This work develops a compute-efficient algorithm to tackle a fundamental problem in transportation: that of urban travel demand estimation. It focuses on the calibration of origin-destination travel demand input parameters for high-resolution traffic simulation models. It considers the use of abundant traffic road speed data.The travel demand calibration problem is formulated as a continuous, high-dimensional, simulation-based optimization (SO) problem with bound constraints. There is a lack of compute efficient algorithms to tackle this problem. We propose the use of an SO algorithm that relies on an efficient, analytical, differentiable, physics-based traffic model, known as a metamodel or surrogate model. We formulate a metamodel that enables the use of road speed data. Tests are performed on a Salt Lake City network. We study how the amount of data, as well as the congestion levels, impact both in-sample and out-of-sample performance. The proposed method outperforms the benchmark for both in-sample and out-of-sample performance by 84.4% and 72.2% in terms of speeds and counts, respectively. Most importantly, the proposed method yields the highest compute efficiency, identifying solutions with good performance within few simulation function evaluations (i.e., with small samples).