in silico
Phase 1: In Silico Validation on Synthetic 2-DOF Data
- Objective
- To falsify the core mechanism of the hybrid UQ framework in a controlled, high-fidelity simulation environment. This phase tests whether the combination of block bootstrap, geostatistical initialization, and homotopy continuation can achieve the target coverage and bias reduction on a known ground truth, before any physical experiments are considered.
- Estimated cost
- €500-2000
- Estimated duration
- 4-6 weeks
- Success criteria
- Coverage probability of the true 99th percentile · ≥ 0.94 (lower bound of 95% CI) · (One-sided z-test for proportions on the 100 synthetic datasets (H0: p ≤ 0.90, alpha=0.05).)
- Median absolute bias reduction vs. single best-fit · ≥ 25% reduction · (Paired Wilcoxon signed-rank test on the 100 datasets (H0: hybrid bias ≥ 90% of single best-fit bias).)
- Homotopy success rate · ≥ 80% of bootstrap resamples · (Exact binomial test comparing homotopy final RMSE vs. multi-start best RMSE (success = ≥5% lower).)
- Go if
- All three success criteria are met. The hybrid method demonstrates superior coverage and bias reduction in the synthetic environment.
- No-go if
- Any of the three success criteria fail. The mechanism is falsified in the ideal case, and the approach should be abandoned or fundamentally rethought.
- Pivot if
- Coverage is met but bias reduction is marginal (e.g., 15-25%). Consider tuning the homotopy path or the geostatistical prior. If homotopy success rate is <80%, investigate the smoothness of the objective function and consider alternative continuation schemes.
- Risks
- The VBPBB algorithm is complex and may be difficult to implement correctly.Probability: mediumMitigation: Start with a simpler block bootstrap (e.g., moving block bootstrap) as a baseline. Validate the VBPBB implementation against a known periodic time series. Use the original paper’s code if available.
- The homotopy continuation may fail to converge for some bootstrap resamples due to non-smooth objective functions.Probability: mediumMitigation: Implement a robust path-following algorithm with adaptive step size. If convergence fails, use a fallback multi-start initialization. Document the failure rate.
- The 2-DOF model may be too simple to exhibit the “local minima” problem that homotopy is designed to solve.Probability: lowMitigation: Introduce a non-convex objective function by adding a sinusoidal penalty term or a multimodal parameter response. This will make the test more challenging and realistic.