  In this paper, we construct new characteristic classes of fiber bundles via
flat connections with values in infinite-dimensional Lie algberas of
derivations. In fact, choosing a fiberwise metric, we construct a chain map to
the de Rham complex on the base space, and show that the induced map on
cohomology groups is independent of the choices. Moreover, we show that
applying the construction to a surface bundle, our construction gives
Morita-Mumford-Miller classes.
