Shearlet Neural Operators improve accuracy over Fourier Neural Operators on anisotropic and shock-dominated PDEs by using directional multiscale shearlet atoms for better feature fidelity.
Fourier neural operator for parametric partial differential equations
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A meta-network learns to adapt Gaussian basis geometry across parametric PDE families, which a physics-informed least-squares corrector then refines for improved accuracy.
AE-ViT combines a convolutional autoencoder with a latent-space transformer and multi-stage parameter plus coordinate injection to deliver stable long-horizon predictions for parametric PDEs, cutting relative rollout error by roughly five times versus prior DL-ROMs and ViTs on advection-diffusion-re
NEON provides uncertainty-aware operator learning for composite Bayesian optimization in function spaces using a single network, achieving claimed SOTA with orders of magnitude fewer parameters than ensembles.
citing papers explorer
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Shearlet Neural Operators for Anisotropic-Shock-Dominated and Multi-scale parametric partial differential equations
Shearlet Neural Operators improve accuracy over Fourier Neural Operators on anisotropic and shock-dominated PDEs by using directional multiscale shearlet atoms for better feature fidelity.
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Meta-Learned Basis Adaptation for Parametric Linear PDEs
A meta-network learns to adapt Gaussian basis geometry across parametric PDE families, which a physics-informed least-squares corrector then refines for improved accuracy.
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AE-ViT: Stable Long-Horizon Parametric Partial Differential Equations Modeling
AE-ViT combines a convolutional autoencoder with a latent-space transformer and multi-stage parameter plus coordinate injection to deliver stable long-horizon predictions for parametric PDEs, cutting relative rollout error by roughly five times versus prior DL-ROMs and ViTs on advection-diffusion-re
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Composite Bayesian Optimization In Function Spaces Using NEON -- Neural Epistemic Operator Networks
NEON provides uncertainty-aware operator learning for composite Bayesian optimization in function spaces using a single network, achieving claimed SOTA with orders of magnitude fewer parameters than ensembles.