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.
Wang , author J
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Spatio-Temporal MeanFlow adapts MeanFlow to PDEs by replacing the generative velocity field with the physical operator and extending the integral constraint to the spatio-temporal domain, yielding a unified solver for time-dependent and stationary equations with improved accuracy and generalization.
AI models of viscous fingering exhibit hallucinations from spectral bias; DeepFingers combines FNO and DeepONet with time-contrast conditioning to predict accurate finger dynamics while preserving mixing metrics.
WaveLiT combines wavelet tokenization, linear attention, and multiscale pyramids to produce parameter-efficient neural PDE solvers that match much larger models on TheWell benchmarks.
Neural operators progressively forget domain geometry with depth due to Markovian layers and global mixing; a geometry memory injection mechanism mitigates this forgetting.
Conditional neural fields combined with LSTM networks predict aircraft ditching loads accurately across heterogeneous spatial discretizations using fewer parameters than convolutional autoencoders.
A systematic review of Kolmogorov-Arnold Networks that maps their relation to Kolmogorov superposition theory, MLPs, and kernels, examines basis-function design choices, summarizes performance advances, and supplies a practitioner's selection guide plus open challenges.
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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.