8 papers · 1 filter
Extension and neural operator approximation of the electrical impedance tomography inverse map
Maarten V. de Hoop, Nikola B. Kovachki, Matti Lassas +1
This paper considers the problem of noise-robust neural operator approximation for the solution map of Calderón's inverse conductivity problem. In this continuum model of electric…
An Unconditional Representation of the Conditional Score in Infinite-Dimensional Linear Inverse Problems
Fabian Schneider, Duc-Lam Duong, Matti Lassas +2
Score-based diffusion models (SDMs) have emerged as a powerful tool for sampling from the posterior distribution in Bayesian inverse problems. However, existing methods often requi…
A Hyperbolic Inverse Problem for lower order terms on a closed manifold with disjoint data
Matti Lassas, Boya Liu, Teemu Saksala +2
We study the unique recovery of time-independent lower order terms appearing in the symmetric first order perturbation of the Riemannian wave equation by sending and measuring wave…
Transformers through the lens of support-preserving maps between measures
Takashi Furuya, Maarten V. de Hoop, Matti Lassas
Transformers are deep architectures that define ``in-context maps'' which enable predicting new tokens based on a given set of tokens (such as a prompt in NLP applications or a set…
An inverse problem for the Standard Model of particle physics
Xi Chen, Matti Lassas, Lauri Oksanen +1
We pose and solve an inverse problem for the classical field equations that arise in the Standard Model of particle physics. Our main result describes natural conditions on the rep…
Reconstruction and interpolation of manifolds II: Inverse problems with partial data for distances observations and for the heat kernel
Charles Fefferman, Sergei Ivanov, Matti Lassas +2
We consider how a closed Riemannian manifold and its metric tensor can be approximately reconstructed from local distance measurements. Moreover, we consider an inverse pro…