Achieving consistent color reproduction across multiple cameras is essential for seamless image fusion and Image Processing Pipeline (ISP) compatibility in modern devices, but it is a challenging task due to variations in sensors and optics. Existing raw-to-raw conversion methods face limitations such as poor adaptability to changing illumination, high computational costs, or impractical requirements such as simultaneous camera operation and overlapping fields-of-view. We introduce the Neural Physical Model (NPM), a lightweight, physically-informed approach that simulates raw images under specified illumination to estimate transformations between devices. The NPM effectively adapts to varying illumination conditions, can be initialized with physical measurements, and supports training with or without paired data. Experiments on public datasets like NUS and BeyondRGB demonstrate that NPM outperforms recent state-of-the-art methods, providing robust chromatic consistency across different sensors and optical systems.