“Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces,” by Joerg Behler and Michele Parrinello, was published in Physical Review Letters in 2007. It introduced what is now regarded as the foundational machine-learning interatomic potential, a way to use a neural network to approximate the energy of a collection of atoms as a function of their positions.
The central difficulty is that calculating the energy and forces on atoms accurately requires quantum-mechanical methods such as density functional theory (DFT), which are far too slow to simulate large systems over long times. Behler and Parrinello showed that a neural network, given a suitable description of each atom’s local environment, could reproduce the DFT energy and forces for systems of arbitrary size while running orders of magnitude faster. They demonstrated the method on bulk silicon, comparing favorably with both empirical potentials and DFT itself.
This paper launched an entire field. Machine-learning potentials now let chemists and materials scientists run molecular-dynamics simulations at near-quantum accuracy on systems that were previously out of reach, and they underpin much of the modern AI-for-materials toolkit. For a general reader, it is an early and durable example of replacing expensive physics calculations with a learned surrogate.