# 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.