in silico
Phase 1 : In Silico Validation (Synthetic ESM Emulator)
- Objectif
- To falsify the core mechanism using a synthetic, computationally cheap surrogate of a high-dimensional ESM, testing whether the HM framework can reduce required evaluations by an order of magnitude under idealized conditions.
- Coût estimé
- €500-2000
- Durée estimée
- 4-6 weeks
- Critères de réussite
- Median reduction in ESM evaluations (HM vs. PPE) · ≥ 10x reduction (i.e., HM median < 1,000 evaluations vs. PPE 10,000) · (Count of synthetic function calls for HM (including initial design + all waves) vs. 10,000 for PPE; computed over 10 replicates.)
- Emulator accuracy (normalized RMSE) after 2nd wave · < 0.10 (10% of observational std dev) · (Hold-out validation: 20% of synthetic runs from 2nd wave held out; RMSE computed on held-out points, normalized by std dev of synthetic observations.)
- Non-implausible volume fraction after 3 waves · < 0.01 (1% of original space) · (Monte Carlo sampling of 10^6 points from final non-implausible region; fraction computed as count of points with I(θ) ≤ 3.0 divided by 10^6.)
- On continue si
- All three success criteria met in at least 8 out of 10 synthetic experiments.
- On arrête si
- Fewer than 5 out of 10 experiments meet the 10x reduction criterion, OR emulator RMSE > 0.15 in more than 3 experiments.
- On réoriente si
- If HM shows >10x reduction but emulator RMSE >0.15, consider using a different emulator (e.g., Deep GP or Random Forest) in Phase 2.
- Risques
- Synthetic function is too smooth; real ESM may be more non-linear or discontinuous.Probabilité : mediumParade : Test with synthetic functions of varying smoothness (Matérn 1/2, 3/2, 5/2) and add a “chaotic” term (e.g., small random perturbation) to simulate non-smoothness.
- HM fails to converge because the initial design is too sparse in 40 dimensions.Probabilité : mediumParade : Use a maximin LHS design with N = 10 * dim = 400 initial points; if that fails, increase to N = 20 * dim = 800.
- Computational cost of training GP emulator in 40 dimensions becomes prohibitive (O(N^3)).Probabilité : lowParade : Use sparse GP approximations (e.g., `DiceKriging` with `covtype = 'gauss'` and `coef.cov = 'MLE'` with a small nugget). If still too slow, limit to 1,000 training points per wave.