AMD have announced they're going to release Mantle, but due to the fact that it offers very low level control of the hardware, it isn't ever going to run on nVidia hardware except via emulation, and then it'll be too slow to beat D3D/OpenGL. Previously, nVidia supposedly offered AMD the ability to use CUDA, but AMD had invested in a rival engine, and so decided that doing something to make PhysX more popular wouldn't be in their best interests. Being much more high level than Mantle, it would have been entirely possible to do, though.
OS: Windows 10 64 bit Professional
CPU: AMD Ryzen 5900X
RAM: 48GB
GPU: Radeon 7800 XT
CPU: AMD Ryzen 5900X
RAM: 48GB
GPU: Radeon 7800 XT