Aachen lies close to the airports Düsseldorf and Köln-Bonn. From there You can travel to Aachen as follows:

From airport Düsseldorf:

There are direct connections by train from the airport to Aachen Hbf (main station). Alternatively You may travel by S-Bahn to Düsseldorf Hbf (main station) and take a train to Aachen Hbf oder Aachen West. From Aachen Hbf You proceed as explained on "Arrival by train" with bus or taxi to "Physikzentrum" (physics center). From railway station "Aachen West" You preferably travel by bus.

From airport Köln-Bonn:

There are regular connections from the airport to railway station "Köln-Deutz" by bus (You will have to walk a short distance from bus stop to railway station.). From "Köln Deutz" You travel by train to Aachen
Update: There is a railway station at the airport, so You do not have to take the bus.

Deutsche Bahn train schedule: online