The paper introduces a novel class of interatomic potential models that can be automatically generated from quantum mechanical data, specifically energies and forces experienced by atoms. These models, called Gaussian Approximation Potentials (GAP), do not have a fixed functional form, allowing them to capture complex potential energy landscapes. The method is systematically improvable with more data and is applied to bulk crystals, particularly carbon, silicon, germanium, iron, and gallium nitride. The GAP model is tested for its accuracy in predicting properties at high temperatures, showing significant improvements over existing potentials in terms of force errors and energy accuracy. The computational cost of the GAP model is significantly lower than that of standard plane-wave DFT codes, making it a promising tool for large-scale simulations. The authors also demonstrate the model's ability to describe reactive processes, such as the $sp^{2}$-$sp^{3}$ transition in diamond. Overall, the GAP model offers a practical and accurate approach to modeling the Born-Oppenheimer potential energy surface without explicitly simulating electrons.The paper introduces a novel class of interatomic potential models that can be automatically generated from quantum mechanical data, specifically energies and forces experienced by atoms. These models, called Gaussian Approximation Potentials (GAP), do not have a fixed functional form, allowing them to capture complex potential energy landscapes. The method is systematically improvable with more data and is applied to bulk crystals, particularly carbon, silicon, germanium, iron, and gallium nitride. The GAP model is tested for its accuracy in predicting properties at high temperatures, showing significant improvements over existing potentials in terms of force errors and energy accuracy. The computational cost of the GAP model is significantly lower than that of standard plane-wave DFT codes, making it a promising tool for large-scale simulations. The authors also demonstrate the model's ability to describe reactive processes, such as the $sp^{2}$-$sp^{3}$ transition in diamond. Overall, the GAP model offers a practical and accurate approach to modeling the Born-Oppenheimer potential energy surface without explicitly simulating electrons.