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Machine learning models are changing the paradigm of molecular modeling,which is a fundamental tool for material science, chemistry, and computationalbiology. Of particular interest is the inter-atomic potential energy surface(PES). Here we develop Deep Potential - Smooth Edition (DeepPot-SE), anend-to-end machine learning-based PES model, which is able to efficientlyrepresent the PES for a wide variety of systems with the accuracy of ab initioquantum mechanics models. By construction, DeepPot-SE is extensive andcontinuously differentiable, scales linearly with system size, and preservesall the natural symmetries of the system. Further, we show that DeepPot-SEdescribes finite and extended systems including organic molecules, metals,semiconductors, and insulators with high fidelity.

End-to-end Symmetry Preserving Inter-atomic Potential Energy Model for Finite and Extended Systems