Non-linear reduced modeling of dynamical systems using kernel methods and low-rank approximation

• URL: http://arxiv.org/abs/1710.10919v6
• Date: Wed, 19 Feb 2025 08:54:07 GMT
• Title: Non-linear reduced modeling of dynamical systems using kernel methods and low-rank approximation
• Authors: Patrick Héas, Cédric Herzet, Benoit Combès,
• Abstract summary: We propose a new efficient algorithm for data-driven reduced modeling of non-linear dynamics based on linear approximations in a kernel Hilbert space.<n>This algorithm takes advantage of the closed-form solution of a low-rank constraint optimization problem while exploiting advantageously kernel-based computations.
• Score: 5.935306543481018
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation by first embedding the trajectories in a reproducing kernel Hilbert space (RKHS), which exhibits appealing approximation and computational capabilities, and then solving the associated reduced model problem. More specifically, we propose a new efficient algorithm for data-driven reduced modeling of non-linear dynamics based on linear approximations in a RKHS. This algorithm takes advantage of the closed-form solution of a low-rank constraint optimization problem while exploiting advantageously kernel-based computations. Reduced modeling with this algorithm reveals a gain in approximation accuracy, as shown by numerical simulations, and in complexity with respect to existing approaches.

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