  We propose a deep learning-based surrogate model for stochastic simulators.
The basic idea is to use generative neural network to approximate the
stochastic response. The challenge with such a framework resides in designing
the network architecture and selecting loss-function suitable for stochastic
response. While we utilize a simple feed-forward neural network, we propose to
use conditional maximum mean discrepancy (CMMD) as the loss-function. CMMD
exploits the property of reproducing kernel Hilbert space and allows capturing
discrepancy between the between the target and the neural network predicted
distributions. The proposed approach is mathematically rigorous, in the sense
that it makes no assumptions about the probability density function of the
response. Performance of the proposed approach is illustrated using four
benchmark problems selected from the literature. Results obtained indicate the
excellent performance of the proposed approach.
