研究人员开发了一种新方法，用于简化非线性动力学系统中 Koopman 算子的核学习。该方法将字典学习扩展到核 EDMD，从而能够对核参数进行基于梯度的优化。该技术旨在生成更有效的核来逼近 Koopman 算子，并已在 Duffing 振子和 Kuramoto-Sivashinsky PDE 等系统上进行了测试。 AI
影响 为动力学系统中的核方法引入了一种新颖的优化技术，有可能提高模型逼近的准确性。
排序理由 学术论文，介绍了一种用于动力学系统分析中核学习的新方法。
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arXiv:2604.25572v1 Announce Type: cross Abstract: Studying nonlinear dynamical systems through their state space behavior can be challenging, and one possible alternative is to analyze them via their associated Koopman operator. This turns the nonlinear problem into a linear, inf…
Studying nonlinear dynamical systems through their state space behavior can be challenging, and one possible alternative is to analyze them via their associated Koopman operator. This turns the nonlinear problem into a linear, infinite-dimensional one. To approximate the operator…
Studying nonlinear dynamical systems through their state space behavior can be challenging, and one possible alternative is to analyze them via their associated Koopman operator. This turns the nonlinear problem into a linear, infinite-dimensional one. To approximate the operator…
arXiv:2604.22386v1 Announce Type: new Abstract: One of the major limits of kernel ridge regression (KRR) is that storing and manipulating the kernel matrix K_n for n samples requires O(n^2) space, which rapidly becomes unfeasible for large n. Nystrom approximations reduce the spa…
One of the major limits of kernel ridge regression (KRR) is that storing and manipulating the kernel matrix K_n for n samples requires O(n^2) space, which rapidly becomes unfeasible for large n. Nystrom approximations reduce the space complexity to O(nm) by sampling m columns fro…