The thicknesses of liquid films on corrugated plate walls at different Reynolds numbers are measured based on the plane laser induced fluorescence method. Using the small data amount method, the maximum Lyapunov exponent of a liquid film thickness time series under different working conditions is calculated, and the chaotic characteristics of the liquid film are analyzed. And a back propagation neural network prediction model is established. The results reveal that the free-falling film thickness under different Reynolds numbers is consistent with the chaotic characteristics and that the maximum Lyapunov exponent of the liquid film thickness time series obtained by the small data amount method is positively correlated with the Reynolds number. To clearly indicate the chaotic characteristics of the liquid film, isolated peaks generated in regions with large Reynolds numbers are coupled with the gravity of the liquid film and the superposition effect between different liquid films.