126 citations · 146 across the 17 of their papers we have counts for
5 papers · 1 filter
Adaptive Kernel Selection for Kernelized Diffusion Maps
Othmane Aboussaad, Adam Miraoui, Boumediene Hamzi +1
Selecting an appropriate kernel is a central challenge in kernel-based spectral methods. In \emph{Kernelized Diffusion Maps} (KDM), the kernel determines the accuracy of the RKHS e…
Bilevel optimization for learning hyperparameters: Application to solving PDEs and inverse problems with Gaussian processes
Nicholas H. Nelsen, Houman Owhadi, Andrew M. Stuart +2
Methods for solving scientific computing and inference problems, such as kernel- and neural network-based approaches for partial differential equations (PDEs), inverse problems, an…
Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis
Yasamin Jalalian, Juan Felipe Osorio Ramirez, Alexander Hsu +2
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and am…
Kernel Mode Decomposition and programmable/interpretable regression networks
Houman Owhadi, Clint Scovel, Gene Ryan Yoo
Mode decomposition is a prototypical pattern recognition problem that can be addressed from the (a priori distinct) perspectives of numerical approximation, statistical inference a…
Kernel Flows: from learning kernels from data into the abyss
Houman Owhadi, Gene Ryan Yoo
Learning can be seen as approximating an unknown function by interpolating the training data. Kriging offers a solution to this problem based on the prior specification of a kernel…