A deep learning based surrogate model for stochastic simulators
This work provides a method for efficiently modeling stochastic systems, which is incremental as it builds on existing surrogate modeling techniques with a specific loss function adaptation.
The authors tackled the problem of approximating stochastic simulators by proposing a deep learning-based surrogate model using a generative neural network with a conditional maximum mean discrepancy loss function, achieving excellent performance on four benchmark problems.
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.