Deep Learning and Low-discrepancy Sampling for Surrogate Modeling with an Application to Urban Traffic Simulation

In this paper we investigate deep learning architectures combined with low-discrepancy sampling as surrogate models. The aim is to provide a quick estimate of the outcome of an expensive process when many evaluations are needed, e.g., for optimization purposes. The simulation of urban traffic, routinely employed for the design and performance evaluation of policies in urban mobility scenarios, is an example of procedure characterized by very complex dynamics, large dimensionality and intensive computational requirements. In this context, the need for a surrogate model arises in many forms, e.g., for origin-destination demand calibration, traffic light optimization, strategic planning. In order to cope with this complexity and large dimensionality we take advantage of the excellent approximating capabilities of deep neural networks as learning models. Then, we employ low-discrepancy sequences as sampling designs for the simulation runs required to create the training set for the deep surrogate model. This kind of sampling guarantees deterministically a good covering of the input space, and is able to exploit possible regularities of the simulation outcome. Extensive experimental tests are presented involving the popular SUMO microsimulator, showing the advantages of the proposed surrogate modeling solution under various performance measures.