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Design of cyber-physical systems (CPSs) is a challenging task that involves searching over a large search space of various CPS configurations and possible values of components composing the system. Hence, there is a need for sample-efficient CPS design space exploration to select the system architecture and component values that meet the target system requirements. We address this challenge by formulating CPS design as a multi-objective optimization problem and propose DISPATCH, a two-step methodology for sample-efficient search over the design space. First, we use a genetic algorithm to search over discrete choices of system component values for architecture search and component selection or only component selection and terminate the algorithm even before meeting the system requirements, thus yielding a coarse design. In the second step, we use an inverse design to search over a continuous space to fine-tune the component values and meet the diverse set of system requirements. We use a neural network as a surrogate function for the inverse design of the system. The neural network, converted into a mixed-integer linear program, is used for active learning to sample component values efficiently in a continuous search space. We illustrate the efficacy of DISPATCH on electrical circuit benchmarks: two-stage and three-stage transimpedence amplifiers. Simulation results show that the proposed methodology improves sample efficiency by 5-14x compared to a prior synthesis method that relies on reinforcement learning. It also synthesizes circuits with the best performance (highest bandwidth/lowest area) compared to designs synthesized using reinforcement learning, Bayesian optimization, or humans.