arXiv AI
Jun 29
Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs
arXiv:2606. 28122v1 Announce Type: cross Abstract: Neural operators provide deep neural networks for learning mappings between function spaces.
Limits of Resolution Equivariance in Fourier Neural Operators
arXiv:2606. 00677v1 Announce Type: new Abstract: Fourier Neural Operators are often assumed to generalize across spatial resolutions, enabling training on a coarse grid and deployment on a finer grid.
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arXiv Machine Learning
Jun 2
Is Zero-Shot Super-Resolution Possible in Operator Learning?
arXiv:2606. 00296v1 Announce Type: cross Abstract: Neural operators are often reported to exhibit zero-shot super-resolution, a phenomenon in which a model trained on coarse grids produces accurate predictions on finer testing grids without additional retraining.
arXiv Machine Learning
Jun 2
Revisiting Neural Processes via Fourier Transform and Volterra Series
arXiv:2606. 01172v1 Announce Type: new Abstract: Modeling unknown latent functions from finite, irregularly sampled measurements is a recurring challenge across science and engineering.
arXiv Machine Learning
Sep 1
Selection, Representation, and Execution in Sparse Fourier Neural Operators
arXiv:2608.30070v1 Announce Type: new Abstract: Sparse representations are often expected to make models smaller and also reduce inference cost. For Fourier Neural Operators (FNOs), these objectives...
arXiv Machine Learning
Aug 18
Iterative Refinement Diffusion for Super-Resolved Data Assimilation of Multiscale Physical Systems
arXiv:2608. 14744v1 Announce Type: new Abstract: Recovering high-resolution states from sparse, low-resolution observations is a central challenge in scientific machine learning and data assimilation.
arXiv AI
Jun 18
Grids Often Outperform Implicit Neural Representations at Compressing Dense Signals
arXiv:2506. 11139v3 Announce Type: replace-cross Abstract: Implicit Neural Representations (INRs) have recently shown impressive results, but their fundamental capacity, implicit biases, and scaling behavior remain poorly understood.
arXiv AI
Jun 11
SirenFNO: Efficient and Full Frequency Learning of Fourier Neural Operators
arXiv:2606. 11518v1 Announce Type: cross Abstract: Fourier neural operators (FNOs) are effective and efficient surrogates for approximating solutions of PDEs and generalize across discretizations.
arXiv Machine Learning
Jun 5
Reformulating Neural Operators in $d+1$ Dimensions for Embedding Evolution
arXiv:2505. 11766v4 Announce Type: replace Abstract: Neural Operators (NOs) are powerful architectures for learning mappings between function spaces.
arXiv Machine Learning
Aug 11
ADEx-FNO: A Unified Ambient-Domain Framework for Fourier Neural Operators on Varying Geometries
arXiv:2608. 08608v1 Announce Type: cross Abstract: Fourier neural operators (FNOs) provide efficient nonlocal spectral learning, but varying geometries and independently chosen discretizations remain difficult to accommodate.
arXiv Machine Learning
Jun 9
SPAMoE: Spectrum-Aware Hybrid Operator Framework for Full-Waveform Inversion
arXiv:2604. 07421v3 Announce Type: replace Abstract: Full-waveform inversion (FWI) is pivotal for reconstructing high-resolution subsurface velocity models but remains computationally intensive and ill-posed.
arXiv Computer Vision
3d ago
Super-Resolving Unseen Hyperspectral Sensors at Any Scale via Spatial Operators
arXiv:2609.39926v1 Announce Type: new Abstract: Achieving cross-sensor generalization and arbitrary-scale reconstruction with a single model remains challenging in hyperspectral super-resolution (HSR...
arXiv Machine Learning
4d ago
SINO: Scale-Invariant Neural Operator
arXiv:2609.36890v1 Announce Type: new Abstract: In scientific machine learning, physical fields governed by partial differential equations exhibit low-rank structure and scale invariance. When solvin...