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.
Data-driven whitney forms for structure-preserving control volume analysis.Journal of Computational Physics, 496:112520
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MuRFiV combines multi-resolution deep learning with finite-volume inductive bias to deliver stable, accurate long-term autoregressive predictions of spatiotemporal PDE dynamics, outperforming standard neural baselines.
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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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A Multi-Resolution Finite-Volume Inspired Deep Learning Framework for Spatiotemporal Dynamics Prediction
MuRFiV combines multi-resolution deep learning with finite-volume inductive bias to deliver stable, accurate long-term autoregressive predictions of spatiotemporal PDE dynamics, outperforming standard neural baselines.