GMC-PINNs: a new general Monte Carlo PINNs method for solving fractional partial differential equations on irregular domains (Q6588348)

scientific article; zbMATH DE number 7897594

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English	GMC-PINNs: a new general Monte Carlo PINNs method for solving fractional partial differential equations on irregular domains	scientific article; zbMATH DE number 7897594

Statements

instance of

scholarly article

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title

GMC-PINNs: a new general Monte Carlo PINNs method for solving fractional partial differential equations on irregular domains (English)

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author

Shupeng Wang

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George Em Karniadakis

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published in

Computer Methods in Applied Mechanics and Engineering

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publication date

15 August 2024

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zbMATH Keywords

PINNs

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Monte Carlo method

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fractional PDEs

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irregular domain

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Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms

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A contour method for time-fractional PDEs and an application to fractional viscoelastic beam equations

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The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator

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A second-order accurate numerical approximation for the fractional diffusion equation

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Galerkin-Legendre spectral schemes for nonlinear space fractional Schrödinger equation

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Unconditionally convergent numerical method for the two-dimensional nonlinear time fractional diffusion-wave equation

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Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications

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A time-space spectral method for the time-space fractional Fokker-Planck equation and its inverse problem

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Improved uniform error bounds of exponential wave integrator method for long-time dynamics of the space fractional Klein-Gordon equation with weak nonlinearity

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Differential quadrature and longterm integration

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Reproducing kernel particle method for two-dimensional time-space fractional diffusion equations in irregular domains

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A semi-alternating direction method for a 2-D fractional Fitzhugh-Nagumo monodomain model on an approximate irregular domain

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Space-fractional advection-dispersion equations by the Kansa method

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A unified Petrov-Galerkin spectral method for fractional PDEs

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A novel unstructured mesh finite element method for solving the time-space fractional wave equation on a two-dimensional irregular convex domain

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A class of RBFs-based DQ methods for the space-fractional diffusion equations on 3D irregular domains

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Efficient Multistep Methods for Tempered Fractional Calculus: Algorithms and Simulations

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Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations

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An efficient second order stabilized scheme for the two dimensional time fractional Allen-Cahn equation

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A fast Euler-Maruyama method for Riemann-Liouville stochastic fractional nonlinear differential equations

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Two fast numerical methods for a generalized Oldroyd-B fluid model

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Monte Carlo method for fractional-order differentiation

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Monte Carlo method for fractional-order differentiation extended to higher orders

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Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

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Physics-informed neural networks for high-speed flows

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NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations

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fPINNs: Fractional Physics-Informed Neural Networks

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Monte Carlo fPINNs: deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations

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Residual-based attention in physics-informed neural networks

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An unstructured mesh finite difference/finite element method for the three-dimensional time-space fractional Bloch-Torrey equations on irregular domains

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.CMA.2024.117189

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Sitelinks

Mathematics(1 entry)

mardi Publication:6588348