Approximate dates reconstructed from paper artifacts
Experiment Note
Processed datasets and scripts were assembled for the paper: Kovasznay five- seed summaries, cavity Re=100 five-seed metrics, Reynolds continuation, controller sensitivity, runtime overhead, variable-awareness ablation, Allen-Cahn and advection-diffusion results, and a Reynolds stress-test trace.
For Allen-Cahn, 30 run summaries were parsed across vanilla, full VARA, local- loss-only, no-guard, no-variable-awareness, and sampling-only variants. Six key metrics were evaluated with paired wins, 10,000 paired bootstrap resamples, and exact paired Wilcoxon signed-rank summaries. With only five nonzero pairs, the smallest possible two-sided exact p-value was 0.0625, so the paper correctly treated these tests as descriptive rather than definitive.
Technical Essay
The manuscript reframed the system from an assortment of adaptive tricks into one closed-loop learning-control method. The method section formalized the diagnostic tensor, candidates, gradient influence, conserved sampling and loss mass, matched probes, Pareto guards, rollback, trust radius, and compute accounting.
The statistical workflow guarded against two common research-log errors. First, it used paired seed comparisons instead of comparing only group means. Second, it did not hide structural ties: full VARA and no-variable-awareness were identical for Allen-Cahn because the problem has a single scalar output.
Reading Note
The related-work section expanded to 48 cited bibliography entries across PINN foundations, optimization pathologies, domain decomposition, adaptive sampling, causal curricula, loss balancing, hard constraints, sparse flow reconstruction, and operator learning. Operator methods such as DeepONet and FNO were positioned as adjacent rather than direct same-budget baselines because they learn across distributions of PDE instances rather than solving one coordinate-network instance.
Progress Update
A complete Elsevier/EAAI-oriented manuscript package existed. The claim was narrowed to what the artifacts supported: improved reconstruction and localized error correction under the reported protocols, not universal improvement of every residual in every run.