Adaptive sampling strategies from model-order reduction can be embedded within amortized optimization frameworks to selectively refine surrogate accuracy near feasibility boundaries.

This discovery has a Claude-generated validation package with a full experimental design.

Precise Hypothesis

Spine & Adversarial ReadReady for validation

“This hypothesis tests whether embedding model-order-reduction-style greedy residual sampling into an amortized surrogate training loop reduces feasibility-boundary classification error by at least 30% relative to uniform sampling at equal oracle-query budget.”

• highBoundary-focused adaptive sampling is already well-established in active learning and Bayesian optimization (uncertainty sampling, margin sampling, constraint-aware BO); the 'model-order-reduction' framing may just be a relabeling of existing acquisition functions without genuine methodological novelty.
  The EVP does not yet cite or differentiate from margin-based active learning or constrained BO literature (e.g., Gelbart et al. constrained BO, Gramacy's active learning for boundaries) because live search was unavailable. This must be resolved before publication — a literature review pass is required to isolate what the ROM-specific greedy/weak-greedy machinery adds beyond standard uncertainty/margin sampling.
• mediumWhy these specific 4 benchmarks and this specific surrogate architecture (3-layer MLP / GP)? The methodology does not justify why truss topology optimization and 2D heat-equation inversion are representative of the broader claimed application space (aerospace, drug discovery, semiconductor design), risking benchmark selection bias.
  Partially addressed via dimensionality ablation (2D/10D/50D) and mixed synthetic+real benchmarks, but no justification is given for architecture choice beyond convenience; a sensitivity study across surrogate model classes (MLP vs GP vs random forest) should be added to strengthen generality claims.
• mediumThe bulk-MSE tradeoff criterion may not be a fair test if the amortized optimization use case genuinely only cares about boundary accuracy (e.g., feasibility classification for constrained optimization) — penalizing bulk accuracy degradation could unfairly disqualify a method that is doing exactly what it's designed to do.
  Acknowledged but not fully resolved: success/failure criteria should be split into two reporting tracks (boundary-only use case vs. general-purpose surrogate use case) rather than a single combined pass/fail threshold, to avoid conflating two different deployment scenarios.

Experimental Protocol

ROI Projection

Implementation Sketch

Initialize: D_labeled = sample_uniform(n_init=50)
Train surrogate S on D_labeled
For iteration in range(budget_steps):
    # Estimate boundary region via surrogate
    candidates = sample_pool(n=10000)  # dense candidate pool
    residual_score = |S.predict_proba(candidates) - 0.5|  # distance to decision boundary
    uncertainty_score = S.predict_variance(candidates)  # if GP; else ensemble disagreement
    acquisition = -residual_score + lambda * uncertainty_score  # greedy weak-residual criterion
    x_next = candidates[argmax(acquisition)]
    y_next = oracle(x_next)  # expensive true feasibility evaluation
    D_labeled.append((x_next, y_next))
    Retrain or warm-start update S on D_labeled
Evaluate S on held-out dense grid:
    boundary_F1 = F1(S, points where |true_boundary_dist| < epsilon)
    bulk_MSE = MSE(S, all held-out points)
Compare across {uniform, Sobol, adaptive} at matched |D_labeled|