4 papers
Kernel Learning of PDE Solution Operators
Jianyu Hu, Juan-Pablo Ortega
A kernel-based approach for the learning of the solution operator of general nonhomogeneous partial differential equations (PDEs) is proposed. The method incorporates physical prio…
Learning the climate of dynamical systems with state-space systems
James Murray Louw, Juan-Pablo Ortega
State-space systems encompass a broad class of algorithms used for modeling and forecasting time series. For such systems to be effective, two objectives must be met: (i) accurate…
Invariant kernels on Riemannian symmetric spaces: a harmonic-analytic approach
Nathael Da Costa, Cyrus Mostajeran, Juan-Pablo Ortega +1
This work aims to prove that the classical Gaussian kernel, when defined on a non-Euclidean symmetric space, is never positive-definite for any choice of parameter. To achieve this…
Geometric Learning with Positively Decomposable Kernels
Nathael Da Costa, Cyrus Mostajeran, Juan-Pablo Ortega +1
Kernel methods are powerful tools in machine learning. Classical kernel methods are based on positive-definite kernels, which map data spaces into reproducing kernel Hilbert spaces…