Abstract Biological intracellular transport is predominantly heterogeneous in both time and space, exhibiting varying non-Brownian behaviour. Characterisation of this movement through averaging methods over an ensemble of trajectories or over the course of a single trajectory often fails to capture this heterogeneity adequately. Here, we have developed a deep learning feedforward neural network trained on fractional Brownian motion, which provides a novel, accurate and efficient characterization method for resolving heterogeneous behaviour of intracellular transport both in space and time. Importantly, the neural network requires significantly fewer data points compared to established methods, such as mean square displacements, rescaled range analysis and sequential range analysis. This enables robust estimation of Hurst exponents for very short time series data, making possible direct, dynamic segmentation and analysis of experimental tracks of rapidly moving cellular structures such as endosomes and lysosomes. By using this analysis, we were able to interpret anomalous intracellular dynamics as fractional Brownian motion with a stochastic Hurst exponent.