# FisMat2017 - Submission - View

**Abstract's title**: Machine learning many body expansions for potential energy surfaces

**Affiliation**: King's College London, Physics Department

**Affiliation Address**: Strand, London WC2R 2LS

**Country**: United Kingdom

In the last decade there has been a proliferation of successful applications of machine learning algorithms to complex physical problems. For instance, Gaussian Process (GP) based inference proved to be a promising route for the approximation of interatomic force fields at the Density Functional Theory (DFT) level of accuracy. The quality of a GP regression is dictated by its kernel function, which encapsulates the prior knowledge on the system studied.

In my talk, I will present a general scheme to build kernel functions that yield controllable predictive accuracy. The procedure extends and clarifies well known previous approaches (e.g. [1] and [2]) and lies in a systematic expansion of the approximating force field into n-body interactions via the design of n-body kernels. In general, the obvious tradeoff between accuracy and computational cost will make the choice of kernel depend on system and application at hand. However, GP predictions coming form 2 or 3-body kernels can be mapped onto explicit basis functions giving rise to non-parametric classical potentials. These are as fast as standard classical potentials but provide consistently lower errors with respect to the target DFT forces. Moreover, they can be generated automatically starting from any set of quantum forces with no need of complex non-linear parametrisation and optimisation.

[1] BartÃ³k et al. (2010). Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons. Physical Review Letters. http://doi.org/10.1103/PhysRevLett.104.136403

[2] Glielmo et al. (2016). Accurate Interatomic Force Fields via Machine Learning with Covariant Kernels. Physical Review B. https://doi.org/10.1103/PhysRevB.95.214302