PS2 was before the GPGPU age and its GPU is fixed functionality, so it's not suitable for general calculations. Your problem would have to align perfectly with the computations done for regular rendering.

If we instead look at something more modern like an early GeForce with programmable shaders what was typically done was to set up your regular rendering of a full screen quad and write a pixel shader which performs your desired computations instead of actual lighting calculations.

APIs such as CUDA and OpenCL were introduced to allow people who weren't making games to make GPU calculations without pretending that they were colour calculations.