Create README.md

README.md

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+# 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.