5 papers · 1 filter
Mixtures of Neural Operators Reduce Active Complexity in Operator Learning
Anastasis Kratsios, Takashi Furuya, Jose Antonio Lara Benitez +2
Operator-learning systems are not governed solely by total parameter count; for one query, the relevant bottleneck can be the model that must be loaded and evaluated. We study this…
Flowers: A Warp Drive for Neural PDE Solvers
Till Muser, Alexandra Spitzer, Matti Lassas +2
We introduce Flowers, a neural architecture for learning PDE solution operators built entirely from multihead warps. Aside from pointwise channel mixing and a multiscale scaffold,…
Function graph transformers universally approximate operators between function spaces
Takashi Furuya, David Mis, Ivan DokmaniÄ +2
We study the approximation of nonlinear operators between function spaces by transformers. Our approach is to lift functions to measures supported on their graphs and leverage a re…
Semialgebraic Neural Networks: From roots to representations
S. David Mis, Matti Lassas, Maarten V. de Hoop
Many numerical algorithms in scientific computing -- particularly in areas like numerical linear algebra, PDE simulation, and inverse problems -- produce outputs that can be repres…
Can neural operators always be continuously discretized?
Takashi Furuya, Michael Puthawala, Maarten V. de Hoop +1
We consider the problem of discretization of neural operators between Hilbert spaces in a general framework including skip connections. We focus on bijective neural operators throu…