CUDA is NVIDIA’s proprietary GPGPU language and environment, so it needs NVIDIA’a card and won’t run on other manufacturers’ cards. So it leaves us with the following options:

Learn to use OpenCL, which is open-source and can run on any platform. Here is OpenCL™ Developer Guide for Intel® Processor Graphics 79. More links for other cards are available in this answer 10.
Use eGPU - external GPU unit. See some possible options here 73, for instance or google for more.
Use any cloud services with GPU support. Check this list: Cloud GPU Vendors 47


Hope this helps a bit.