Asymptotic-preserving neural networks for hyperbolic systems with diffusive scaling

DOI10.1007/978-3-031-29875-2_2zbMATH Open1548.65246MaRDI QIDQ6613475

Giulia Bertaglia

Publication date: 2 October 2024

zbMATH Keywords

diffusion limitphysics-informed neural networksasymptotic-preserving methodsmultiscale hyperbolic systemsdiscrete-velocity kinetic models

Mathematics Subject Classification ID

Epidemiology (92D30) Computational learning theory (68Q32) Artificial neural networks and deep learning (68T07) Numerical optimization and variational techniques (65K10) Asymptotic behavior of solutions to PDEs (35B40) Population dynamics (general) (92D25) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) First-order hyperbolic equations (35L02) PDE constrained optimization (numerical aspects) (49M41)

Cites Work

• Unnamed Item
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• Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings
• A generalization of the Kermack-McKendrick deterministic epidemic model
• Diffusive limit for finite velocity Boltzmann kinetic models
• A contribution to the mathematical theory of epidemics.
• Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties
• An SIR-like kinetic model tracking individuals' viral load
• Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty
• Modelling lockdown measures in epidemic outbreaks using selective socio-economic containment with uncertainty
• Uncertainty quantification of viscoelastic parameters in arterial hemodynamics with the a-FSI blood flow model
• Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation
• Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
• Diffusion-reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study
• Propagation of epidemics along lines with fast diffusion
• Numerical solution and bifurcation analysis of nonlinear partial differential equations with extreme learning machines
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• The mathematics of infectious diseases
• The diffusive limit for Carleman-type kinetic models
• Particle, kinetic, and hydrodynamic models of swarming
• Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
• On the Basic Reproduction Number of Reaction-Diffusion Epidemic Models
• Numerical methods for kinetic equations
• The Dawning of a New Era in Applied Mathematics
• Hyperbolic models for the spread of epidemics on networks: kinetic description and numerical methods
• Hyperbolic compartmental models for epidemic spread on networks with uncertain data: Application to the emergence of COVID-19 in Italy
• Kinetic Modelling of Epidemic Dynamics: Social Contacts, Control with Uncertain Data, and Multiscale Spatial Dynamics
• A multiscale model of virus pandemic: Heterogeneous interactive entities in a globally connected world
• Implicit-Explicit Multistep Methods for Hyperbolic Systems With Multiscale Relaxation
• Modeling and simulating the spatial spread of an epidemic through multiscale kinetic transport equations
• Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
• Deep Learning: An Introduction for Applied Mathematicians
• A Unified IMEX Runge--Kutta Approach for Hyperbolic Systems with Multiscale Relaxation
• Asymptotic-preserving schemes for multiscale physical problems
• Delay differential equations for the spatially resolved simulation of epidemics with specific application to COVID‐19
• Asymptotic-Preserving Neural Networks for multiscale hyperbolic models of epidemic spread

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