| # Description: | |
| ## - 2D heat equation (diffusion) simulated on a 64x64 grid using an explicit finite-difference solver. | |
| ## - Time integration: forward Euler with stable timestep dt = 0.25 * dx^2 / alpha, where dx = 1/64. | |
| ## - Boundary conditions included (separate folders): | |
| - periodic | |
| - neumann (zero-flux) | |
| - dirichlet (fixed temperature = 0.0) | |
| ## - Initial condition modes: | |
| blobs, step, ring, collide, moving | |
| - 'moving' mode includes a moving heat source in the simulation for non-stationary scenarios. | |
| ## - Trajectory length (timesteps): 60 | |
| ## - Samples per BC: 4000 | |
| ## - Alpha (thermal diffusivity) sampled uniformly in [0.005, 0.02]. | |
| ## - Data formats: | |
| - Numeric (high precision): npz files saved under /npy/<bc>/<variant>/sample_*.npz | |
| Each npz contains: trajectory (float32 array shape (T, H, W)), alpha (float32), metadata (json string) | |
| - Visuals: png heatmaps for selected timesteps saved under /jpg/<bc>/<variant>/ | |
| - Metadata: /metadata/metadata.json and summary_stats.json (per-bc stats) | |
| ## - Noisy variants: optional measurement-noise version saved in 'noisy' subfolders (gaussian noise, std=0.005) | |
| # Quality checks: | |
| ## - For each trajectory, we compute total energy across the grid at each timestep: | |
| energy[t] = sum_{i,j} T(t,i,j) | |
| ## - We record initial and final energy and flag any samples where relative drift exceeds 0.001. | |
| # Usage: | |
| ## - For training physics-informed applications: load the .npz files and feed the float32 arrays directly as targets. | |
| ## - For visualization, preview PNGs or animate the trajectory using matplotlib or imageio. | |