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China Three Gorges University

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Representative Papers

Nyström-Accelerated Primal LS-SVMs: Breaking the $O(an^3)$ Complexity Bottleneck for Scalable ODEs Learning

Oct 05, 2025

To address the high computational complexity—O(an³), where a=1 for linear and a=27 for nonlinear ODEs—of kernel-based methods (e.g., LS-SVM) in solving ordinary differential equations (ODEs), this paper proposes a Nyström-accelerated primal-space LS-SVM framework. The core method constructs, for the first time, a one-dimensional temporal domain-to-m-dimensional explicit feature-space Nyström mapping and its analytical derivatives, enabling direct embedding of differential constraints into the primal space. This reduces computational complexity from O(n³) to O(m³), with m ≪ n. The approach achieves both high accuracy and scalability: on 16 benchmark ODEs, it accelerates computation by 10–6,000× over classical LS-SVM and physics-informed neural networks (PINNs), attains errors <0.13%, improves RMSE by up to 72%, and supports solutions with tens of thousands of time steps.

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Nyström-Accelerated Primal LS-SVMs: Breaking the $O(an^3)$ Complexity Bottleneck for Scalable ODEs Learning

Oct 05, 2025

To address the high computational complexity—O(an³), where a=1 for linear and a=27 for nonlinear ODEs—of kernel-based methods (e.g., LS-SVM) in solving ordinary differential equations (ODEs), this paper proposes a Nyström-accelerated primal-space LS-SVM framework. The core method constructs, for the first time, a one-dimensional temporal domain-to-m-dimensional explicit feature-space Nyström mapping and its analytical derivatives, enabling direct embedding of differential constraints into the primal space. This reduces computational complexity from O(n³) to O(m³), with m ≪ n. The approach achieves both high accuracy and scalability: on 16 benchmark ODEs, it accelerates computation by 10–6,000× over classical LS-SVM and physics-informed neural networks (PINNs), attains errors <0.13%, improves RMSE by up to 72%, and supports solutions with tens of thousands of time steps.

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