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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".