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.
On generalized moving least squares and diffuse derivatives.IMA Journal of Numerical Analysis, 32(3):983–1000
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A point-cloud discretization via GMLS local charts for high-order curvature and singular-integral approximation in the Hele-Shaw problem with surface tension, supported by consistency/stability analysis and numerical tests showing high-order spatial convergence.
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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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Geometric local parameterization for solving Hele-Shaw problems with surface tension
A point-cloud discretization via GMLS local charts for high-order curvature and singular-integral approximation in the Hele-Shaw problem with surface tension, supported by consistency/stability analysis and numerical tests showing high-order spatial convergence.