The Physics Engine (spectral_ops)

The Physics Engine is the heart of SpectraLoRA. It operates directly on raw, multi-spectral PyTorch tensors to extract physical meaning before the deep learning model sees the data.

The engine currently tracks 5 distinct indices, optimized for both dense vegetation and arid, desert environments.

The Spectral Fingerprint

The function get_spectral_fingerprint(x, band_indices) takes a satellite image tensor and returns a global context vector \(z\) of shape (Batch, 5). This vector acts as the input to the Gating Network.

1. NDVI (Normalized Difference Vegetation Index)

The standard metric for identifying live green vegetation.

\[NDVI = \frac{NIR - Red}{NIR + Red + \epsilon}\]

2. SAVI (Soil-Adjusted Vegetation Index)

Crucial for arid regions (like Sudan or the Middle East) where bright sand reflects light and drowns out the chlorophyll signal of sparse shrubs.

\[SAVI = \frac{(NIR - Red) \cdot (1 + L)}{NIR + Red + L + \epsilon}\]

(Default \(L = 0.5\))

3. NDWI (Normalized Difference Water Index)

Used to identify open water bodies.

\[NDWI = \frac{Green - NIR}{Green + NIR + \epsilon}\]

4. NDBI (Normalized Difference Built-up Index)

Used to map urban areas, concrete, and asphalt.

\[NDBI = \frac{SWIR - NIR}{SWIR + NIR + \epsilon}\]

5. BSI (Bare Soil Index)

Distinguishes "Bare Earth" (Sand/Dirt) from "Built Structures". This is essential to stop the AI from confusing desert dunes with concrete buildings.

\[BSI = \frac{(SWIR + Red) - (NIR + Blue)}{(SWIR + Red) + (NIR + Blue) + \epsilon}\]