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Merge pull request brucefan1983#759 from brucefan1983/doc_nep5
doc for NEP5
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doc/nep/input_files/nep_in.rst

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This file specifies hyperparameters used for training neuroevolution potential (:term:`NEP`) models, the functional form of which is outline :ref:`here <nep_formalism>`.
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The :term:`NEP` approach was proposed in [Fan2021]_ (NEP1) and later improved in [Fan2022a]_ (NEP2) and [Fan2022b]_ (NEP3).
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Currently, we support NEP3 and NEP4 (to be published), which can be chosen by the :ref:`version keyword <kw_version>`.
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Currently, we support NEP3, NEP4 (to be published), and NEP5 (to be published), which can be chosen by the :ref:`version keyword <kw_version>`.
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File format
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-----------
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* - Keyword
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- Brief description
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* - :ref:`version <kw_version>`
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- select between NEP3 and NEP4
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- select the NEP version
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* - :ref:`type <kw_type>`
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- number of atom types and list of chemical species
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* - :ref:`type_weight <kw_type_weight>`

doc/nep/input_parameters/version.rst

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version <version_number>
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Here, :attr:`<version_number>` must be an integer, which can be 3 or 4, corresponding to NEP3 and NEP4, respectively.
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Here, :attr:`<version_number>` must be an integer, which can be 3 or 4 or 5, corresponding to NEP3, NEP4, and NEP5, respectively.
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The default is 4.
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More information about the :term:`NEP` formalism can be found :ref:`here <nep_formalism>`.

doc/potentials/nep.rst

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************************
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The neuroevolution potential (:term:`NEP`) approach was proposed in [Fan2021]_ (NEP1) and later improved in [Fan2022a]_ (NEP2) and [Fan2022b]_ (NEP3).
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Currently, :program:`GPUMD` supports NEP3 and NEP4 (to be published).
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Both versions have comparable accuracy for single-component systems.
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For multi-component systems, NEP4 usually has higher accuracy, if all the other hyperparameters are the same.
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Currently, :program:`GPUMD` supports NEP3, NEP4 (to be published), and NEP5 (to be published).
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All versions have comparable accuracy for single-component systems.
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For multi-component systems, NEP4 and NEP5 usually have higher accuracy, if all the other hyperparameters are the same.
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:program:`GPUMD` not only allows one to carry out simulations using :term:`NEP` models via the :ref:`gpumd executable <gpumd_executable>` but even the construction of such models via the :ref:`nep executable <nep_executable>`.
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- :math:`N_\mathrm{nn} = (N_\mathrm{des} +2) N_\mathrm{neu}+1` (NEP3)
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* -
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- :math:`N_\mathrm{nn} = (N_\mathrm{des} +2) N_\mathrm{neu} N_\mathrm{typ}+1` (NEP4)
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* -
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- :math:`N_\mathrm{nn} = ((N_\mathrm{des} +2) N_\mathrm{neu} + 1) N_\mathrm{typ}+1` (NEP5)
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The total number of trainable parameters is the sum of the number of trainable descriptor parameters and the number of :term:`NN` parameters :math:`N_\mathrm{nn}`.
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