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Here we introduce data driven discretization , a method for automatically learning effective long-wavelength dynamics from actual solutions to the known underlying equations. We use a neural network to learn a discretization for the true spatial derivatives of partial differential equations. We demo…
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Here we introduce data driven discretization , a method for automatically learning effective long-wavelength dynamics from actual solutions to the known underlying equations. We use a neural network to learn a discretization for the true spatial derivatives of partial differential equations. We demonstrate that this approach is remarkably accurate, allowing us to integrate in time a collection of nonlinear equations in one spatial dimension at resolutions 4-8x coarser than is possible with standard finite difference methods.