Data for uncertainty quantification via adaptive ANN

The Monte Carlo method (MCM) is known as the gold standard technique for uncertainty quantification (UQ). However, it requires a considerable number of simulations leading to excessive computational resources. Though some UQ techniques such as the non-intrusive polynomial chaos (NIPC) expansion method are ideal alternatives to MCM, the computational cost remains unaffordable when systems consist of a high number of random variables. This paper proposes an adaptive artificial neural network (ANN) aiming to replace thousands of system-runs required in the MCM, thereby improving computational efficiency of the MCM. We design an activation function with which an ANN learns from the data to the greatest extent. Furthermore, in order to improve the accuracy of the estimation of the system output via ANN, methods for hyperparameter optimisation and a series of termination criteria of ANN are proposed based on the leave-one-out cross-validation method. In the application of the finite difference time domain computation, the proposed method achieves up to 13 times speedup and 20\% improvement of the accuracy of the UQ estimation compared to the traditional NIPC expansion method.