  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.
