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Hierarchical Gradient-Based Genetic Sampling for Accurate Prediction of Biological Oscillations
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Proposes HGGS, a two-layer sampling framework (gradient-based filtering plus multigrid genetic sampling driven by residuals) that improves neural network prediction of oscillatory frequency in biological ODE systems.
Problem
Neural network prediction of biological oscillation frequency from ODE coefficients suffers from non-oscillatory bias (most samples non-periodic) and oscillatory boundary sensitivity (small coefficient changes near boundaries cause large frequency changes), which existing importance and uncertainty
Approach
A hierarchical sampler: gradient-based filtering ranks samples by local output-gradient magnitude to extract boundary samples and prune redundant non-oscillatory ones into a balanced coarse set, then multigrid genetic sampling (crossover and mutation between residual-stratified points, with Gaussian mixture stratification) iteratively adds new high-residual samples during training.
Key results
- On the Cell Cycle system HGGS reaches overall RMSE 0.0098 and lowest IR (1.10) and GI (0.58) among compared methods.
- On the Activator Inhibitor system HGGS reduces imbalance ratio from 11.84 (LHS) to 2.88 and achieves minority RMSE 0.0099 and overall RMSE 0.0044.
- HGGS reports 18%-31% minority and 16%-28% boundary error improvements over baselines on the Activator Inhibitor system and 8%-28% minority improvements on the Cell Cycle system.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HGGS instead of the compared sampling baselines | MLP biological oscillation prediction · Brusselator | overall RMSE | Helped |
| Use HGGS instead of the compared sampling baselines | MLP biological oscillation prediction · Cell Cycle | overall RMSE | Helped |
| Use HGGS instead of the compared sampling baselines | MLP biological oscillation prediction · MPF | overall RMSE | Helped |
| Use HGGS instead of the compared sampling baselines | MLP biological oscillation prediction · Activator Inhibitor | overall RMSE | Helped |
| Replace random sampling after Gradient-based Filtering with Multigrid Genetic Sampling (ablation) | HGGS · Four biological systems | RMSE | Helped |
| Add Gradient-based Filtering before Multigrid Genetic Sampling (ablation) | HGGS · Four biological systems | minority RMSE | Helped |
| Set MGS crossover-to-mutation sampling ratio to 6:4 rather than using only either operation (ablation) | HGGS on MPF · MPF | RMSE | Helped |
| Increase MGS sampling size (ablation) | HGGS on MPF · MPF minority subset | RMSE | Helped |
| Increase MGS sampling size beyond 2k new samples (ablation) | HGGS on MPF · MPF majority subset | RMSE | No clear effect |
| Increase GF filtering ratio (ablation) | HGGS on Cell Cycle · Cell Cycle majority subset | RMSE | Hurt |
| Increase GF filtering ratio (ablation) | HGGS on Cell Cycle · Cell Cycle minority subset | RMSE | Helped |
Surprising findings
- On the Brusselator system, US-P achieves slightly lower IR and GI than HGGS, and the differences among US-S, US-P and HGGS are minimal due to mild imbalance.
Limitations
- Evaluated only on four low-dimensional ODE systems with synthetic data
- Theoretical justification of residual-based sampling relies on a variance argument with approximations
- Method performance on Brusselator is comparable to US-P, showing limited gains under mild imbalance
Experimental setup
Datasets: Brusselator system simulations Cell Cycle system simulations MPF system simulations Activator Inhibitor system simulations
Benchmarks: Brusselator Cell Cycle MPF Activator Inhibitor
Metrics: RMSE imbalance ratio Gini index
Baselines: LHS WRS VeSSAL US-S US-P IS IS-dagger
Builds on: Importance Sampling Uncertainty Sampling SMOTE Latin Hypercube Sampling
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