Approximate date reconstructed from report files
Experiment Note
The experiments were reorganized into an eight-week research narrative:
Week 1: literature and failure analysis. Week 2: baseline reproduction. Week 3: variable-region diagnostics and controller design. Week 4: gradient screening, matched probes, rollback, and trust radius. Week 5: Kovasznay and sparse cavity repeated-seed experiments. Week 6: Allen-Cahn and advection-diffusion transient experiments. Week 7: ablation, sensitivity, baseline audit, bootstrap, and Wilcoxon summaries. Week 8: Reynolds stress test, figures, reproducibility audit, and report.
This schedule is a retrospective project summary rather than a Git-exact weekly calendar, but it captures the intended research progression.
Technical Essay
The report articulated four research questions:
- Can localized PINN failure be diagnosed without dense reference access by physical variable and region?
- Can sampling and weighting be changed without increasing the collocation or supervision budget?
- Can matched probes and rollback prevent a locally helpful action from damaging other objectives?
- Can the same controller transfer across steady flow, sparse reconstruction, reaction-diffusion, and transport?
These questions became the clearest high-level description of the project.
Reading Note
The final report connected the technical work to sparse sensing, inverse problems, and engineering AI. It also retained operator learning as a future direction: VARA could potentially act as an inner-loop residual/data allocator inside a learned operator, but the current evidence concerned instance-wise coordinate networks.
Progress Update
The eight-week fellowship deliverable was completed with a self-contained technical report, figures, tables, bibliography, official cover, conclusions, limitations, and acknowledgements to the fellowship academies and supervisor.