  We present a method to automatically approximate moment-based invariants of
probabilistic programs with non-polynomial updates of continuous state
variables to accommodate more complex dynamics. Our approach leverages
polynomial chaos expansion to approximate non-linear functional updates as sums
of orthogonal polynomials. We exploit this result to automatically estimate
state-variable moments of all orders in Prob-solvable loops with non-polynomial
updates. We showcase the accuracy of our estimation approach in several
examples, such as the turning vehicle model and the Taylor rule in monetary
policy.
