20 papers
Generic Recovery of Permittivity and Permeability in Anisotropic Maxwell Systems
Antonio Cocan, Maarten V. de Hoop, Joonas Ilmavirta +3
We study the inverse problem of recovering the constitutive tensors of a homogeneous anisotropic electromagnetic medium without magnetoelectric coupling (non-chiral) from its Fresn…
Unveiling topology in imaging problems via quasi-isometry and persistent homology
Elli Karvonen, Matti Lassas, Pekka Pankka
We show that the topological structures, such as loops, voids, and higher-dimensional holes of unknown objects (of flow of an object in space-time) can be recovered from noisy and…
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…
Denoising data using convex relaxations
Charles Fefferman, Aalok Gangopadhyay, Matti Lassas +2
We study the problem of denoising observations \(Y_i=X_i+Z_i\), where the latent variables \(X_i\) are sampled from a low-dimensional manifold in \(\mathbb{R}^n\) and the noise var…