PDE Simulation Analysis

PDE-Specific Metric Ideas

• Conservative transport / compressible Euler / wave-like conservative systems:

  • Mass conservation
  • Momentum or energy trends when relevant
  • Positivity of density and pressure
  • Shock localization without checkerboard artifacts or obvious Gibbs ringing

• Heat / diffusion:

  • Mass conservation when boundary conditions imply zero net flux
  • Decay of variance or L2 energy
  • Monotone smoothing
  • No creation of new extrema for pure diffusion problems

• Reaction-diffusion:

  • Positivity or known bounds
  • Growth or decay rates consistent with the reaction terms
  • Pattern wavelength and amplitude evolution
  • Note explicitly when mass is not expected to be conserved

• Incompressible flow:

  • Divergence-related quantities if recoverable from outputs
  • Kinetic-energy trends consistent with viscosity and forcing
  • Boundary-condition consistency near walls, inlets, and outlets

• Maxwell / Helmholtz / wave problems:

  • Energy or norm balance
  • Damping or resonance expectations
  • Symmetry and boundary-condition consistency

If exact conservation is not expected, say why and pick a better metric. The point is to test the physics the preset is supposed to represent, not to force a generic invariant.

4. Extract representative image frames and inspect them visually.

   • Use the saved GIFs when present.
   • Extract at least the start, middle, and end frames for one or more key fields.
   • Use scripts/extract_gif_frames.py in this skill folder for deterministic extraction.
   • Actually open the extracted PNGs with the available image-viewing tool. Do not stop after writing them to disk.
   • Look for boundary leaks, symmetry breaking, checkerboarding, ringing, clipping, dead or static fields, sign mistakes, scale mistakes, and domain-mask artifacts.

5. Synthesize the evidence.

   • Combine metadata, logs, computed metrics, and visual inspection into a final verdict.
   • Separate hard failures from softer concerns.
   • State whether the run looks physically plausible, numerically suspicious, or clearly broken.
   • End with the single most informative next check if uncertainty remains.

Analyzing multiple simulations

If you analyze multiple runs to compare them, generate a plot which compare the start, middle, and end frames for one (important) field across the runs. This can be done by extracting the frames as PNGs and then using a plotting library to create a side-by-side comparison. Look for differences in the patterns, magnitudes, and any artifacts that may indicate differences in the underlying physics or numerical stability of the runs.

Practical Notes

• Prefer inspecting the most physically interpretable outputs first, such as density, pressure, temperature, concentration, total_energy, and velocity components or magnitude.
• If only .npy outputs exist, render representative PNGs from those arrays and inspect them instead of GIFs.
• If the run failed early, say which parts of the workflow were unavailable rather than pretending the analysis is complete.

Reporting Format

Report these sections in order:

1. Run summary
2. Metadata findings from run_meta.json and frames_meta.json
3. Log findings
4. Computed metrics and whether they match the PDE expectations
5. Visual findings from start, middle, and end frames
6. Final verdict and next action