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The optimization of electricity–gas coupled systems is typically complicated by the nonconvex relationships such as gas flow equations. Piecewise linearization, despite being one of the few solutions that guarantee exactness and optimality, is often discarded for an exceptionally long computational time. In this paper, we present a novel data-driven approach based on artificial neural networks, to enable fast economic dispatch in electricity–gas coupled systems, by utilizing simulation data from the piecewise-linearization-based model-driven method. Load profiles at each electric bus and gas node are fed into the artificial neural network as input neurons; optimal economic dispatch results are set as output neurons, where the dispatch results can be either continuous (e.g. power and gas output) or binary (e.g. scenario feasibility). In generating power and gas outputs, the slack generator method is proposed to further eliminate load mismatch. Case studies on an integrated Belgium 20-node gas/IEEE 24-bus power system show that, after the artificial neural network is properly trained, the data-driven economic dispatch method is 1 0 4 ∼ 1 0 5 times faster than model-driven piecewise linearization. It even outperforms second-order cone programming, a well-known convex relaxation technique to model natural gas systems, in terms of both the coupled system's state recovery accuracy and computational efficiency. Furthermore, the data-driven method is applied to a multi-period dispatch problem to demonstrate its scalability. • Proposed data-driven economic dispatch in the electricity–gas coupled system. • The data-driven approach is 104 to 105 times faster than model-driven counterparts. • State-recovery, accuracy, optimality, and scalability are confirmed by case study. • A "slack generator" is introduced to eliminate load mismatch in the approach. [ABSTRACT FROM AUTHOR]