I have used VkFFT to create GPU version of a magnetic simulation software Spirit (https://github.com/DTolm/spirit). Except for FFT it also has a lot of general linear algebra routines, like efficient GPU reduce/scan and system solvers, like CG, LBFGS, VP, Runge-Kutta and Depondt. This version of Spirit is faster than CUDA based software that has been out and updated for ~6 years due to the fact that I have full control over all the code I use. You might want to check the discussions on reddit for this project: https://www.reddit.com/r/MachineLearning/comments/ilcw2f/p_v... and https://www.reddit.com/r/programming/comments/il9sar/vulkan_...

Likely any HPC application that has an FFT somewhere in its pipeline and is otherwise amenable to being run on a GPU.

Fluid flow, heat transfer, and other such physical phenomena that you might want to simulate.

Phase correlation in image processing is another example. (https://en.wikipedia.org/wiki/Phase_correlation)

MD simulations rely on FFT but I'm not sure how much is typically (or can be) done on the GPU. For example, NAMD employs cuFFT on the GPU in some cases. (https://aip.scitation.org/doi/10.1063/5.0014475)

Machine learning uses CNNs, which are directly based on FFTs.

How are CNNs directly based on FFTs? Sure you can use CNNs with FFT features, but in my experience this is not common.

Convolutions are typically computed using FFTs.

https://en.wikipedia.org/wiki/Convolution_theorem

He is not wrong, convolutions between an image and a small kernel can be done faster by direct multiplication than by padding the kernel and performing FFT + iFFT. This is what tensor cores are aiming to do really fast. However, doing a convolution betwen an image and a kernel with the similar size is the general use case for the convolution theorem and is the thing that is currently implemented in VkFFT.

It could be used to accelerate Convolutional Neural Nets training [0]

[0] https://arxiv.org/abs/1312.5851

If you could filter and focus raw radar data in realtime it would be really cool!

Software defined radio / RF DSP is another area where FFT and IFFT performance and accuracy are critical.

Imaging. E.g., large convolutions.

The same as any FFT, but accelerated; with the tradeoff that the cost of moving data from and to the GPU needs to be amortized. It's also a good proof of concept for other kinds of GPU computations.