Fig. 1. Schematic illustration of the CO-tip AFM imaging process and the proposed solution for the inverse imaging problem.

(A to D) The imaging process Φ : X→ Y of molecular geometry X (A) originates predominantly from probe particle (PP) displacement due to interactions with sample atoms (B). The resulting PP displacement $\mathrm{\Delta }\overrightarrow{r}$ is plotted in (C). The fibers show deflection of the PP as it approaches the surface, with the red-blue gradient representing the tip-sample distance (red, far; blue, close). (D) The resulting AFM frequency shift [$\mathrm{\Delta }f(\overrightarrow{r})$] images Y obtained by integrating the forces felt by the relaxed PP over its path. (E to G) The inverse imaging process (i.e., reconstruction of geometry) Φ⁻¹ : Y→ X approximated by a convolutional NN (F) transforming a 3D stack of AFM images Y (E) to a description of the molecular geometry X [represented by, e.g., van der Waals spheres (G)].