GAIA introduces a geometry-adaptive integral autoencoder that unifies forward, boundary-value, and inverse PDE operator learning on arbitrary domains via geometry tokens and cross-attention.
Improved operator learning by orthogonal attention
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CATO learns a continuous latent chart for efficient axial attention on PDE meshes and adds derivative-aware supervision to improve accuracy and reduce oversmoothing on general geometries.
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GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems
GAIA introduces a geometry-adaptive integral autoencoder that unifies forward, boundary-value, and inverse PDE operator learning on arbitrary domains via geometry tokens and cross-attention.
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CATO: Charted Attention for Neural PDE Operators
CATO learns a continuous latent chart for efficient axial attention on PDE meshes and adds derivative-aware supervision to improve accuracy and reduce oversmoothing on general geometries.