Efficient recurrent neural network methods for anomalously diffusing single particle short and noisy trajectories

Abstract

Anomalous diffusion occurs at very different scales in nature, from atomic systems to motions in cell organelles, biological tissues or ecology, and also in artificial materials, such as cement. Being able to accurately measure the anomalous exponent associated to a given particle trajectory, thus determining whether the particle subdiffuses, superdiffuses or performs normal diffusion, is of key importance to understand the diffusion process. Also it is often important to trustingly identify the model behind the trajectory, as it this gives a large amount of information on the system dynamics. Both aspects are particularly difficult when the input data are short and noisy trajectories. It is even more difficult if one cannot guarantee that the trajectories output in experiments are homogeneous, hindering the statistical methods based on ensembles of trajectories. We present a data-driven method able to infer the anomalous exponent and to identify the type of anomalous diffusion process behind single, noisy and short trajectories, with good accuracy. This model was used in our participation in the anomalous diffusion (AnDi) challenge. A combination of convolutional and recurrent neural networks was used to achieve state-of-the-art results when compared to methods participating in the AnDi challenge, ranking top 4 in both classification and diffusion exponent regression.

Bayesian deep learning for error estimation in the analysis of anomalous diffusion

“…Complementing the discussion of the regression in section V A, we now evaluate the trained Multi-SWAG models on the test data set. The achieved accuracies depicted in figure 9a are in line with the best performing participants of the AnDi-Challenge [59,62,63,[65][66][67][68][69][70][71][72][73][74][75][76][77]. As one would expect the achieved accuracy increases with trajectory length, starting from 44.9% for T = 10 and reaching 91.7% for T = 500.…”

“…In order to quantify the performance of our Multi-SWAG [88] models we test them on a new set of computer generated trajectories using the andi-datasets package. For the general prediction of the anomalous diffusion exponent α we obtain results comparable to the best participants in the AnDi-Challenge [59,62,63,[65][66][67][68][69][70][71][72][73][74][75][76][77]. The achieved mean average error for different trajectory lengths in figure 4a shows an expected decreasing trend with trajectory length.…”

“…The challenge consisted of three tasks, among them the determination of the anomalous diffusion exponent α and the underlying diffusion model from single particle trajectories. The entries included a wide variety of methods ranging from mathematical analysis of trajectory features [63,64], to Bayesian Inference [65][66][67], to a wide variety of machine learning techniques [59,[68][69][70][71][72][73][74][75][76][77]. While the best results were achieved by deep learning (neural networks), this approach suffers from the so-called Black Box Problem, delivering answers without providing explanations as to how these are obtained or how reliable they are [78].…”

Inferring the fractional nature of Wu Baleanu trajectories

“…Recently, within the frame of the Andi Challenge [26], machine learning methods, alone or combined with some statistical measures, have demonstrated their efficiency in (i) classifying anomalous diffusion noisy trajectories according to one of the previous five generative models and (ii) inferring the anomalous diffusion exponent. We refer the reader to [25] and some subsequent works in which some of these models were fully developed [9,1,7]; see also [24,6,8]. It is also worth mentioning the recent interest in incorporating machine learning methods and intelligent algorithms in the study of formal mathematical problems.…”

“…In this work, we study if we can infer the µ parameter and the scaling factor ν of Wu-Baleanu trajectories. We have chosen an architecture based on recurrent neural networks (RNN), the same that provided the best results in inferring the exponent α of onedimensional trajectories in the Andi Challenge [25,7], for trying to infer these parameters and measuring up to which point there is a straightforward relation any given trajectory of this type and the corresponding parameters µ and ν involved in generating it. In Section 2, we give some details of the model architecture, revisiting some basic fundamentals of our machine learning models.…”