Complex networks are used to model many real-world systems. However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like POD can be used in such cases. However, these models are susceptible to perturbations in the input data. We propose an algorithmic framework that combines techniques from pattern recognition (PR) and stochastic filtering theory to enhance the output of such models. The results of our study show that our method can improve the accuracy of the surrogate model under perturbed inputs. Deep Neural Networks (DNNs) are susceptible to adversarial attacks. However, recent research has revealed that neural Ordinary Differential Equations (ODEs) exhibit robustness in specific applications. We benchmark our algorithmic framework with a Neural ODE-based approach as a reference.

翻译：复杂网络被广泛用于模拟许多现实系统，然而其高维特性常导致分析困难。针对此类问题，可采用本征正交分解（POD）等降维技术进行处理，但这些模型易受输入数据扰动的影响。本文提出一种融合模式识别（PR）与随机滤波理论的计算框架，旨在增强该类模型的输出性能。研究结果表明，所提方法能在扰动输入条件下有效提升代理模型的精度。值得注意的是，深度神经网络（DNN）易受对抗攻击影响，而近期研究揭示神经常微分方程（ODE）在特定应用中具有鲁棒性。本研究以基于神经ODE的方法为基准，对所提算法框架进行了性能评估。