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 digital twins via conditional neural whitney forms
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The authors combine H(div)-L2 subspaces from Raviart-Thomas and dgP0 elements with a transformer and GP regression on fluxes to create real-time structure-preserving surrogates with closed-form posterior uncertainty for Dirichlet-to-Neumann maps.
Cellular Sheaf Neural Operators use cell complexes, learned restriction maps, and structure-aware message passing to create discretization-aware neural surrogates that preserve constraints in multiphysics PDEs such as MHD.
Neural-NF learns a mapping from intrinsic Laplacian features to local PDE coefficients whose solution yields a collision-free, monotonically descending navigation function with global goal minimum by construction, achieving up to 5x better zero-shot transfer than direct value-function predictors.
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.
citing papers explorer
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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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Structure-Preserving Neural Surrogates with Tractable Uncertainty Quantification
The authors combine H(div)-L2 subspaces from Raviart-Thomas and dgP0 elements with a transformer and GP regression on fluxes to create real-time structure-preserving surrogates with closed-form posterior uncertainty for Dirichlet-to-Neumann maps.
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Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEs
Cellular Sheaf Neural Operators use cell complexes, learned restriction maps, and structure-aware message passing to create discretization-aware neural surrogates that preserve constraints in multiphysics PDEs such as MHD.
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Neural Navigation Functions for Zero-Shot Generalizable Motion Planning
Neural-NF learns a mapping from intrinsic Laplacian features to local PDE coefficients whose solution yields a collision-free, monotonically descending navigation function with global goal minimum by construction, achieving up to 5x better zero-shot transfer than direct value-function predictors.
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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.