22 papers
An inverse free boundary problem
Cătălin I. Cârstea, Matti Lassas, Jinpeng Lu +2
We study inverse problems for the elliptic and parabolic obstacle problems from boundary measurements. For the classical elliptic obstacle problem with strictly superharmonic obsta…
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…