Recorded by commits 5fbc60e and 17bd6f7
Experiment Note
The Kovasznay prototype was converted into a full research repository. The initial commit added 104 files and roughly 5,600 lines: model definitions, Navier-Stokes residuals, loss functions, sampling modules, diagnostics, local controllers, constrained policy logic, trainers, evaluation, plots, tests, configs, experiment runners, and three notebooks. The first working full_vara path included training, diagnostic maps, patch scores, weak-region detection, local interventions, adaptive sampling, action logs, plots, checkpoints, and final metrics.
The second commit refined control from a coarse controller step into per-intervention local constrained control. Each proposed action could be evaluated and accepted or rejected on its own, instead of treating a collection of changes as one opaque update.
Technical Essay
The V1 architecture separated concerns early:
- src/models represented the coordinate network, including ordinary MLP, multi-head, SIREN, and Fourier-feature options.
- src/physics computed differentiable Navier-Stokes quantities and benchmark solutions.
- src/diagnostics converted predictions and residuals into channel-specific spatial maps, normalized patch scores, and persistent weak regions.
- src/controllers mapped weak variable-region pairs to actions such as local velocity, pressure, pressure-gradient, vorticity, divergence, momentum, or boundary emphasis.
- src/sampling redistributed collocation effort.
- src/training owned optimizer state, snapshots, checkpoints, intervention execution, and logging.
- src/evaluation and src/visualization kept scientific reporting separate from the controller itself.
The controller needed rollback from the beginning. A local action might improve its target while damaging another variable or the global physics objective. Snapshotting the control state and model trajectory made a proposed adaptation testable rather than irreversible.
Reading Note
At this stage, the main conceptual distinction from RAR became explicit. RAR asks where the residual is large. VARA asks which physical channel is weak in which region, then chooses an action suited to that pair. The connection to multi-objective optimization also became clearer: each physical term has its own scale and gradient direction, so a local gain must be checked for spillover damage.
Progress Update
The idea was no longer only a notebook. A reproducible modular codebase existed, with tests for residuals, sampling, diagnostics, controller decisions, local losses, logging, and the analytical Kovasznay solution. The research direction had a concrete novelty boundary: variable-region control, not merely another global loss schedule or residual sampler.