论文标题
NP-ODE：神经过程有助于普通微分方程，用于不确定性量化有限元分析
NP-ODE: Neural Process Aided Ordinary Differential Equations for Uncertainty Quantification of Finite Element Analysis
论文作者
论文摘要
有限元分析（FEA）已被广泛用于生成复杂和非线性系统的模拟。尽管具有强度和准确性，但FEA的局限性可以总结为两个方面：a）运行高保真性FEA通常需要大量的计算成本，并且会消耗大量时间； b）FEA是一种确定性方法，在对具有多种类型的不确定性的复杂系统进行建模时，不足以进行不确定性定量（UQ）。在本文中，提出了一个物理信息的数据驱动的替代模型，称为神经过程辅助普通微分方程（NP-ODE），以对FEA模拟进行建模并捕获输入和输出不确定性。为了验证所提出的NP-ODE的优势，我们对从给定的普通微分方程生成的仿真数据进行了实验，以及从真实的FEA平台中收集的数据进行的摩擦腐蚀数据。比较了提出的NP-ODE和几种基准方法的性能。结果表明，所提出的NP-ODE优于基准方法。 NP-ODE方法实现了最小的预测误差，并生成了最合理的置信区间，具有测试数据点上最佳覆盖率。
Finite element analysis (FEA) has been widely used to generate simulations of complex and nonlinear systems. Despite its strength and accuracy, the limitations of FEA can be summarized into two aspects: a) running high-fidelity FEA often requires significant computational cost and consumes a large amount of time; b) FEA is a deterministic method that is insufficient for uncertainty quantification (UQ) when modeling complex systems with various types of uncertainties. In this paper, a physics-informed data-driven surrogate model, named Neural Process Aided Ordinary Differential Equation (NP-ODE), is proposed to model the FEA simulations and capture both input and output uncertainties. To validate the advantages of the proposed NP-ODE, we conduct experiments on both the simulation data generated from a given ordinary differential equation and the data collected from a real FEA platform for tribocorrosion. The performances of the proposed NP-ODE and several benchmark methods are compared. The results show that the proposed NP-ODE outperforms benchmark methods. The NP-ODE method realizes the smallest predictive error as well as generates the most reasonable confidence interval having the best coverage on testing data points.
