New framework enables norm-optimal model reduction in RKHSs

Researchers have developed a new framework for model order reduction (MOR) within reproducing kernel Hilbert spaces (RKHSs). This framework extends existing necessary interpolatory conditions for norm-optimal reduced-order models, originally applied to rational functions in Hardy-Hilbert spaces. The proposed method utilizes generalized Malmquist-Takenaka functions to create orthonormal bases in RKHSs, enabling norm-optimal MOR for models with both differentiable and non-differentiable kernels. The approach has been demonstrated through numerical experiments on machine learning models like support vector machines and deep ReLU networks, and also applied to polynomial fitting and solving partial differential equations. AI

IMPACT This research could lead to more efficient machine learning models by enabling better approximation of complex functions.

RANK_REASON The cluster contains a single academic paper detailing a new mathematical framework and algorithms for model order reduction. [lever_c_demoted from research: ic=1 ai=0.7]

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• female
• Graph Memory Transformer
• Hardy-Hilbert spaces
• Irka
• Iterative rational Krylov algorithm
• Malmquist-Takenaka
• partial differential equations
• rectifier
• Reproducing Kernel Hilbert Spaces
• support vector machine

• paper
• other

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