Flight Instructor reported an engine power loss during initial climb while conducting landing pattern training. The Instructor turned to land on the opposite direction parallel runway where a safe landing was completed.

Narrative

Date at around XA:30 Local time I experience engine roughness and loss of engine power on climb out from Runway XXL at ZZZ around 350 feet +/-. After doing pattern work (Touch & Gos) for about 45 minutes the engine sputter and had a series of vibrations on the 10th Takeoff; the RPM decrease under 1;500 while the throttle was all the way open. The Student was confused and taken by surprise; asking me; What's going on?.I took the control of the airplane and advised Tower that I needed to land on Runway XL due to loss of engine power. As I pitch down to maintain airspeed and turned towards Runway XL the engine power came back; at that point I was already committed to making the precautionary landing; I took the throttle all the way out and used flaps once I had the landing secured on Runway XL; safely landing with no other issues. As I exited the runways Tower asked me if I required any assistance and I declined; I was able to taxi back to the ramp and safely secured the airplane. I made the decision to turn back towards the parallel runway because I am very familiar with that airport and the environment around it; I understood that even if the power did not come back fully I would be able to make the parallel runway or at least stay within the airport environment and grass around it. I maintained complete control of the airplane and focused on regaining airspeed and not increasing the angle of attack. I believe I took the correct course of actions and right decision performing the precautionary landing. and even though the engine power came back there was not way of knowing if it was gonna be able to maintain it during the climb and for how long.