Interpretable Forecasting in Multivariate Time Series Using Koopman Autoencoder and Fuzzy Transform
Bibliographic record
Abstract
This study investigates the modeling efficacy of Koopman Autoencoder (KAE) in comparison with LSTM, GRU, and Transformer architectures for multivariate time series (MTS) prediction tasks. We additionally evaluate the effect of fuzzy logic-based feature transformations (triangular and Gaussian membership functions) on learning dynamics and predictive performance. Synthetic MTS data comprising 16 channels with varying levels of additive Gaussian noise (0.0 and 0.1) are used to simulate realistic conditions. Experiments are conducted both with fuzzy-transformed inputs and raw features to assess comparative robustness. Results indicate that Transformers with triangular fuzzy transformation achieved the best predictive accuracy. Quantitative results show that fuzzy-transformed inputs significantly reduce prediction error across all models, with Transformer achieving the best MSE (0.0516) and R² (0.043) under triangular F-transform. PCA and t-SNE visualizations affirmed the distinct latent separability of Transformer and LSTM embeddings. While KAE yielded slightly lower predictive performance (MSE > 0.06), KAE embedding demonstrated advantages in latent space linearized embedding with more compressed, interpretability via saliency maps, and robustness to structured signal evolution. The results suggest KAE with fuzzy-transformed features offers a promising trade-off between interpretability and performance for explainable AI in time series feature embedding and forecasting.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.013 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".