Nowadays, there is a large number of time series of natural data to study geophysical and astrophysical phenomena and their characteristics. However, short length and data gaps pose a substantial problem for obtaining results on properties of the underlying physical phenomena with existing algorithms. Using only an equidistant subset of the data with coarse steps leads to loss of information. We present a method to recover missing data in time series. The approach is based on modeling the time series with manifolds of small dimension, and it is implemented with the help of neural networks. We applied this approach to real data on cosmogenic isotopes, demonstrating that it could successfully repair gaps where data was purposely left out. Multi-fractal analysis was applied to a true radiocarbon time series after recovering missing data.