Integrate High Dimension highly oscillating integral

Hi, everyone, I’m considering to compute the integral
for d>2.
I have already read the paper QUADRATURE METHODS FOR MULTIVARIATE HIGHLY OSCILLATORY INTEGRALS USING DERIVATIVES and noticed that for d=2, there is a doable method, but the method introduced in the paper could be intractable when d>2.

Is there any progress for this topic? And is there anyone package for such kinds of methods?

Not that I’m aware of (student of the author of that paper)

In 1D there’s

OK. Got it. Thanks!