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cs.CE2025
Physics-based deep kernel learning for parameter estimation in high dimensional PDEs
Weihao Yan, Christoph Brune, Mengwu Guo
Inferring parameters of high-dimensional partial differential equations (PDEs) poses significant computational and inferential challenges, primarily due to the curse of dimensional…
cs.LG2025
PDE-DKL: PDE-constrained deep kernel learning in high dimensionality
Weihao Yan, Christoph Brune, Mengwu Guo
Many physics-informed machine learning methods for PDE-based problems rely on Gaussian processes (GPs) or neural networks (NNs). However, both face limitations when data are scarce…
cs.LG2025
Deep Networks are Reproducing Kernel Chains
Tjeerd Jan Heeringa, Len Spek, Christoph Brune
Identifying an appropriate function space for deep neural networks remains a key open question. While shallow neural networks are naturally associated with Reproducing Kernel Banac…