Tejaskumar/Time-variant-Heat-Equation-2D

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.