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Learning from Polar Representation: An Extreme-Adaptive Model for Long-Term Time Series Forecasting
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Proposes DAN, an extreme-adaptive long-term (h=288) streamflow forecasting network with polar (far/near/indicator) representation learning, distance-weighted multi-loss, GMM indicators, and Kruskal-Wallis oversampling.
Problem
Long-term streamflow forecasting is hard because of rare extreme events and long-range dependencies; existing models handle one of these but not both.
Approach
DAN splits the target into far (extreme) and near (normal) polar representations plus an indicator series, trained with distance-weighted RMSE losses and a gate control vector, and oversamples extreme-containing windows via Kruskal-Wallis H-statistic sampling; the RepGen/RepMerg stacks are expandable.
Key results
- DAN achieved about 19% relative RMSE reduction over the second-best multivariate model on average, and 30% on UpperPen.
- In the univariate setting DAN beat NBeats by 18%, 49%, and 52% RMSE reduction on Ross, Saratoga, and SFC; NBeats was 6% better on UpperPen.
- Kruskal-Wallis oversampling with p=20-40% (epsilon=10) lowered RMSE_far to 23.5 on Ross and 118.1 on SFC versus 28.7 and 129.0 without oversampling.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DAN instead of the strongest reported baseline | Multivariate streamflow forecasting · Ross, Saratoga, UpperPen, and SFC | RMSE: overall 19% relative RMSE reduction | Helped |
| Use DAN instead of the strongest reported baseline | Univariate streamflow forecasting · Ross, Saratoga, and SFC | RMSE: 18%, 49%, and 52% | Helped |
| Use DAN instead of NBeats | Univariate streamflow forecasting · UpperPen | RMSE: 6% relative RMSE reduction compared to DAN | Hurt |
| Decrease p for Kruskal-Wallis sampling (epsilon=10) (ablation) | DAN · Ross and SFC extreme points | RMSE_far: Ross: 28.7 -> 23.5; SFC: 129.0 -> 118.1 | Helped |
| Add the double-CNN indicator refine layer (ablation) | DAN with the EDR architecture and ground-truth rainfall indicator · Ross | prediction quality | Helped |
| Add the RepMerg layer (ablation) | DAN with the EDR architecture and ground-truth rainfall indicator · Ross | prediction quality | Helped |
| Add the remaining regularization loss items beyond L3 (ablation) | DAN with the EDR architecture and ground-truth rainfall indicator · Ross | prediction quality | Helped |
| Add polar representation of the basic series (ablation) | DAN · Ross | prediction accuracy at fluctuation corners | Helped |
| Add the gate control vector mechanism (ablation) | DAN · Ross | prediction quality | Helped |
Surprising findings
- Informer and NLinear follow extreme events better than other baselines but overpredict peaks, while DLinear and Attention-LSTM underpredict them.
- Simple linear models (NLinear, DLinear) are competitive with transformer baselines on some sensors, while transformers are inconsistent across datasets.
Limitations
- Evaluated only on four streamflow series from one county (Santa Clara), limiting generality.
- Results for the main table come from a single seed; multi-seed statistics are in the appendix and show slight variance, with DAN's mean sometimes above the best-seed values in the main table.
Experimental setup
Datasets: Ross streamflow and rainfall Saratoga streamflow and rainfall UpperPen streamflow and rainfall SFC streamflow and rainfall
Benchmarks: Santa Clara County streamflow (Ross, Saratoga, UpperPen, SFC) h=288 forecasting
Metrics: RMSE MAPE RMSE_far
Baselines: FEDFormer Informer NLinear DLinear NEC+ Attention-LSTM N-BEATS
Builds on: NEC+ N-BEATS Informer FEDFormer DLinear
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