NP-ODE: Neural process aided ordinary differential equations for uncertainty quantification of finite element analysis
NP-ODE: Neural process aided ordinary differential equations for uncertainty quantification of finite element analysis
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DOI：
10.1080/24725854.2021.1891485
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发表时间：
2020-12
影响因子：
2.6
通讯作者：
Yinan Wang;Kaiwen Wang;W. Cai;Xiaowei Yue
中科院分区：
文献类型：
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作者：
Yinan Wang;Kaiwen Wang;W. Cai;Xiaowei Yue
摘要有限元分析（FEA）已被广泛应用于复杂非线性系统的仿真。尽管有限元分析的强度和精度很高，但它通常有两个局限性：(1)运行高保真的有限元分析通常需要高的计算成本和大量的时间；（ii） FEA是一种确定性方法，在对具有各种不确定性类型的复杂系统建模时，对不确定性进行量化是不够的。在本文中，提出了一种基于物理的数据驱动代理模型，称为神经过程辅助常微分方程（NP-ODE），用于模拟有限元模拟并捕获输入和输出的不确定性。为了验证所提出的NP-ODE的优点，我们对给定常微分方程生成的模拟数据和从实际摩擦腐蚀有限元分析平台收集的数据进行了实验。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，并在测试数据点上生成最合理的置信区间和最佳的覆盖率。附录、代码和数据可在补充文件中获得。
Abstract Finite Element Analysis (FEA) has been widely used to generate simulations of complex nonlinear systems. Despite its strength and accuracy, FEA usually has two limitations: (i) running high-fidelity FEA often requires high computational cost and consumes a large amount of time; (ii) FEA is a deterministic method that is insufficient for uncertainty quantification when modeling complex systems with various types of uncertainties. In this article, 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 results show that the proposed NP-ODE outperforms benchmark methods. The NP-ODE method realizes the smallest predictive error as well as generating the most reasonable confidence intervals with the best coverage on testing data points. Appendices, code, and data are available in the supplementary files.