Overview
Can a PINN adapt locally without hiding damage to other physical objectives—or confusing a lower aggregate loss with a better physical solution?
Global losses can look satisfactory while a pressure, velocity, vorticity, or residual field remains wrong in a small region. Residual-only refinement preserves location but collapses the identity of the physical channel that is failing.
Contribution
What was built—and what I did.
VARA preserves the channel × region structure of failure, proposes local sampling or loss-emphasis actions, screens compatibility, compares each action with a matched neutral trajectory, and rolls back model, optimizer, controller, sampler, and random state when protected objectives deteriorate.
Formulated the controller, built the modular research codebase and benchmark harness, developed guarded probes and rollback, ran multi-seed and cross-PDE studies, audited fairness and leakage boundaries, and prepared the manuscript evidence package under Prof. Gopal Chandra Shit’s supervision.
Selected verified evidence
Results with their context attached.
Relative to the matched baseline, reported five-seed Kovasznay means fell by approximately 33–46% across velocity, pressure, vorticity, residual, and the global objective.
Lower full-field velocity L2 / sparse-velocity MSE at Re=100 with 2% sparse CFD, across five seeds.
Allen–Cahn / advection–diffusion; reported mean normalized reductions were 35.1% / 58.6%.
Full VARA versus regional control without variable identity; +1.6% average, showing a smaller incremental multi-field effect.
- Re=100/400/1000 continuation produced 9/9 sparse-velocity-MSE wins and 8/9 full-velocity-L2 wins.
- A single-seed Re=100–10,000 stress trace favoured VARA in 14/15 reference-free aggregates.
- The Re=5000 reversal, where VARA was 13.8% worse, remained in the record.
- Reported runtime varied by protocol: some matched cavity schedules were 2.6–4.9% faster, while transient raw runs were about 9% slower.
Failures and reversals
Negative results belong in the record.
- A technically appealing hard-boundary cavity formulation was reverted when it changed the problem rather than isolating the controller effect.
- L-BFGS refinements and final physics repair were separated in compute accounting instead of folded into an adaptive-control claim.
- Continuity residual moved slightly in the unfavourable direction in some cavity comparisons even as reconstruction improved.
Limitations
The boundary of the claim.
- 01Five-seed studies do not support strong asymptotic inference, especially when baseline errors are very small.
- 02Most evidence is two-dimensional and benchmark-specific; the method is not a universal PINN improvement guarantee.
- 03Some full-field references exist only for evaluation, while sparse cavity profiles support a narrower claim.
- 04Controller overhead and benefits depend on the exact budget definition and protocol.
Repository
Code and reproducibility surface.
- Typed configurations and experiment runners
- Saved raw and summary CSVs
- Seeded matched trajectories and full-state rollback
- Tests for residuals, sampling, diagnostics, policies, local losses, logging, and analytical solutions
Related research log