  DNA replication stands as one of the fundamental biological processes crucial
for cellular functioning. Recent experimental developments enable the study of
replication dynamics at the single-molecule level for complete genomes,
facilitating a deeper understanding of its main parameters. In these new data,
replication dynamics is reported by the incorporation of an exogenous chemical,
whose intra-cellular concentration follows a nonlinear function. The analysis
of replication traces thus gives rise to a nonlinear inverse problem,
presenting a nonconvex optimization challenge. We demonstrate that under
noiseless conditions, the replication dynamics can be uniquely identified by
the proposed model. Computing a global solution to this optimization problem is
specially challenging because of its multiple local minima. We present the
DNA-inverse optimization method that is capable of finding this global solution
even in the presence of noise. Comparative analysis against state-of-the-art
optimization methods highlights the superior computational efficiency of our
approach. DNA-inverse enables the automatic recovery of all configurations of
the replication dynamics, which was not possible with previous methods.
