20260210 meeting

Background

In this experiment, the MERRA-2 dataset is adopted as the experimental sample. From the previous experiment (20260203 meeting), it was observed that setting the diffusion parameters to

• T: 500
• beta_0: 0.0008
• beta_T: 0.08

yields superior time-series forecasting performance. Therefore, all experiments in this study are conducted using this parameter configuration.

Time-Series Distortion Issue

The parameters adjusted in this experiment are s4_state_dim and s4_dropout, aiming to examine whether these adjustments influence the predictive performance.

All following experiments also include spatial standardization (SP) and the corresponding imputation results for unknown locations.

Naming Scheme

Experiments are named using the format XXX-XXXX-XX, where XXX means whether $autoFRK$ is used during training; XXXX for number of training iterations; XX means whether spatial standardization is applied. For example, NoFRK-4000-NoSP means no $autoFRK$ during training, 4,000 iterations, no spatial normalization during inference.

s4_state_dim128-s4_dropout0.1

FRK-4000-SP

FRK-4000-NoSP

NoFRK-4000-SP

NoFRK-4000-NoSP

s4_state_dim512-s4_dropout0.1

FRK-4000-SP

FRK-4000-NoSP

NoFRK-4000-SP

NoFRK-4000-NoSP

s4_state_dim128-s4_dropout0.5

FRK-4000-SP

FRK-4000-NoSP

NoFRK-4000-SP

NoFRK-4000-NoSP

s4_state_dim512-s4_dropout0.5

FRK-4000-SP

FRK-4000-NoSP

NoFRK-4000-SP

The experiment for this configuration has not yet been conducted.

NoFRK-4000-NoSP

The experiment for this configuration has not yet been conducted.

Conclusion

The experimental results show that when s4_state_dim is set to 128 and s4_dropout is 0.5, the model achieves the best predictive performance among all experiment configurations. The findings indicate that a smaller state dimension (128) combined with a higher dropout rate (0.5) most effectively captures spatiotemporal patterns while suppressing overfitting, thereby significantly enhancing the model’s generalization capability on unseen spatial and temporal regions.

The experiments also confirm that applying spatial standardization (SP) during the final unknown-location imputation step effectively reduces imputation errors.

FRK-SP

Using the most stable configuration, FRK-SP (i.e., with AutoFRK and spatial standardization), we compare the metrics for Unknown Locs & Future:

• s4_state_dim = 128 (Dropout 0.1)
  MSPE is 174.77, and RMSPE is 13.22.

• s4_state_dim = 128 (Dropout 0.5)
  MSPE is 166.19, and RMSPE is 12.89.

• s4_state_dim = 512 (Dropout 0.1)
  MSPE is 200.62, and RMSPE is 14.16.

• s4_state_dim = 512 (Dropout 0.5)
  MSPE is 177.84, and RMSPE is 13.34.

These results suggest that, for this dataset and task scale, a 128-dimensional state space is sufficient to capture the spatiotemporal structure. Increasing the dimension to 512 likely introduces too many parameters, causing overfitting under limited training data and degrading the model’s inference performance on unknown locations.

SP

The experiments highlight that spatial standardization is crucial for stable data imputation and prevents catastrophic prediction explosions.

• With SP (SP)

  All SP configurations maintain MSPE within a reasonable range (35–200).

• Without SP (NoSP)

  Nearly all NoSP configurations, regardless of 128/512 dimension or FRK usage, show extreme MSPE explosions for Unknown Locs, reaching $10^{27}$ to $10^{29}$ magnitudes.

AutoFRK

Under the use of SP, the results show that:

• s4_state_dim = 128

  Incorporating FRK during training improves prediction accuracy for unknown locations.

• s4_state_dim = 512

  Omitting FRK during training yields better prediction performance.

Effect of s4_dropout

A comparison of the two experiments with state dimension 128 shows that increasing the dropout rate has a significant positive impact when working with the MERRA-2 dataset:

• s4_dropout = 0.5 (Best)
  Achieves an MSPE of 166.19 on the Unknown Locs & Future metric.

• s4_dropout = 0.1
  Achieves an MSPE of 174.77 on the same metric.

These results indicate that a higher dropout rate substantially reduces prediction error.

References

• Zhu X, Xiong Y, Wu M, et al. Weather2K: A Multivariate Spatio-Temporal Benchmark Dataset for Meteorological Forecasting Based on Real-Time Observation Data from Ground Weather Stations[C]//International Conference on Artificial Intelligence and Statistics. PMLR, 2023: 2704-2722.
• Juan Lopez Alcaraz, Nils Strodthoff (2022). Diffusion-based time series imputation and forecasting with structured state space models. Transactions on Machine Learning Research. Retrieved from https://openreview.net/forum?id=hHiIbk7ApW
• SSSD (2022). GitHub. Retrieved from https://github.com/AI4HealthUOL/SSSD