NP-ODE: Neural process aided ordinary differential equations for uncertainty quantification of finite element analysis

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.