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Kernel models of potential energy surfaces (PES) for polyatomic molecules areoften restricted by a specific choice of the kernel function. This can beavoided by optimizing the complexity of the kernel function. For regressionproblems with very expensive data, the functional form of the model kernels canbe optimized in the Gaussian process (GP) setting through compositionalfunction search guided by the Bayesian information criterion. However, thecompositional kernel search is computationally demanding and relies on greedystrategies, which may yield sub-optimal kernels. An alternative strategy ofincreasing complexity of GP kernels treats a GP as a Bayesian neural network(NN) with a variable number of hidden layers, which yields NNGP models. Here,we present a direct comparison of GP models with composite kernels and NNGPmodels for applications aiming at the construction of global PES for polyatomicmolecules. We show that NNGP models of PES can be trained much more efficientlyand yield better generalization accuracy without relying on any specific formof the kernel function. We illustrate that NNGP models trained by distributionsof energy points at low energies produce accurate predictions of PES at highenergies. We also illustrate that NNGP models can extrapolate in the inputvariable space by building the free energy surface of the Heisenberg modeltrained in the paramagnetic phase and validated in the ferromagnetic phase. Byconstruction, composite kernels yield more accurate models than kernels with afixed functional form. Therefore, by illustrating that NNGP models outperformGP models with composite kernels, our work suggests that NNGP models should bea preferred choice of kernel models for PES.

Neural network Gaussian processes as efficient models of potential energy surfaces for polyatomic molecules