  We present a simple and general way to accurately describe long-range
interactions between atoms and molecules through combining neural networks with
physical models. Demonstrations on the H$_3$, Li$_3$ and 2KRb systems
illustrate the exceptional extrapolation capabilities of the trained model,
supported by underlying physical models. More importantly, the model exhibits
high accuracy at energy scales below a few hundred millikelvin, where the
reliability of $ab~initio$ methods diminishes.
