11 citations · 19 across the 12 of their papers we have counts for
14 papers
Universality and Generalization of Causal Transformers Across Context Lengths
Takashi Furuya, Maarten V. de Hoop, Gabriel Peyré
Long contexts are central to modern transformer systems, but most expressivity results choose a different network for each fixed sequence length. We study whether one masked transf…
Classification of singularities of planar slowness surfaces
Antonio Cocan, Maarten V. de Hoop, Joonas Ilmavirta +2
Slowness surfaces are algebraic varieties arising from propagation of elastic waves. In dimensions , we completely classify the types of singularities slowness surfaces can have…
Propagation of singularities and inverse problems for the viscoacoustic wave equation
Giovanni Covi, Maarten de Hoop, Mikko Salo
We study an inverse problem for the viscoacoustic wave equation, an integro-differential model describing wave propagation in viscoacoustic media with memory in the leading order t…
Neural Operators Can Discover Functional Clusters
Yicen Li, Jose Antonio Lara Benitez, Ruiyang Hong +3
Operator learning is reshaping scientific computing by amortizing inference across infinite families of problems. While neural operators (NOs) are increasingly well understood for…
Hybrid operator learning of wave scattering maps in high-contrast media
Advait Balaji, Trevor Teolis, S. David Mis +3
Surrogate modeling of wave propagation and scattering (i.e. the wave speed and source to wave field map) in heterogeneous media has significant potential in applications such as se…
Rates and architectures for learning geometrically non-trivial operators
T. Mitchell Roddenberry, Leo Tzou, Ivan Dokmanić +2
Deep learning methods have proven capable of recovering operators between high-dimensional spaces, such as solution maps of PDEs and similar objects in mathematical physics, from v…
Preconditioned Langevin Dynamics with Score-Based Generative Models for Infinite-Dimensional Linear Bayesian Inverse Problems
Lorenzo Baldassari, Josselin Garnier, Knut Solna +1
Designing algorithms for solving high-dimensional Bayesian inverse problems directly in infinite-dimensional function spaces - where such problems are naturally formulated - is cru…
Principal spectral rigidity implies subprincipal spectral rigidity
Maarten V. de Hoop, Joonas Ilmavirta, Vitaly Katsnelson
We study the inverse spectral problem of jointly recovering a radially symmetric Riemannian metric and an additional coefficient from the Dirichlet spectrum of a perturbed Laplace-…
Neural equilibria for long-term prediction of nonlinear conservation laws
J. Antonio Lara Benitez, Kareem Hegazy, Junyi Guo +3
Nonlinear conservation laws govern a broad class of important physical systems in science and industry and are central to scientific machine learning (SciML). Large general-purpose…
Geometrical optics for the fractional Helmholtz equation and applications to inverse problems
Giovanni Covi, Maarten de Hoop, Mikko Salo
In this paper we construct a parametrix for the fractional Helmholtz equation making use of geometrical optics solutions. We show that the a…
SeisLM: a Foundation Model for Seismic Waveforms
Tianlin Liu, Jannes Münchmeyer, Laura Laurenti +3
We introduce the Seismic Language Model (SeisLM), a foundational model designed to analyze seismic waveforms -- signals generated by Earth's vibrations such as the ones originating…
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…
Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation
J. Antonio Lara Benitez, Takashi Furuya, Florian Faucher +3
Despite their remarkable success in approximating a wide range of operators defined by PDEs, existing neural operators (NOs) do not necessarily perform well for all physics problem…
Conditional Injective Flows for Bayesian Imaging
AmirEhsan Khorashadizadeh, Konik Kothari, Leonardo Salsi +3
Most deep learning models for computational imaging regress a single reconstructed image. In practice, however, ill-posedness, nonlinearity, model mismatch, and noise often conspir…