A deep learning based surrogate model for stochastic simulators

TL;DR

This paper introduces a deep learning surrogate model for stochastic simulators using generative neural networks and a novel loss function, CMMD, to accurately approximate stochastic responses without density assumptions.

Contribution

It presents a new deep learning framework employing CMMD as a loss function for stochastic response approximation, with rigorous mathematical foundation and demonstrated effectiveness.

Findings

Excellent performance on benchmark problems

No assumptions on probability density functions

Effective capture of stochastic response distributions

Abstract

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.