Yes, you can travel with DSB (Danish State Railways) and train operator GoCollective between several stations in the Aarhus Region.

DSB

DSB runs between Aarhus, Favrskov and Randers on the national route between Copenhagen and Aalborg.

Find out more here.

GoCollective

GoCollective operates between Aarhus and Silkeborg (Route: Aarhus - Herning - Struer) and between Aarhus, Favrskov and Viborg (Route: Aarhus Langå Struer)

See routes here.