An immersed interface neural network for elliptic interface problems

Artificial neural networks and deep learning (68T07) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Cites Work

Immersed finite element method
Weak adversarial networks for high-dimensional partial differential equations
A simple implementation of the immersed interface methods for Stokes flows with singular forces
New Cartesian grid methods for interface problems using the finite element formulation
The blob projection method for immersed boundary problems
A vortex/impulse method for immersed boundary motion in high Reynolds number flows
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DGM: a deep learning algorithm for solving partial differential equations
PPINN: parareal physics-informed neural network for time-dependent PDEs
INN: interfaced neural networks as an accessible meshless approach for solving interface PDE problems
nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications
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A mesh-free method using piecewise deep neural network for elliptic interface problems
A mesh-free method for interface problems using the deep learning approach
Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Modeling biofilm processes using the immersed boundary method
Improved deep neural networks with domain decomposition in solving partial differential equations
Immersed virtual element methods for elliptic interface problems in two dimensions
A discontinuity capturing shallow neural network for elliptic interface problems
The immersed boundary method
An Algorithm for Least-Squares Estimation of Nonlinear Parameters
The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
A Fast Iterative Algorithm for Elliptic Interface Problems
New Formulations for Interface Problems in Polar Coordinates
Deep Unfitted Nitsche Method for Elliptic Interface Problems
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fPINNs: Fractional Physics-Informed Neural Networks
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The Immersed Interface Method
Accurate projection methods for the incompressible Navier-Stokes equations
A cusp-capturing PINN for elliptic interface problems
An Efficient Neural-Network and Finite-Difference Hybrid Method for Elliptic Interface Problems with Applications

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