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

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  • Henrik Seckler

    (University of Potsdam)

  • Ralf Metzler

    (University of Potsdam
    Asia Pacific Centre for Theoretical Physics)

Abstract

Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety of systems, from single-molecule motion in living-cells to movement ecology. The quest is to decipher the physical mechanisms encoded in the data and thus to better understand the probed systems. We here augment recently proposed machine-learning techniques for decoding anomalous-diffusion data to include an uncertainty estimate in addition to the predicted output. To avoid the Black-Box-Problem a Bayesian-Deep-Learning technique named Stochastic-Weight-Averaging-Gaussian is used to train models for both the classification of the diffusion model and the regression of the anomalous diffusion exponent of single-particle-trajectories. Evaluating their performance, we find that these models can achieve a well-calibrated error estimate while maintaining high prediction accuracies. In the analysis of the output uncertainty predictions we relate these to properties of the underlying diffusion models, thus providing insights into the learning process of the machine and the relevance of the output.

Suggested Citation

  • Henrik Seckler & Ralf Metzler, 2022. "Bayesian deep learning for error estimation in the analysis of anomalous diffusion," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
  • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-34305-6
    DOI: 10.1038/s41467-022-34305-6
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    References listed on IDEAS

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    1. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169, January.
    2. Qi Wang & Yue Ma & Kun Zhao & Yingjie Tian, 2022. "A Comprehensive Survey of Loss Functions in Machine Learning," Annals of Data Science, Springer, vol. 9(2), pages 187-212, April.
    3. S. Condamin & O. Bénichou & V. Tejedor & R. Voituriez & J. Klafter, 2007. "First-passage times in complex scale-invariant media," Nature, Nature, vol. 450(7166), pages 77-80, November.
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    1. Pauline Formaglio & Marina E. Wosniack & Raphael M. Tromer & Jaderson G. Polli & Yuri B. Matos & Hang Zhong & Ernesto P. Raposo & Marcos G. E. Luz & Rogerio Amino, 2023. "Plasmodium sporozoite search strategy to locate hotspots of blood vessel invasion," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    2. Guo, Wei & Liu, Ying-Zhou & Huang, Fei-Jie & Shi, Hong-Da & Du, Lu-Chun, 2023. "Brownian particles in a periodic potential corrugated by disorder: Anomalous diffusion and ergodicity breaking," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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