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 (neural ODEs) exhibit robustness in specific applications. We benchmark our algorithmic framework with the neural ODE-based approach as a reference.

翻译：复杂网络被广泛用于模拟诸多实际系统，然而这些系统的高维特性使其分析颇具挑战。在此类场景中，可采用本征正交分解（POD）等降维技术。但这类模型易受输入数据摄动的影响。我们提出一种融合模式识别（PR）与随机滤波理论的算法框架，以增强该类模型的输出性能。研究结果表明，该方法能提升代理模型在扰动输入下的精度。深度神经网络（DNNs）易受对抗攻击，但最新研究揭示神经常微分方程（neural ODEs）在特定应用中具有鲁棒性。我们将所提算法框架与基于神经常微分方程的方法进行基准对比分析。