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.
Structure-preserving learning improves geometry generalization in neural pdes
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A hybrid transformer-FEM integrator provides provable discrete energy preservation and gradient bounds for stable autoregressive forecasting of chaotic systems, with 65x fewer parameters and 9000x speedup in a fusion surrogate trained on 12 simulations.
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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 Hybridizable Neural Time Integrator for Stable Autoregressive Forecasting
A hybrid transformer-FEM integrator provides provable discrete energy preservation and gradient bounds for stable autoregressive forecasting of chaotic systems, with 65x fewer parameters and 9000x speedup in a fusion surrogate trained on 12 simulations.