MONTE CARLO — GENERATE ROBUSTNESS CURVES¶
Generates N synthetic curves around one or more input curves for robustness studies and uncertainty propagation. Two sampling methods are available. Pointwise (default) computes empirical pointwise mean and std and draws RBF-smoothed Gaussian noise around them — fast, intuitive, but tends to produce roughly parallel sigma bands. PCA (recommended when 3+ input curves available) decomposes the input family into principal components, samples in PCA score space, and reconstructs; this preserves the spatially-varying scatter pattern (narrow where inputs cluster, wide where they diverge). Optional monotonic guard keeps stress-strain draws non-decreasing.
When to use¶
Tagged: curve, monte_carlo, robustness, uncertainty, variance, generator, gaussian_process, sampling.
Inputs¶
| Label | ID | Type | Default | Required | Description |
|---|---|---|---|---|---|
| Input Curves | curves | vector | — | ✓ | One or more reference curves on a common x-axis. Multiple curves drive an empirical pointwise mean and std; a single curve falls back to sigma_percent. |
| Number of Curves to Generate | n_samples | integer | 100 | ✓ | How many synthetic curves to produce. Typical 50-200 for robustness sweeps. |
| Sigma Percent (single-curve fallback) | sigma_percent | scalar | 0.1 | Relative noise level used only when a single input curve is provided. 0.10 = 10% of /y/ at each x. Ignored when 2+ input curves are connected. | |
| Correlation Length (fraction of x-range) — pointwise mode only | correlation_length | scalar | 0.05 | Smoothness knob for pointwise mode, expressed as a fraction of the x-range (0.05 = 5%). Larger values produce smoother, more shape-faithful draws; values near 0 produce jagged per-point noise. Ignored when sampling_method = pca. | |
| Sampling Method | sampling_method | select | pointwise | pointwise = empirical mean/std + RBF noise (fast, default). pca = principal-component decomposition of the input family + sampling in score space (preserves spatially-varying scatter; recommended when 3+ input curves are available). PCA mode falls back to pointwise when fewer than 3 input curves are provided. | |
| PCA Variance Threshold | pca_variance_threshold | scalar | 0.95 | PCA mode only. Cumulative variance fraction at which the worker stops retaining principal components (0.95 = retain enough components to explain 95% of input family variance). Higher values keep more components and capture finer detail; lower values produce smoother but less faithful draws. | |
| Enforce Monotonic (Non-Decreasing) | enforce_monotonic | select | no | When ‘yes’, each generated curve is clamped to be non-decreasing along x. Required for MAT_024 / hardening-curve material cards. | |
| Random Seed | seed | integer | 0 | Integer seed for reproducible draws. 0 means choose a random seed; the actual seed is reported in the output for re-runs. | |
| Output Curve Name Prefix | output_name_prefix | scalar | mc | Prefix for generated curve names. Curves are named ‘<prefix>_0001’, ‘<prefix>_0002’, etc. |
Outputs¶
| Label | ID | Type | Description |
|---|---|---|---|
| Generated Curves | generated_curves | vector | Curve group containing the N generated curves on the shared x-grid. |
| Mean + 2 sigma Band + Generated Mean | mean_and_band | vector | Four-curve group for validating generation quality: input mean, generated mean (mean of the N generated curves), input mean + 2sigma, input mean - 2sigma. Overlay input mean and generated mean to confirm the generator preserved the central tendency of the input family. |
| Seed Used | seed_used | integer | The random seed actually used (the input seed, or a randomly chosen seed if input was 0). |
| Mean Agreement RMSE | mean_rmse | scalar | RMSE between the input pointwise mean and the generated pointwise mean. A low value (relative to the y-range of the curves) confirms the generator preserved the central tendency. Use as a quick quality gate. |
| Status | status | string | Human-readable summary of the run: input count, grid size, sampling method used (pointwise / pca), PCA components retained (if applicable), monotonic flag, RMSE of mean agreement, seed. |
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