126 citations · 151 across the 29 of their papers we have counts for
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Kernel Methods for Some Transport Equations with Application to Learning Kernels for the Approximation of Koopman Eigenfunctions: A Unified Approach via Variational Methods, Green's Functions and the Method of Characteristics
Boumediene Hamzi, Houman Owhadi, Umesh Vaidya
We present a unified theoretical and computational framework for constructing reproducing kernels tailored to transport equations and adapted to Koopman eigenfunctions of nonlinear…
KROM: Kernelized Reduced Order Modeling
Aras Bacho, Jonghyeon Lee, Houman Owhadi
We propose KROM, a kernel-based reduced-order framework for fast solution of nonlinear partial differential equations. KROM formulates PDE solution as a minimum-norm (Gaussian-proc…
Data-efficient Kernel Methods for Learning Hamiltonian Systems
Yasamin Jalalian, Mostafa Samir, Boumediene Hamzi +2
Hamiltonian dynamics describe a wide range of physical systems. As such, data-driven simulations of Hamiltonian systems are important for many scientific and engineering problems.…
Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks
Ricardo Baptista, Edoardo Calvello, Matthieu Darcy +3
We consider the use of Gaussian Processes (GPs) or Neural Networks (NNs) to numerically approximate the solutions to nonlinear partial differential equations (PDEs) with rough forc…
Solving and Learning Nonlinear PDEs with Gaussian Processes
Yifan Chen, Bamdad Hosseini, Houman Owhadi +1
We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identificat…
Fast eigenpairs computation with operator adapted wavelets and hierarchical subspace correction
Hehu Xie, Lei Zhang, Houman Owhadi
We present a method for the fast computation of the eigenpairs of a bijective positive symmetric linear operator . The method is based on a combination of operator ada…