Robust deep neural network surrogate models with uncertainty quantification via adversarial training

Surrogate models have been used to emulate mathematical simulators of physical or biological processes for computational efficiency. High-speed simulation is crucial for conducting uncertainty quantification (UQ) when the simulation must repeat over many randomly sampled input points (aka the Monte Carlo method). A simulator can be so computationally intensive that UQ is only feasible with a surrogate model. Recently, deep neural network (DNN) surrogate models have gained popularity for their state-of-the-art emulation accuracy. However, it is well-known that DNN is prone to severe errors when input data are perturbed in particular ways, the very phenomenon which has inspired great interest in adversarial training. In the case of surrogate models, the concern is less about a deliberate attack exploiting the vulnerability of a DNN but more of the high sensitivity of its accuracy to input directions, an issue largely ignored by researchers using emulation models. In this paper, we show the severity of this issue through empirical studies and hypothesis testing. Furthermore, we adopt methods in adversarial training to enhance the robustness of DNN surrogate models. Experiments demonstrate that our approaches significantly improve the robustness of the surrogate models without compromising emulation accuracy.