Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Controlled Differential Equations on Long Sequences via Non-standard Wavelets
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add partially un-shared convolution (PUC) instead of fully unshared locally connected layers in the BCR decomposition | BCR-DE · general | validation/test performance | No clear effect |
| add perturbation (noise) of wavelet coefficients during training (ablation) | BCR-DE · EigenWorms classification | accuracy (%): +0.9 (77.8 to 78.7) | Helped |
| increase wavelet decomposition levels from 6 to 8 or more (ablation) | BCR-DE · Hodgkin-Huxley (20k) | MSE: MSE about 1e-2 or lower at level 6 to about 1e-4 at 8+ levels | Helped |
| use few decomposition levels (e.g., 2 or 3) instead of more levels (ablation) | BCR-DE · Hodgkin-Huxley (20k) | MSE / memory | Hurt |
| replace NCDE/NRDE with BCR-DE (wavelet-based integral transform) | NRDE baseline comparison · BIDMC regression (RR, HR, SpO2) | RMSE: BCR-DE better on SpO2 (1.18 vs 1.29) but worse on RR (1.53 vs 1.49) and HR (3.27 vs 2.97) | Mixed |
| replace NRDE with BCR-DE | EigenWorms classification · EigenWorms | accuracy (%): 77.8 vs 83.8 for best NRDE | Hurt |
| replace NRDE/NCDE with BCR-DE for auto-encoding and coupled DE tasks | BCR-DE · Coupled DEs (Lotka-Volterra, Van der Pol, Lorenz, Hodgkin-Huxley) and PPG/ECG auto-encoding | MSE and training time: BCR-DE lower MSE in most coupled DE settings; NCDE lower MSE on PPG/ECG auto-encoding (6.05e-5 vs 0.012) | Mixed |
| replace NRDE/NCDE with BCR-DE on masked reconstruction | BCR-DE · PPG masked reconstruction | MSE: 0.024 vs 0.106 for NRDE | Helped |
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