Flow-Guided Neural Operator for Self-Supervised Learning on Time Series Data

Self-supervised learning (SSL) is a powerful paradigm for learning from unlabeled time-series data. However, traditional methods such as masked autoencoders (MAEs) rely on reconstructing inputs from a fixed, predetermined masking ratio. Instead of this static design, we propose treating the corruption level as a new degree of freedom for representation learning. To achieve this, we introduce the Flow-Guided Neural Operator (FGNO), the first framework to combine operator learning with flow matching for SSL training. By leveraging Short-Time Fourier Transform (STFT) to enable computation under different time resolutions, our approach effectively learns mappings in functional spaces. We extract a rich hierarchy of features by tapping into different network layers ($l$) and generative time steps ($s$) that apply varying strengths of noise to the input data. This enables the extraction of versatile, task-specific representations—from low-level patterns to high-level semantics—all from a single model. We evaluated our model performance on two different biomedical domains, where our flow-based operator significantly outperforms established baselines. When applied to a sleep health dataset, it achieved 16\% RMSE improvement over MAE in skin temperature regression, while showing 1\% AUROC gain in classification tasks. On a neural decoding task for binary speech classification, our approach achieves a significant 20\% AUROC improvement compared to MAE, highlighting its ability to learn powerful, task-adaptable representations.