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 $10^6$ simulated trajectories. We associate this data efficiency with the emergence of distinct scale fingerprints disentangling underlying diffusion mechanisms in the wavelet spectra.

翻译：机器学习已成为分析异常扩散轨迹的通用工具，但现有方法大多基于大量模拟数据进行训练。相比之下，实验轨迹（如单粒子追踪所得）通常稀缺，且可能与模拟所用的理想化模型存在显著差异，导致机器学习方法应用于真实数据时性能下降甚至失效。为解决这一不匹配问题，我们提出一种基于小波的异常扩散表示方法，能够直接从实验记录中实现数据高效学习。该表示通过将六种互补小波族应用于每条轨迹，并融合所得的小波模量尺度图构建而成。我们首先在andi-datasets基准的模拟轨迹上评估小波表示方法，结果显示仅用1000条训练轨迹时，其性能已明显优于基于特征和基于轨迹的方法，且在大规模训练集上仍保持优势。随后，我们利用该表示方法直接学习荧光微球在F-肌动蛋白网络中扩散的实验单粒子追踪轨迹，结果表明小波表示在扩散指数回归和网格尺寸分类任务中均优于现有方法。特别地，在预测实验轨迹的扩散指数时，使用小波表示基于1200条实验轨迹训练的模型，其误差显著低于完全基于$10^6$条模拟轨迹训练的最先进深度学习模型。我们将这种数据高效性归因于小波谱中解耦潜在扩散机制的独特尺度指纹的出现。