conservation laws (35L65) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Constraint-aware neural networks for Riemann problems
• Splitting methods for partial differential equations with rough solutions. Analysis and Matlab programs
• A new TVD flux-limiter method for solving nonlinear hyperbolic equations
• Entropy solutions for nonlinear degenerate problems
• Weighted essentially non-oscillatory schemes
• Convergence of a finite volume scheme for nonlinear degenerate parabolic equations
• Viscous splitting approximation of mixed hyperbolic-parabolic convection-diffusion equations
• Convergence of finite volume schemes for a degenerate convection-diffusion equation arising in flows in porous media
• New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
• Fast and optimal WENO schemes for degenerate parabolic conservation laws
• Physics-informed graph neural Galerkin networks: a unified framework for solving PDE-governed forward and inverse problems
• A data-driven physics-informed finite-volume scheme for nonclassical undercompressive shocks
• PhyGeoNet: physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain
• PDE-Net 2.0: learning PDEs from data with a numeric-symbolic hybrid deep network
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Numerical identification of constitutive functions in scalar nonlinear convection-diffusion equations with application to batch sedimentation
• An artificial neural network as a troubled-cell indicator
• A posteriorierror estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations
• On the convergence rate of finite difference methods for degenerate convection-diffusion equations in several space dimensions
• Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data
• 𝐿¹ error estimates for difference approximations of degenerate convection-diffusion equations
• Automated reverse engineering of nonlinear dynamical systems
• Algorithm 778: L-BFGS-B
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Convergence Results for the Flux Identification in a Scalar Conservation Law
• Parameter identification for a model of chromatographic column
• A Hölder continuous ODE related to traffic flow
• Monotone Difference Approximations Of BV Solutions To Degenerate Convection-Diffusion Equations
• A multilevel Monte Carlo finite difference method for random scalar degenerate convection–diffusion equations
• Learning partial differential equations via data discovery and sparse optimization
• Diffusive BGK approximations for nonlinear multidimensional parabolic equations
• An Error Estimate for Viscous Approximate Solutions of Degenerate Parabolic Equations
• SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics
• Data-driven discovery of coordinates and governing equations
• Shock Waves on the Highway
• On an inverse problem for scalar conservation laws
• Inverse problems for scalar conservation laws
• On kinematic waves II. A theory of traffic flow on long crowded roads
• Generalized solutions of degenerate second-order quasilinear parabolic and elliptic equations
• Learning the nonlinear flux function of a hidden scalar conservation law from data
• Identification of the flux function of nonlinear conservation laws with variable parameters

This page was built for publication: Learning the flux and diffusion function for degenerate convection-diffusion equations using different types of observations