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Data-efficient learning of anomalous diffusion with wavelet representations: Enabling direct learning from experimental trajectories

Gongyi Wang, Yu Zhang, and Zihan Huang*

  • *Contact author: huangzih@hnu.edu.cn
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Phys. Rev. Research 8, 023122 – Published 5 May, 2026

DOI: https://doi.org/10.1103/sx22-92gh

Abstract

Machine learning (ML) has become a versatile tool for analyzing anomalous diffusion trajectories, yet most existing pipelines are trained on large collections of simulated data. In contrast, experimental trajectories, such as those from single-particle tracking (SPT), are typically scarce and may differ substantially from the idealized models used for simulation, leading to degradation or even breakdown of performance when ML methods are applied to real data. To address this mismatch, we introduce a wavelet-based representation of anomalous diffusion that enables data-efficient learning directly from experimental recordings. This representation is constructed by applying six complementary wavelet families to each trajectory and combining the resulting wavelet modulus scalograms. We first evaluate the wavelet representation on simulated trajectories from the andi-datasets benchmark, where it clearly outperforms both feature-based and trajectory-based methods with as few as 1000 training trajectories and still retains an advantage on large training sets. We then use this representation to learn directly from experimental SPT trajectories of fluorescent beads diffusing in F-actin networks, where the wavelet representation remains superior to existing alternatives for both diffusion-exponent regression and mesh-size classification. In particular, when predicting the diffusion exponents of experimental trajectories, a model trained on 1200 experimental tracks using the wavelet representation achieves significantly lower errors than state-of-the-art deep learning models trained purely on 106 simulated trajectories. We associate this data efficiency with the emergence of distinct scale fingerprints disentangling underlying diffusion mechanisms in the wavelet spectra. These findings position the wavelet representation as a data-efficient basis for machine-learning analysis of anomalous diffusion, reducing reliance on simulation-based training and enabling more direct use of experimental trajectories.

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Phys. Rev. Research 8, 023122– Published 5 May, 2026
  • Received 10 December 2025
  • Accepted 18 April 2026
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