Highly Accurate Description of Long-Range Interactions through the Combination of Neural Networks and Physical Models

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.