Measurement of anomalous diffusion using recurrent neural networks

Bò, Stefano; Schmidt, Falko; Eichhorn, Ralf; Volpe, Giovanni

doi:10.1103/physreve.100.010102

Cited by 96 publications

(109 citation statements)

References 47 publications

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“…For dataset (ii), we present results two training datasets: dark blue for a mixed dataset and light blue for a FBM dataset. trajectory characterization [29,38]. The development of these methods and of other deep learning architectures may help to avoid the preprocessing procedure and could lead to increase the accuracy on the problems described in this work.…”

Section: Discussionmentioning

confidence: 99%

Single trajectory characterization via machine learning

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In order to study transport in complex environments, it is extremely important to determine the physical mechanism underlying diffusion and precisely characterize its nature and parameters. Often, this task is strongly impacted by data consisting of trajectories with short length (either due to brief recordings or previous trajectory segmentation) and limited localization precision. In this paper, we propose a machine learning method based on a random forest architecture, which is able to associate single trajectories to the underlying diffusion mechanism with high accuracy. In addition, the algorithm is able to determine the anomalous exponent with a small error, thus inherently providing a classification of the motion as normal or anomalous (subor super-diffusion). The method provides highly accurate outputs even when working with very short trajectories and in the presence of experimental noise. We further demonstrate the application of transfer learning to experimental and simulated data not included in the training/test dataset. This allows for a full, high-accuracy characterization of experimental trajectories without the need of any prior information.In the last decades, the research in biophysics has conveyed large efforts toward the development of experimental techniques allowing the visualization of biological processes one molecule at a time [1-4]. These efforts have been mainly driven by the concept that ensemble-averaging hides important features that are relevant for cellular function. Somehow expectedly, experiments performed by means of these techniques have shown a large heterogeneity in the behavior of biological molecules, thus fully justifying the use of these raffinate tools.Besides, experiments performed using single particle tracking [3] have revealed that even chemically-identical molecules in biological media can display very different behaviors, as a consequence of the complex environment where diffusion takes place. By way of example, this heterogeneity is reflected in the broad distribution of dynamic parameters of distinct individual trajectories corresponding to the same molecular species, such as the diffusion coefficient, well above stochastic indetermination. Typically, the trajectories are analyzed by quantifying the (time-averaged) mean square displacement (tMSD) as a function of the time lag τ [5]:The calculation of this quantity-expected to scale linearly for a Brownian walker in a homogeneous environment-has provided a ubiquitous evidence of anomalous behaviors in biological systems, characterized by an asymptotic nonlinear scaling of the tMSD curve d t a 2. More experiments have shown that the anomalous exponent can vary from particle to particle ( figure 1(a)) as a consequence of molecular interactions and that these changes can be experienced by the same particle in space/time [6]. Several methods have been OPEN ACCESS RECEIVED

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Section: Discussionmentioning

confidence: 99%

Single trajectory characterization via machine learning

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“…As another example, motile cells, bacteria or artificial active particles may exhibit anomalous diffusion 7 . Their subdiffusive and superdiffusive dynamics have been classified and characterized using recurrent nets 47 (Fig. 3b) and random forests 48 , determining the value of the anomalous diffusion exponent and its temporal fluctuations, which is essential to discover the mechanisms that generate motility, and determine anisotropic and heterogeneous motility patterns 49,50 .…”

Section: Box 1 | Overview Of Machine-learning Methodsmentioning

confidence: 99%

“…However, in the case of machine-learning models, a danger is that extrapolation occurs unintentionally and in an uncontrolled fashion. For example, recurrent nets may correctly predict an anomalous diffusion exponent in a certain range, but fail for data with smaller or larger exponents than the training set 47 . More fundamentally, it is not known how the method would perform on data that is generated by different models from those in the training set.…”

Section: Improvement Of Data Acquisition and Analysismentioning

confidence: 99%

“…b, recurrent nets (rNN) allow the characterization of the anomalous diffusion exponent α better than the standard mean square displacement (MSD), especially for very few sample point numbers (left panel), even in situations where standard methods fail, for example for irregularly sampled and intermittent processes (the right panel shows the accuracy of the prediction for an irregularly sampled trajectory).Figure adaptedwith permission from ref 46 ,. aPS (a); and ref 47 ,. aPS (b).…”

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Machine learning for active matter

et al. 2020

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“…Deep learning has been redefining the state-of-the-art for processing various signals collected and digitized by different sensors, monitoring physical processes for, e.g., biomedical image analysis [1][2][3][4], speech recognition [5,6] and holography [7][8][9][10], among many others [11][12][13][14][15][16][17]. Furthermore, deep learning and related optimization tools have been harnessed to find data-driven solutions for various inverse problems arising in, e.g., microscopy [18][19][20][21][22], nanophotonic designs and plasmonics [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Misalignment resilient diffractive optical networks

et al. 2020

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AbstractAs an optical machine learning framework, Diffractive Deep Neural Networks (D2NN) take advantage of data-driven training methods used in deep learning to devise light–matter interaction in 3D for performing a desired statistical inference task. Multi-layer optical object recognition platforms designed with this diffractive framework have been shown to generalize to unseen image data achieving, e.g., >98% blind inference accuracy for hand-written digit classification. The multi-layer structure of diffractive networks offers significant advantages in terms of their diffraction efficiency, inference capability and optical signal contrast. However, the use of multiple diffractive layers also brings practical challenges for the fabrication and alignment of these diffractive systems for accurate optical inference. Here, we introduce and experimentally demonstrate a new training scheme that significantly increases the robustness of diffractive networks against 3D misalignments and fabrication tolerances in the physical implementation of a trained diffractive network. By modeling the undesired layer-to-layer misalignments in 3D as continuous random variables in the optical forward model, diffractive networks are trained to maintain their inference accuracy over a large range of misalignments; we term this diffractive network design as vaccinated D2NN (v-D2NN). We further extend this vaccination strategy to the training of diffractive networks that use differential detectors at the output plane as well as to jointly-trained hybrid (optical-electronic) networks to reveal that all of these diffractive designs improve their resilience to misalignments by taking into account possible 3D fabrication variations and displacements during their training phase.

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Measurement of anomalous diffusion using recurrent neural networks

Cited by 96 publications

References 47 publications

Single trajectory characterization via machine learning

Single trajectory characterization via machine learning

Machine learning for active matter

Misalignment resilient diffractive optical networks

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