Neural network-based anomalous diffusion parameter estimation approaches for Gaussian processes

Anomalous diffusion behavior can be observed in many single-particle (contained in crowded environments) tracking experimental data. Numerous models can be used to describe such data. In this paper, we focus on two common processes: fractional Brownian motion (fBm) and scaled Brownian motion (sBm). We proposed novel methods for sBm anomalous diffusion parameter estimation based on the autocovariance function (ACVF). Such a function, for centered Gaussian processes, allows its unique identification. The first estimation method is based solely on theoretical calculations, and the other one additionally utilizes neural networks (NN) to achieve a more robust and well-performing estimator. Both fBm and sBm methods were compared between the theoretical estimators and the ones utilizing artificial NN. For the NN-based approaches, we used such architectures as multilayer perceptron (MLP) and long short-term memory (LSTM). Furthermore, the analysis of the additive noise influence on the estimators’ quality was conducted for NN models with and without the regularization method.