Neural Green's Operators approximate the Green's function and its parametric dependence for linear PDEs via neural networks, preserving linearity and enabling use in time-stepping, nonlinear solvers, and preconditioning.
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
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Neural Green's Operators for Parametric Partial Differential Equations
Neural Green's Operators approximate the Green's function and its parametric dependence for linear PDEs via neural networks, preserving linearity and enabling use in time-stepping, nonlinear solvers, and preconditioning.