  An inversion method for time-resolved data from ultrafast experiments is
introduced, based on forward-optimisation 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 for noisy data.
