Deep learning for gravitational potentials, based on a snapshot of well-mixed tracer particles in phase space.
The basic idea of this approach is to first model the distribution function of the tracers using a normalizing flow. One can then calculate gradients of the distribution function at a large number of points in phase space. Then, we find the potential that renders the distribution function stationary at these points. We model the potential using a feed-forward neural network, which is both extremely flexible and easily differentiable. This latter property is critical, as the collisionless Boltzmann equation contains gradients of the potential (and of the distribution function).
See notebooks/plummer_sphere_example.ipynb for an explanation of the method
and a demonstration with a simple toy system - the Plummer Sphere with
isotropic velocities.
This version is implemented in Tensorflow 2.x. There is a matching PyTorch implementation at tingyuansen/deep-potential.