4 papers
Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs
Alex Colagrande, Paul Caillon, Eva Feillet +1
Neural operators provide deep neural networks for learning mappings between function spaces. Among them, the Fourier Neural Operator (FNO) is particularly effective: its spectral c…
Limits of Resolution Equivariance in Fourier Neural Operators
Alex Colagrande, Paul Caillon, Eva Feillet +1
Fourier Neural Operators are often assumed to generalize across spatial resolutions, enabling training on a coarse grid and deployment on a finer grid. We test this assumption by c…
Forward Only Learning for Orthogonal Neural Networks of any Depth
Paul Caillon, Alex Colagrande, Erwan Fagnou +2
Backpropagation is still the de facto algorithm used today to train neural networks. With the exponential growth of recent architectures, the computational cost of this algorithm a…
Linear Attention with Global Context: A Multipole Attention Mechanism for Vision and Physics
Alex Colagrande, Paul Caillon, Eva Feillet +1
Transformers have become the de facto standard for a wide range of tasks, from image classification to physics simulations. Despite their impressive performance, the quadratic comp…