  Fast and accurate simulation of imaging through atmospheric turbulence is
essential for developing turbulence mitigation algorithms. Recognizing the
limitations of previous approaches, we introduce a new concept known as the
phase-to-space (P2S) transform to significantly speed up the simulation. P2S is
build upon three ideas: (1) reformulating the spatially varying convolution as
a set of invariant convolutions with basis functions, (2) learning the basis
function via the known turbulence statistics models, (3) implementing the P2S
transform via a light-weight network that directly convert the phase
representation to spatial representation. The new simulator offers 300x --
1000x speed up compared to the mainstream split-step simulators while
preserving the essential turbulence statistics.
