MEEC equips point clouds with a discrete exterior calculus that satisfies exact conservation and is differentiable in point positions, allowing a single trained kernel to produce compatible physics on unseen geometries and parameters.
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DeepONet learns nonlinear operators for differential equations via branch and trunk sub-networks, achieving high-order error convergence on small datasets.
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A meshfree exterior calculus for generalizable and data-efficient learning of physics from point clouds
MEEC equips point clouds with a discrete exterior calculus that satisfies exact conservation and is differentiable in point positions, allowing a single trained kernel to produce compatible physics on unseen geometries and parameters.
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DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
DeepONet learns nonlinear operators for differential equations via branch and trunk sub-networks, achieving high-order error convergence on small datasets.