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…
A kernel method for the learning of Wasserstein geometric flows
Jianyu Hu, Juan-Pablo Ortega, Daiying Yin
Wasserstein gradient and Hamiltonian flows have emerged as essential tools for modeling complex dynamics in the natural sciences, providing a unifying geometric formulation of many…
A global structure-preserving kernel method for the learning of Poisson systems
Jianyu Hu, Juan-Pablo Ortega, Daiying Yin
A structure-preserving kernel ridge regression method is presented that allows the recovery of globally defined, potentially high-dimensional, and nonlinear Hamiltonian functions o…
A Structure-Preserving Kernel Method for Learning Hamiltonian Systems
Jianyu Hu, Juan-Pablo Ortega, Daiying Yin
A structure-preserving kernel ridge regression method is presented that allows the recovery of nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamilto…