  We consider approximations formed by the sum of a linear combination of given
functions enhanced by ridge functions -- a Linear/Ridge expansion. For an
explicitly or implicitly given function, we reformulate finding a best
Linear/Ridge expansion in terms of an optimization problem. We introduce a
particle grid algorithm for its solution. Several numerical results underline
the flexibility, robustness and efficiency of the algorithm.
  One particular source of motivation is model reduction of parameterized
transport or wave equations. We show that the particle grid algorithm is able
to produce a Linear/Ridge expansion as an efficient nonlinear model reduction.
