90 citations · 503 across the 77 of their papers we have counts for
79 papers
Target-adapted Green-Bessel SVGD: uniform-in-time propagation of chaos and last-iterate consistency
Trevor Teolis, Maarten V. de Hoop
We prove uniform-in-time propagation of chaos and last-iterate consistency for a target-adapted Stein variational gradient descent (SVGD) flow on compact connected manifolds. The t…
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…
Riesz-Kernel Stein Variational Gradient Descent: Renormalized Entropy and Long-Time Particle Limits
Trevor Teolis, Maarten V. de Hoop
Stein variational gradient descent (SVGD) transports interacting particles toward a target distribution through deterministic kernelized dynamics. Singular Riesz kernels are attrac…
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…
Training Infinitely Deep and Wide Transformers
Raphaël Barboni, Maarten V. de Hoop, Takashi Furuya +1
Transformers have become the dominant architecture in modern machine learning, yet the theoretical understanding of their training dynamics remains limited. This paper develops a r…
Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixtures
Lorenzo Baldassari, Josselin Garnier, Knut Solna +1
Obtaining stable diffusion-based samplers in high- and infinite-dimensional settings is challenging because errors can accumulate across high-frequency coordinates and make the dyn…
Moving localized observations and Ces{à}ro asymptotic observability for conservative PDEs
Maarten V. de Hoop, Antti Kykkänen, Emmanuel Trélat
We develop a deterministic large-time mechanism yielding Ces{à}ro asymptotic observability inequalities from moving localized observations for conservative evolutions. On each obse…
Boundary observability for gas giant metrics
Maarten V. de Hoop, Antti Kykkänen, Emmanuel Trélat
We study the observability of waves on gas giant manifolds which are a class of Riemannian manifolds whose metrics are singular at the boundary. Such manifolds arise naturally in m…
On Observation Time for Recovering Latent Hawkes Networks
Jonas Linkerhägner, Michele Bortolasi, Lorenzo Baldassari +2
Dynamics of interacting systems in engineering, society, and nature often evolve over latent networks that govern which entities can interact. We study the problem of inferring the…
Measure flow path recovery in Bayes Hilbert spaces
S. David Mis, Maarten V. de Hoop
We study the ill-posed problem of recovering a probability measure flow from finitely many moving localized sensors using a Bayes Hilbert framework. Relative to a fixed reference p…
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,…
Dimension-Free Multimodal Sampling via Preconditioned Annealed Langevin Dynamics
Lorenzo Baldassari, Josselin Garnier, Knut Solna +1
Designing sampling algorithms for multimodal targets that remain stable under refinement of the finite-dimensional approximation of an underlying function-space problem is a centra…
The head-wave transform
Maarten V. de Hoop, Antti Kykkänen, Rohit Kumar Mishra
We introduce and study a new integral ray transform called the head-wave transform. The head-wave transform integrates a function along a piecewise linear (in general geodesic) pat…
Exact Boundary Controllability for Reduced System Associated to Extended Maxwell Systems
Maarten V. de Hoop, Ching-Lung Lin, Gen Nakamura
In the theory of viscoelasticity, an important class of models admits a representation in terms of springs and dashpots. Widely used members of this class are the Maxwell model and…
Transformers are Universal In-context Learners
Takashi Furuya, Maarten V. de Hoop, Gabriel Peyré
Transformers are deep architectures that define "in-context mappings" which enable predicting new tokens based on a given set of tokens (such as a prompt in NLP applications or a s…
Anisotropic extended Burgers model, its relaxation tensor and properties of the associated Boltzmann viscoelastic system
Maarten de Hoop, Masato Kimura, Ching-Lung Lin +2
We provide a new method for constructing the anisotropic relaxation tensor and proving its exponential decay property for the extended Burgers model (abbreviated by EBM). The EBM i…
Weyl formulae for some singular metrics with application to acoustic modes in gas giants
Yves Colin de Verdìère, Charlotte Dietze, Maarten V. de Hoop +1
This paper is motivated by recent works on inverse problems for acoustic wave propagation in the interior of gas giant planets. In such planets, the speed of sound is isotropic and…
Taming Score-Based Diffusion Priors for Infinite-Dimensional Nonlinear Inverse Problems
Lorenzo Baldassari, Ali Siahkoohi, Josselin Garnier +2
This work introduces a sampling method capable of solving Bayesian inverse problems in function space. It does not assume the log-concavity of the likelihood, meaning that it is co…
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…
Geometric inverse problems on gas giants
Maarten V. de Hoop, Joonas Ilmavirta, Antti Kykkänen +1
On gas giant planets the speed of sound is isotropic and goes to zero at the surface. Geometrically, this corresponds to a Riemannian manifold whose metric tensor has a conformal b…
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…
Implicit Neural Representations and the Algebra of Complex Wavelets
T. Mitchell Roddenberry, Vishwanath Saragadam, Maarten V. de Hoop +1
Implicit neural representations (INRs) have arisen as useful methods for representing signals on Euclidean domains. By parameterizing an image as a multilayer perceptron (MLP) on E…
Resolvent Estimates for Viscoelastic Systems of Extended Maxwell Type and their Applications
Maarten V. de Hoop, Masato Kimura, Ching-Lung Lin +1
In the theory of viscoelasticity, an important class of models admits a representation in terms of springs and dashpots. Widely used members of this class are the Maxwell model and…
Coupling of flow, contact mechanics and friction, generating waves in a fractured porous medium
Maarten V. de Hoop, Kundan Kumar
We present a mixed dimensional model for a fractured poro-elasic medium including contact mechanics. The fracture is a lower dimensional surface embedded in a bulk poro-elastic mat…