标题： 高斯过程回归结合加性周期核在耦合相振子中分析二体相互作用 显示英文标题

标题： Gaussian process regression with additive periodic kernels for two-body interaction analysis in coupled phase oscillators

摘要： 我们提出了一种高斯过程回归框架，采用加性周期核来分析耦合振荡器系统中的二体相互作用。虽然由贝叶斯方法确定的有限阶傅里叶展开仍然可能导致诸如高振幅高频振动等伪影，但我们的加性周期核方法已经证明能够有效避免这些问题。此外，通过利用耦合函数的加性和周期性特征，我们显著降低了推理问题的有效维度。我们首先在一个简单的耦合相位振荡器上验证了该方法，并展示了其在有偏见或数据受限的情况下对更复杂系统的鲁棒性，包括范德波尔振荡器和FitzHugh-Nagumo振荡器。接下来，我们将这种方法应用于由霍奇金-赫克斯利方程建模的脉冲神经网络中，在其中成功恢复了潜在的相互作用函数。这些结果突显了高斯过程回归在捕捉振荡器网络中的非线性和周期性相互作用方面的灵活性和稳定性。我们的框架为传统方法提供了一个实用的替代方案，使得能够在物理、生物和工程领域开展基于数据的研究，以研究同步节律系统。 显示英文摘要

摘要： We propose a Gaussian process regression framework with additive periodic kernels for the analysis of two-body interactions in coupled oscillator systems. While finite-order Fourier expansions determined by Bayesian methods can still yield artifacts such as a high-amplitude, high-frequency vibration, our additive periodic kernel approach has been demonstrated to effectively circumvent these issues. Furthermore, by exploiting the additive and periodic nature of the coupling functions, we significantly reduce the effective dimensionality of the inference problem. We first validate our method on simple coupled phase oscillators and demonstrate its robustness to more complex systems, including Van der Pol and FitzHugh-Nagumo oscillators, under conditions of biased or limited data. We next apply our approach to spiking neural networks modeled by Hodgkin-Huxley equations, in which we successfully recover the underlying interaction functions. These results highlight the flexibility and stability of Gaussian process regression in capturing nonlinear, periodic interactions in oscillator networks. Our framework provides a practical alternative to conventional methods, enabling data-driven studies of synchronized rhythmic systems across physics, biology, and engineering.