An inversion method
for time-resolved data from ultrafast
experiments
is introduced, based on forward-optimization in a trajectory basis.
The method is applied to experimental data from X-ray scattering of
the photochemical ring-opening reaction of 1,3-cyclohexadiene and
electron diffraction of the photodissociation of CS2. In
each case, inversion yields a model that reproduces the experimental
data, identifies the main dynamic motifs, and agrees with independent
experimental observations. Notably, the method explicitly accounts
for continuity constraints and is robust even for noisy data.