# Data-Efficient Learning of Anomalous Diffusion with Wavelet Representations: Enabling Direct Learning from Experimental Trajectories

arXiv: https://arxiv.org/abs/2512.08510 · HTML: https://mlsanity.com/paper/2512.08510/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 122 references that are in the map.
- First posted on arXiv 9 Dec 2025.

## Builds on (most cited first, 20 of 20)

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- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Fast and Accurate Model Scaling](https://mlsanity.com/paper/2103.06877/) (2021)
- [Geometric deep learning reveals the spatiotemporal fingerprint of microscopic motion](https://mlsanity.com/paper/2202.06355/) (2022)
- [Learning physical properties of anomalous random walks using graph neural networks](https://mlsanity.com/paper/2103.11738/) (2021)
- [WaveNet-Based Deep Neural Networks for the Characterization of Anomalous Diffusion (WADNet)](https://mlsanity.com/paper/2106.08887/) (2021)
- [Learning minimal representations of stochastic processes with variational autoencoders](https://mlsanity.com/paper/2307.11608/) (2023)
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- [Characterization of anomalous diffusion through convolutional transformers](https://mlsanity.com/paper/2210.04959/) (2022)
- [Extreme Learning Machine for the Characterization of Anomalous Diffusion from Single Trajectories (AnDi-ELM)](https://mlsanity.com/paper/2105.02597/) (2021)
- [Variational inference of fractional Brownian motion with linear computational complexity](https://mlsanity.com/paper/2203.07961/) (2022)
- [Reinforcement Learning for Active Matter](https://mlsanity.com/paper/2503.23308/) (2025)
- [Preface: Characterisation of Physical Processes from Anomalous Diffusion Data](https://mlsanity.com/paper/2301.00800/) (2023)
- [Machine Learning Analysis of Anomalous Diffusion](https://mlsanity.com/paper/2412.01393/) (2024)
- [Multifractal-spectral features enhance classification of anomalous diffusion](https://mlsanity.com/paper/2401.07646/) (2024)
- [Bottom-up Iterative Anomalous Diffusion Detector (BI-ADD)](https://mlsanity.com/paper/2503.11529/) (2025)
- [AnomalousNet: A Hybrid Approach with Attention U-Nets and Change Point Detection for Accurate Characterization of Anomalous Diffusion in Video Data](https://mlsanity.com/paper/2504.05271/) (2025)
- [AI-Driven Consensus: Modeling Multi-Agent Networks with Long-Range Interactions through path-Laplacian Matrices](https://mlsanity.com/paper/2504.06894/) (2025)

## Abstract (arXiv)

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.