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
1d ago
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 Machine Learning
Jun 9
Multi-resolution Enhancement for Full Spectrum Neural Representations
arXiv:2509. 15494v2 Announce Type: replace Abstract: Scientific data acquisition continues to outpace storage and analysis capabilities, making voxel-based representations increasingly intractable.
arXiv Machine Learning
Jul 1
Mind the Residual Gap: Probabilistic Downscaling under Real-World Bias
arXiv:2606. 30821v1 Announce Type: new Abstract: Probabilistic downscaling is the task of modeling the conditional distribution of high-resolution fields given coarse inputs, and is a central challenge to atmospheric science, climate modeling, and other multiscale physical systems.
arXiv AI
Jul 15
Sparse Inter-Layer Dependencies of Transformer FFN Neurons
arXiv:2607. 11990v1 Announce Type: cross Abstract: Feedforward network (FFN) blocks account for a large fraction of the parameters and computation in Transformer architectures, yet their internal structure remains difficult to interpret due to the additive superposition induced by the residual stream.