  We develop a chemical evolution model in order to study the star formation
history of the Milky Way. Our model assumes that the Milky Way is formed from a
closed box-like system in the inner regions, while the outer parts of the disc
experience some accretion. Unlike the usual procedure, we do not fix the star
formation prescription (e.g. Kennicutt law) in order to reproduce the chemical
abundance trends. Instead, we fit the abundance trends with age in order to
recover the star formation history of the Galaxy. Our method enables one to
recover with unprecedented accuracy the star formation history of the Milky Way
in the first Gyrs, in both the inner (R<7-8kpc) and outer (R>9-10kpc) discs as
sampled in the solar vicinity. We show that, in the inner disc, half of the
stellar mass formed during the thick disc phase, in the first 4-5 Gyr. This
phase was followed by a significant dip in the star formation activity (at 8-9
Gyr) and a period of roughly constant lower level star formation for the
remaining 8 Gyr. The thick disc phase has produced as many metals in 4 Gyr as
the thin disc in the remaining 8 Gyr. Our results suggest that a closed box
model is able to fit all the available constraints in the inner disc. A closed
box system is qualitatively equivalent to a regime where the accretion rate, at
high redshift, maintains a high gas fraction in the inner disc. In such
conditions, the SFR is mainly governed by the high turbulence of the ISM. By
z~1 it is possible that most of the accretion takes place in the outer disc,
while the star formation activity in the inner disc is mostly sustained by the
gas not consumed during the thick disc phase, and the continuous ejecta from
earlier generations of stars. The outer disc follows a star formation history
very similar to that of the inner disc, although initiated at z~2, about 2 Gyr
before the onset of the thin disc formation in the inner disc.
