25 papers
Inverse Scattering for Single Photons in Quantum Optics
Giovanni Covi, Matti Lassas, Medet Nursultanov +3
We study inverse problems for a time-harmonic one-photon model describing the interaction of a single photon with a medium of stationary two-level atoms. After time-harmonic reduct…
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 +2
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…
Function graph transformers universally approximate operators between function spaces
Takashi Furuya, David Mis, Ivan Dokmanić +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…
Determination of an anisotropic perturbation in elastic inverse scattering
Matti Lassas, Shiqi Ma, Lauri Oksanen +2
We consider a linearized inverse scattering problem for elastic waves. We prove that a fully anisotropic perturbation of the elastic parameters around an isotropic and homogeneous…
An inverse problem for semilinear wave equations on metric tree graphs
Sergei Avdonin, Matti Lassas, Jinpeng Lu +2
We study the inverse problem for a semilinear wave equation on metric tree graphs. From the Dirichlet-to-Neumann map defined at all but one of the boundary vertices, we recover unk…
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,…
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 electrica…
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…
Lens rigidity in 2D: The reconstruction of a Riemann surface from its geodesic lengths
Spyros Alexakis, Matti Lassas
We address the question of whether a Riemannian manifold-with-boundary (M,g) in dimension two is uniquely determined from knowledge of the distances between points on its boundary.…
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…
On Exponential Instability of an Inverse Problem for the Wave Equation
Leonard Busch, Matti Lassas, Lauri Oksanen +1
For a time-independent potential , consider the source-to-solution operator that maps a source to the solution of in Euclidean space wit…
Quantum field theory and inverse problems: Imaging with Entangled Photons
Matti Lassas, Medet Nursultanov, Lauri Oksanen +1
We consider the quantum field theory for a scalar model of the electromagnetic field interacting with a system of two-level atoms. In this setting, we show that it is possible to u…
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…
An inverse Signorini obstacle problem
Maarten V. de Hoop, Matti Lassas, Jinpeng Lu +2
We study the inverse problem of determining a Signorini obstacle from boundary measurements for the isotropic elasticity system. We prove that the obstacle can be uniquely determin…
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…
Learning sparsity-promoting regularizers for linear inverse problems
Giovanni S. Alberti, Ernesto De Vito, Tapio Helin +3
This paper introduces a novel approach to learning sparsity-promoting regularizers for solving linear inverse problems. We develop a bilevel optimization framework to select an opt…
Inverse problems for quantum graph associated with square and hexagonal lattices
K. Ando, E. Blåsten, P. Exner +5
We solve inverse problems from the D-N map for the quantum graph on a finite domain in a square lattice and that on a hexagonal lattice, as well as inverse scattering problems from…
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…
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…
Stable recovery of coefficients in an inverse fault friction problem
Maarten V. de Hoop, Matti Lassas, Jinpeng Lu +1
We consider the inverse fault friction problem of determining the friction coefficient in the Tresca friction model, which can be formulated as an inverse problem for differential…