Viaduct, n : bridge consisting of a series of arches supported by piers used to carry a road (railroad)over a valley, canal, city; etc. from the [Latin via, road; see via + (aque)duct.]
Aqueduct, n: 1. A pipe or channel designed to transport water from a remote source, usually by gravity.
2. A bridgelike structure supporting a conduit or canal passing over a river or low ground.
3. Anatomy. A channel or passage in an organ or a body part, especially such a channel for conveying fluid. [Latin aquaeductus : aquae, genitive of aqua, water; aqua + ductus, a leading;]
Since both were built by the Romans to convey troops, etc over roads, water (given examples) and water through channels, I would say the Romans are credited with inventing both. Look at the pictures of some of the remaining Roman roads and look for the arched bridges crossing a canal (for example) and you have your viaduct. The term viaduct today commonly refers to a single road overpass which usually crosses railroad lines and canals, or rivers. Hope that helps.
Take care,
Stargazer