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.
Multi-grid tensorized Fourier neural operator for high-resolution PDEs.arXiv preprint arXiv:2310.00120, 2023
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
representative citing papers
HO-FNO extends standard FNO with n-linear spectral mixing and shows improved accuracy on nonlinear PDE benchmarks, sometimes with a single layer beating deeper FNO models.
Isotropic Fourier Neural Operators enforce spatial symmetries in Fourier layers, improving PDE-solving performance while reducing parameters by up to 16x in 2D and 96x in 3D.
Wavelet Flow Matching emulates multi-scale PDE-governed systems by transporting velocities directly in a hierarchical wavelet representation via U-Net, yielding improved long-horizon stability and spectral accuracy on fluid benchmarks.
FEDONet augments DeepONet with Fourier-embedded trunk networks using random Fourier features, yielding lower L2 reconstruction errors than standard DeepONet on Burgers', 2D Poisson, Eikonal, Allen-Cahn, and Kuramoto-Sivashinsky equations across dataset sizes and noise levels.
citing papers explorer
-
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.
-
Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs
HO-FNO extends standard FNO with n-linear spectral mixing and shows improved accuracy on nonlinear PDE benchmarks, sometimes with a single layer beating deeper FNO models.
-
Isotropic Fourier Neural Operators
Isotropic Fourier Neural Operators enforce spatial symmetries in Fourier layers, improving PDE-solving performance while reducing parameters by up to 16x in 2D and 96x in 3D.
-
Wavelet Flow Matching for Multi-Scale Physics Emulation
Wavelet Flow Matching emulates multi-scale PDE-governed systems by transporting velocities directly in a hierarchical wavelet representation via U-Net, yielding improved long-horizon stability and spectral accuracy on fluid benchmarks.
-
FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learning
FEDONet augments DeepONet with Fourier-embedded trunk networks using random Fourier features, yielding lower L2 reconstruction errors than standard DeepONet on Burgers', 2D Poisson, Eikonal, Allen-Cahn, and Kuramoto-Sivashinsky equations across dataset sizes and noise levels.
- Performance-Carbon Trade-Offs across Architectural Biases in Shear Flow Forecasting