Friction Welding
Friction Welding is an exotic type of welding that needs some large precision machines to handle the forces involved in performing the process. One piece of metal is spun and then forced into a secondary piece of metal. This causes intense heat and fuses the two metals together.
Thermite Welding
Thermite Welding is when you harness the insane heat generated by burning thermite to weld two pieces of metal together. The above video shows it in use to weld two sections of train track together.
Explosion Welding
Explosion Welding is the most insane welding process I have ever seen. A large explosion generate a downward force that causes a metal sandwich to permanently fuse together. There is significant work that is needed to straighten the metal flat again after the explosion but if you have a 3 million pound press that should not be a problem.