maml.apps.pes package

This package contains PotentialMixin classes representing Interatomic Potentials.

class maml.apps.pes.DefectFormation(ff_settings, specie, lattice, alat, **kwargs)

Bases: LMPStaticCalculator

Defect formation energy calculator.

_parse()

Parse results from dump files.

_sanity_check(structure)

Check if the structure is valid for this calculation.

_setup()

Setup a calculation, writing input files, etc.

calculate()

Calculate the vacancy formation given Potential class.

static get_unit_cell(specie, lattice, alat)

Get the unit cell from specie, lattice type and lattice constant.

• Parameters
  • specie (str) – Name of specie.
  • lattice (str) – The lattice type of structure. e.g. bcc or diamond.
  • alat (float) – The lattice constant of specific lattice and specie.

class maml.apps.pes.ElasticConstant(ff_settings, potential_type=’external’, deformation_size=1e-06, jiggle=1e-05, maxiter=400, maxeval=1000, full_matrix=False, **kwargs)

Bases: LMPStaticCalculator

Elastic constant calculator.

RESTART_CONFIG( = {‘external’: {‘read_command’: ‘read_restart’, ‘restart_file’: ‘restart.equil’, ‘write_command’: ‘write_restart’}, ‘internal’: {‘read_command’: ‘read_restart’, ‘restart_file’: ‘restart.equil’, ‘write_command’: ‘write_restart’}_ )

_parse()

Parse results from dump files.

_sanity_check(structure)

Check if the structure is valid for this calculation.

_setup()

Setup a calculation, writing input files, etc.

class maml.apps.pes.EnergyForceStress(ff_settings, **kwargs)

Bases: LMPStaticCalculator

Calculate energy, forces and virial stress of structures.

_parse()

Parse results from dump files.

static _rotate_force_stress(structure, forces, stresses)

_sanity_check(structure)

Check if the structure is valid for this calculation.

_setup()

Setup a calculation, writing input files, etc.

calculate(structures)

Calculate the energy, forces and stresses of structures. Proper rotation of the results are applied when the structure is triclinic.

• Parameters structures (list) – a list of structures

Returns: list of (energy, forces, stresses) tuple

class maml.apps.pes.GAPotential(name=None, param=None)

Bases: LammpsPotential

This class implements Smooth Overlap of Atomic Position potentials.

abc_impl( = <_abc.abc_data object )

static _line_up(structure, energy, forces, virial_stress)

Convert input structure, energy, forces, virial_stress to proper configuration format for MLIP usage.

• Parameters
  • structure (Structure) – Pymatgen Structure object.
  • energy (float) – DFT-calculated energy of the system.
  • forces (list) – The forces should have dimension (num_atoms, 3).
  • virial_stress (list) – stress should has 6 distinct elements arranged in order [xx, yy, zz, xy, yz, xz].

Returns:

evaluate(test_structures, test_energies, test_forces, test_stresses=None, predict_energies=True, predict_forces=True, predict_stress=False)

Evaluate energies, forces and stresses of structures with trained interatomic potentials.

• Parameters
  • test_structures ([Structure]) – List of Pymatgen Structure Objects.
  • test_energies ([float]) – List of DFT-calculated total energies of each structure in structures list.
  • test_forces ([np.array]) – List of DFT-calculated (m, 3) forces of each structure with m atoms in structures list. m can be varied with each single structure case.
  • test_stresses (list) – List of DFT-calculated (6, ) viriral stresses of each structure in structures list.
  • predict_energies (bool) – Whether to predict energies of configurations.
  • predict_forces (bool) – Whether to predict forces of configurations.
  • predict_stress (bool) – Whether to predict virial stress of configurations.

static from_config(filename)

Initialize potentials with parameters file.

• Parameters filename (str) – The file storing parameters of potentials, filename should ends with “.xml”.
• Returns GAPotential.

pair_coeff(_ = ‘pair_coeff * * {} {} {}_ )

pair_style(_ = ‘pair_style quip_ )

static read_cfgs(filename, predict=False)

Read the configuration file.

• Parameters filename (str) – The configuration file to be read.

save(filename=’param.yaml’)

Save parameters of the potentials.

• Parameters filename (str) – The file to store parameters of potentials.
• Returns (str)

train(train_structures, train_energies, train_forces, train_stresses=None, default_sigma=(0.0005, 0.1, 0.05, 0.01), use_energies=True, use_forces=True, use_stress=False, **kwargs)

Training data with gaussian process regression.

• Parameters
  • train_structures ([Structure]) – The list of Pymatgen Structure object. energies ([float]): The list of total energies of each structure in structures list.
  • train_energies ([float]) – List of total energies of each structure in structures list.
  • train_forces ([np.array]) – List of (m, 3) forces array of each structure with m atoms in structures list. m can be varied with each single structure case.
  • train_stresses (list) – List of (6, ) virial stresses of each structure in structures list.
  • default_sigma (list) – Error criteria in energies, forces, stress and hessian. Should have 4 numbers.
  • use_energies (bool) – Whether to use dft total energies for training. Default to True.
  • use_forces (bool) – Whether to use dft atomic forces for training. Default to True.
  • use_stress (bool) – Whether to use dft virial stress for training. Default to False.
  • kwargs – l_max (int): Parameter to configure GAP. The band limit of

spherical harmonics basis function. Default to 12.

n_max (int): Parameter to configure GAP. The number of radial basis

  function. Default to 10.

atom_sigma (float): Parameter to configure GAP. The width of gaussian

  atomic density. Default to 0.5.

zeta (float): Present when covariance function type is do product.

  Default to 4.

cutoff (float): Parameter to configure GAP. The cutoff radius.

  Default to 4.0.

cutoff_transition_width (float): Parameter to configure GAP.

  The transition width of cutoff radial. Default to 0.5.

delta (float): Parameter to configure Sparsification.

  The signal variance of noise. Default to 1.

f0 (float): Parameter to configure Sparsification.

  The signal mean of noise. Default to 0.0.

n_sparse (int): Parameter to configure Sparsification.

  Number of sparse points.

covariance_type (str): Parameter to configure Sparsification.

  The type of convariance function. Default to dot_product.

sparse_method (str): Method to perform clustering in sparsification.

  Default to ‘cur_points’.

sparse_jitter (float): Intrisic error of atomic/bond energy,

  used to regularise the sparse covariance matrix.
  Default to 1e-8.

e0 (float): Atomic energy value to be subtracted from energies

  before fitting. Default to 0.0.

e0_offset (float): Offset of baseline. If zero, the offset is

  the average atomic energy of the input data or the e0
  specified manually. Default to 0.0.

write_cfgs(filename, cfg_pool)

Write the formatted configuration file.

• Parameters
  • filename (str) – The filename to be written.
  • cfg_pool (list) – The configuration pool contains structure and energy/forces properties.

write_param(xml_filename=’gap.2020.01.xml’)

Write xml file to perform lammps calculation.

• Parameters xml_filename (str) – Filename to store xml formatted parameters.

class maml.apps.pes.LMPStaticCalculator(**kwargs)

Bases: object

Abstract class to perform static structure property calculation using LAMMPS.

COMMON_CMDS( = [‘units metal’, ‘atom_style charge’, ‘box tilt large’, ‘read_data data.static’, ‘run 0’_ )

abstract _parse()

Parse results from dump files.

abstract _sanity_check(structure)

Check if the structure is valid for this calculation.

abstract _setup()

Setup a calculation, writing input files, etc.

allowed_kwargs(_ = [‘lmp_exe’_ )

calculate(structures)

Perform the calculation on a series of structures.

• Parameters structures – Input structures in a list.
• Returns List of computed data corresponding to each structure, varies with different subclasses.

set_lmp_exe(lmp_exe: str)

Set lammps executable for the instance.

• Parameters lmp_exe (str) – lammps executable path

Returns:

class maml.apps.pes.LatticeConstant(ff_settings, box_relax=True, box_relax_keywords=’aniso 0.0 vmax 0.001’, box_triclinic=False, min_style=’cg’, etol=1e-15, ftol=1e-15, maxiter=5000, maxeval=5000, **kwargs)

Bases: LMPRelaxationCalculator

Lattice Constant Relaxation Calculator.

calculate(structures)

Calculate the relaxed lattice parameters of a list of structures.

• Parameters structures ([Structure]) – Input structures in a list.
• Returns List of relaxed lattice constants (a, b, c in Å) of the input structures.

class maml.apps.pes.MTPotential(name=None, param=None, version=None)

Bases: LammpsPotential

This class implements moment tensor potentials. Installation of the mlip package is needed. Please refer to https://mlip.skoltech.ru.

abc_impl( = <_abc.abc_data object )

_line_up(structure, energy, forces, virial_stress)

Convert input structure, energy, forces, virial_stress to proper configuration format for mlip usage.

• Parameters
  • structure (Structure) – Pymatgen Structure object.
  • energy (float) – DFT-calculated energy of the system.
  • forces (list) – The forces should have dimension (num_atoms, 3).
  • virial_stress (list) – stress should has 6 distinct elements arranged in order [xx, yy, zz, yz, xz, xy].

evaluate(test_structures, test_energies, test_forces, test_stresses=None, **kwargs)

Evaluate energies, forces and stresses of structures with trained interatomic potentials.

• Parameters
  • test_structures ([Structure]) – List of Pymatgen Structure Objects.
  • test_energies ([float]) – List of DFT-calculated total energies of each structure in structures list.
  • test_forces ([np.array]) – List of DFT-calculated (m, 3) forces of each structure with m atoms in structures list. m can be varied with each single structure case.
  • test_stresses (list) – List of DFT-calculated (6, ) viriral stresses of each structure in structures list.
  • kwargs – Parameters of write_param method.

static from_config(filename, elements)

Initialize potentials with parameters file.

• Parameters
  • filename (str) – The file storing parameters of potentials, filename should ends with “.mtp”.
  • elements (list) – The list of elements.
• Returns MTPotential

pair_coeff(_ = ‘pair_coeff * *_ )

pair_style(_ = ‘pair_style mlip {}_ )

read_cfgs(filename)

• Parameters filename (str) – The configuration file to be read.

train(train_structures, train_energies, train_forces, train_stresses, unfitted_mtp=’08g.mtp’, max_dist=5, radial_basis_size=8, max_iter=1000, energy_weight=1, force_weight=0.01, stress_weight=0.001, init_params=’same’, scale_by_force=0, bfgs_conv_tol=0.001, weighting=’vibration’)

Training data with moment tensor method.

• Parameters
  • train_structures ([Structure]) – The list of Pymatgen Structure object. energies ([float]): The list of total energies of each structure in structures list.
  • train_energies ([float]) – List of total energies of each structure in structures list.
  • train_forces ([np.array]) – List of (m, 3) forces array of each structure with m atoms in structures list. m can be varied with each single structure case.
  • train_stresses (list) – List of (6, ) virial stresses of each structure in structures list.
  • unfitted_mtp (str) – Define the initial mtp file. Default to the mtp file stored in .params directory.
  • max_dist (float) – The actual radial cutoff.
  • radial_basis_size (int) – Relevant to number of radial basis function.
  • max_iter (int) – The number of maximum iteration.
  • energy_weight (float) – The weight of energy.
  • force_weight (float) – The weight of forces.
  • stress_weight (float) – The weight of stresses. Zero-weight can be assigned.
  • init_params (str) – How to initialize parameters if a potential was not pre-fitted. Choose from “same” and “random”.
  • scale_by_force (float) – Default=0. If >0 then configurations near equilibrium (with roughly force < scale_by_force) get more weight.
  • bfgs_conv_tol (float) – Stop training if error dropped by a factor smaller than this over 50 BFGS iterations.
  • weighting (str) – How to weight configuration with different sizes relative to each other. Choose from “vibrations”, “molecules” and “structures”.

write_cfg(filename, cfg_pool)

Write configurations to file :param filename: filename :type filename: str :param cfg_pool: list of configurations. :type cfg_pool: list

Returns:

write_ini(mtp_filename=’fitted.mtp’, select=False, **kwargs)

Write mlip.ini file for mlip packages of version mlip-2 or mlip-dev. Supported keyword arguments are parallel with options stated in the mlip manuals. mlip-2 is recommended, as it is the only officially supported version by mlip. Please refer to https://mlip.skoltech.ru.

• Parameters
  • mlip-2 – mtp_filename (str): Name of file with MTP to be loaded. write_cfgs (str): Name of file for mlp processed configurations to be written to. write_cfgs_skip (int): Skipped number of processed configurations before writing. select (bool): activates or deactivates calculation of extrapolation grades and

optionally writing configurations with high extrapolation grades. False is recommended for large-scale MD run.

select_save_selected (str): Name of file for saving configurations with grade

  exceeding select_threshold.

select_threshold (float): Configurations with extrapolation grade exceeding the

  value will be saved to the specified file.

select_threshold_break (float): The mlip execution will be interrupted if the

  extrapolation grade exceeds this value.

select_load_state (str): Name of file for loading the active learning state,

  typically created by the mlp calc-grade command.

select_log (str): Name of file (or standard output stream stdout/stderr) for

  writing a log of the configuration selection process.

* **mlip-dev** – Abinitio (int): Defines Ab-initio models. Default to 1.

0: If Ab-initio models is not required. 1: Used if driver provides EFS data with configurations. 2: Use embedded Lennard-Jones pair potentials.

r_min (float): Distance to minimum of pair function (in Angstroms).

Default to 2.0.

scale (float): Value of pair function in minimum (in eV).

Default to 1.0.

cutoff (float): Cutoff radius (in Angstroms). Default to 5.0. 3: Use DFT models by VASP. Linking via files exchange. POSCAR (str): Relative path of POSCAR file. OUTCAR (str): Relative path of OUTCAR file. Start_command (str): Relative path of command file. 4: Use potentials calculating by LAMMPS. Linking via files exchange. Input_file (str): File with configuration to be read by lammps. Output_file (str): File with configuration and EFS data to be read by MLIP. Start_command (str): Relative path of command file. 5: Use MTP as Ab-initio potentials. MTP_filename (str): MTP file name.

MLIP (str): MTP.

load_from (str): Potential filename. Cacluate_EFS (bool): Whether to perform EFS calculation by MTP. Fit (bool): Whether to perform MTP learning.

Save (str): Output MTP file name (for trained MTP). Energy_equation_weight (float): Weight for energy equation in

fitting procedure. Default to 1.0. Forces_equation_weight (float): Weight for forces equations in

fitting procedure. Default to 0.001.

Stress_equation_weight (float): Weight for stresses equations in

fitting procedure.  Default to 0.1.

Relative_forces_weight (float): If greater than zero, large forces

will be fitted less accurate than small. Default to 0.0.

Fit_log (str): File to write fitting log. No logging if not specified.

Default to None.

Select (bool): Whether to activate active learning. Default to False. Site_E_weight (float): Weight for site energy equations in

selection procedure. Default to 1.0.

Energy_weight (float): Weight for energy equation in

selection procedure. Default to 0.0.

Forces_weight (float): Weight for forces equations in

selection procedure. Default to 0.0.

Stress_weight (float): Weight for stresses equations in

selection procedure. Default to 0.0.

Threshold_slct (float): Selection threshold - maximum

allowed extrapolation level. Default to 0.1.

Save_TS (str): Filename where selected configurations

will be saved. No configuration saving if not specified.
Default to None.

Save_state (str): Filename where state of the selection

will be saved. No saving if not specified. Default to None.

Load_state (str): Filename where state of the selection

will be loaded. No saving if not specified. Default to None.

Select_log (str): File to write fitting log. No logging

if not specified. Default to None.

LOFT (bool): Whether to perform learning on the fly. Default to False EFSviaMTP (bool): Works only on LOFT regime. If True,

only MTP-calculated EFS will be passed to driver, else
pass to driver ab-initio EFS while LOTF when learning occurs.

Log (str): Filename to write log of learning on the fly process.

No logging if not specified. Default to None.

Check_errors (bool): If True, comparison and accumulation of

error statistics for EFS calculated by ab-initio models and MTP.
Default to False.

Log (str): Filename to write log of learning on the fly process.

    No logging if not specified. Default to None.

Write_cfgs (bool): File for writing all processed configurations.

No configuration recording if not specified. Default to None.

Skip_N (int): The number of configurations to skip while writing.

    Default to 0.

Log (str): Filename to write MLIP log. No logging if not specified.

Default to None.

Driver (int): Defines the configuration driver. Default to 1.

0: No driver or external MD driver. 1: Read configurations from database file.

Database_filename (str): Configuration file name. Max_count (int): Maximal number of configurations to read. Log (str): Filename to write reading log. No logging

if not specified. Default to None. 2: Embedded algorithm for relaxation. Pressure (float): External pressure (in GPa).

If not zero enthalpy is minimized. Default to 0.0.

Iteration_limit (int): Maximal number of iteration of

the relaxation process. Default to 500.

Min_dist (float): Minimal interatomic distance constraint

(in Angstroms). Default to 1.0.

Forces_tolerance (float): Forces on atoms in relaxed

configuration should be smaller than this value
(in eV/Angstroms). Default to 0.0001.

Stress_tolerance (float): Stresses in relaxed configuration

should be smaller than this value (in GPa). Default to 0.001.

Max_step (float): Maximal allowed displacement of atoms and

lattice vectors in Cartesian coordinates (in Angstroms).
Default to 0.5.

Min_step (float): Minimal displacement of atoms and

lattice vectors in Cartesian coordinates (in Angstroms).
Default to 1.0e-8.

BFGS_Wolfe_C1 (float): Wolfe condition constant on the function

decrease (linesearch stopping criterea). Default to 1.0e-3.

BFGS_Wolfe_C2 (float): Wolfe condition constant on the gradient

decrease (linesearch stopping criterea). Default to 0.7.

Save_relaxed (str): Filename for output results of relaxation.

No configuration will be saved if not specified.
Default to None.

Log (str): Filename to write relaxation log. No logging

if not specified. Default to None.

write_param(fitted_mtp=’fitted.mtp’, **kwargs)

Write fitted mtp parameter file to perform lammps calculation.

• Parameters fitted_mtp (str) – Filename to store xml formatted parameters.

class maml.apps.pes.NNPotential(name=None, param=None, weight_param=None, scaling_param=None)

Bases: LammpsPotential

This class implements Neural Network Potential.

abc_impl( = <_abc.abc_data object )

_line_up(structure, energy, forces, virial_stress)

Convert input structure, energy, forces, virial_stress to proper configuration format for n2p2 usage. Note that n2p2 takes bohr as length unit and Hartree as energy unit.

• Parameters
  • structure (Structure) – Pymatgen Structure object.
  • energy (float) – DFT-calculated energy of the system.
  • forces (list) – The forces should have dimension (num_atoms, 3).
  • virial_stress (list) – stress should has 6 distinct elements arranged in order [xx, yy, zz, xy, yz, xz].

bohr_to_angstrom(_ = 0.52917721090_ )

eV_to_Ha(_ = 0.03674932217565_ )

evaluate(test_structures, test_energies, test_forces, test_stresses=None)

Evaluate energies, forces and stresses of structures with trained interatomic potentials.

• Parameters
  • test_structures ([Structure]) – List of Pymatgen Structure Objects.
  • test_energies ([float]) – List of DFT-calculated total energies of each structure in structures list.
  • test_forces ([np.array]) – List of DFT-calculated (m, 3) forces of each structure with m atoms in structures list. m can be varied with each single structure case.
  • test_stresses (list) – List of DFT-calculated (6, ) viriral stresses of each structure in structures list.

static from_config(input_filename, scaling_filename, weights_filenames)

Initialize potentials with parameters file.

• Parameters
  • input_filename (str) – The file storing the input configuration of Neural Network Potential.
  • scaling_filename (str) – The file storing scaling info of Neural Network Potential.
  • weights_filenames (list) – List of files storing weights of each specie in Neural Network Potential.

load_input(filename=’input.nn’)

Load input file from trained Neural Network Potential.

• Parameters filename (str) – The input filename.

load_scaler(scaling_filename)

Load scaling info of trained Neural Network Potential.

• Parameters scaling_filename (str) – The scaling file.

load_weights(weights_filename, specie)

Load weights file of trained Neural Network Potential.

• Parameters
  • weights_filename (str) – The weights file.
  • specie (str) – The name of specie.

pair_coeff(_ = ‘pair_coeff * * {}_ )

pair_style(_ = ‘pair_style nnp dir “./” showew no showewsum 0 maxew 10000000 resetew yes cflength 1.8897261328 cfenergy 0.0367493254_ )

read_cfgs(filename=’output.data’)

Read the configuration file.

• Parameters filename (str) – The configuration file to be read.

train(train_structures, train_energies, train_forces, train_stresses=None, **kwargs)

Training data with moment tensor method.

• Parameters
  • train_structures ([Structure]) – The list of Pymatgen Structure object. energies ([float]): The list of total energies of each structure in structures list.
  • train_energies ([float]) – List of total energies of each structure in structures list.
  • train_forces ([np.array]) – List of (m, 3) forces array of each structure with m atoms in structures list. m can be varied with each single structure case.
  • train_stresses (list) – List of (6, ) virial stresses of each structure in structures list.
  • kwargs – Parameters in write_input method.

write_cfgs(filename, cfg_pool)

Write the formatted configuration file.

• Parameters
  • filename (str) – The filename to be written.
  • cfg_pool (list) – The configuration pool contains structure and energy/forces properties.

write_input(**kwargs)

Write input.nn file to train the Neural Network Potential.

• Parameters
  • atom_energy (float) – Atomic reference energy.
  • kwargs – General nnp settings:

atom_energy (dict): Free atom reference energy for each specie. cutoff_type (int): Type of cutoff function. Default to 1

(i.e., cosine function).

scale_features (int): Determine the method to scale the

  symmetry function.
  0: no scaling.
  1: scale_symmetry_functions.
  2: center_symmetry_functions.
  3. scale_symmetry_functions_sigma.

scale_min_short (float): Minimum value for scaling.

  Default to 0.0.

scale_max_short (float): Maximum value for scaling.

  Default to 1.

hidden_layers (list): List of the numbers of

  nodes in each hidden layer.

activations (str): Activation function for each hidden layer.

  ’t’: tanh, ‘s’: logistic, ‘p’: softplus.

normalize_nodes (boolean): Whether to normalize input of nodes.

Additional settings for training:

  epoch (int): Number of training epochs.
  updater_type (int): Weight update method

  > 0: gradient Descent, 1: Kalman filter.

  parallel_mode (int): Training parallelization used.

      Default to serial mode.

  jacobian_mode (int): Jacobian computation mode.

      0: Summation to single gradient,
      1: Per-task summed gradient,
      2: Full Jacobian.

  update_strategy (int): Update strategy.

      0: combined, 1: per-element.

  selection_mode (int): Update candidate selection mode.

      0: random, 1: sort, 2: threshold

  task_batch_size_energy (int): Number of energy update

      candidates prepared per task for each update.

  task_batch_size_force (int): Number of force update

      candidates prepared per task for each update.

  test_fraction (float): Fraction of structures kept for

      testing.

  force_weight (float): Weight of force updates relative

      to energy updates. Default to 10.0

  short_energy_fraction (float): Fraction of energy updates

      per epoch. Default to 1.0.

  short_force_fraction (float): Fraction of force updates

      per epoch. Default to 0.02315.

  short_energy_error_threshold (float): RMSE threshold for

      energy update candidates. Default to 0.0.

  short_force_error_threshold (float): RMSE threshold for

      force update candidates. Default to 1.0.

  rmse_threshold_trials (int): Maximum number of RMSE

      threshold trials. Default to 3.

  weights_min (float): Minimum value for initial random

      weights. Default to -1.

  weights_max (float): Maximum value for initial random

      weights. Default to 1.

  write_trainpoints (int): Write energy comparison every

      this many epochs. Default to 1.

  write_trainforces (int): Write force comparison every

      this many epochs. Default to 1.

  write_weights_epoch (int): Write weights every this many

      epochs. Default to 1.

  write_neuronstats (int): Write neuron statistics every

      this many epochs. Default to 1.

  # Kalman Filter
  kalman_type (int): Kalman filter type. Default to 0.
  kalman_epsilon (float): General Kalman filter parameter

  > epsilon. Default to 0.01.

  kalman_q0 (float): General Kalman filter parameter q0.

      Default to 0.01.

  kalman_qtau (float): General Kalman filter parameter

      qtau. Default to 2.302.

  kalman_qmin (float): General Kalman filter parameter qmin.

      Default to 1e-6.

  kalman_eta (float): Standard Kalman filter parameter eta.

      Default to 0.01.

  kalman_etatau (float): Standard Kalman filter parameter

      etatau. Defaults to 2.302.

  kalman_etamax (float): Standard Kalman filter parameter

      etamax. Default to 1.0.

Symmetry functions:

  r_cut (float): Cutoff distance (unit: Å).
  r_etas (numpy.array): η in radial function.
  r_shift (numpy.array): Rs in radial function.
  a_etas (numpy.array): η in angular function.
  zetas (numpy.array): ζ in angular function.
  lambdas (numpy.array): λ in angular function. Default to (1, -1).

write_param()

Write optimized weights file to perform energy and force prediction.

class maml.apps.pes.NudgedElasticBand(ff_settings, specie, lattice, alat, num_replicas=7, **kwargs)

Bases: LMPStaticCalculator

NudgedElasticBand migration energy calculator.

_parse()

Parse results from dump files.

_sanity_check(structure)

Check if the structure is valid for this calculation.

_setup()

Setup a calculation, writing input files, etc.

calculate()

Calculate the NEB barrier given Potential class.

static get_unit_cell(specie, lattice, alat)

Get the unit cell from specie, lattice type and lattice constant.

• Parameters
  • specie (str) – Name of specie.
  • lattice (str) – The lattice type of structure. e.g. bcc or diamond.
  • alat (float) – The lattice constant of specific lattice and specie.

class maml.apps.pes.Potential(model, describer: BaseDescriber | None = None, **kwargs)

Bases: PotentialMixin, BaseModel

Potential models that can be used to fit structure-[energy, force, stress] pairs.

class maml.apps.pes.SNAPotential(model, name=None)

Bases: LammpsPotential

This class implements Spectral Neighbor Analysis Potential.

abc_impl( = <_abc.abc_data object )

evaluate(test_structures, test_energies, test_forces, test_stresses=None, include_stress=False, stress_format=’VASP’)

Evaluate energies, forces and stresses of structures with trained machinea learning potentials.

• Parameters
  • test_structures ([Structure]) – List of Pymatgen Structure Objects.
  • test_energies ([float]) – List of DFT-calculated total energies of each structure in structures list.
  • test_forces ([np.array]) – List of DFT-calculated (m, 3) forces of each structure with m atoms in structures list. m can be varied with each single structure case.
  • test_stresses (list) – List of DFT-calculated (6, ) viriral stresses of each structure in structures list.
  • include_stress (bool) – Whether to include stress components.
  • stress_format (str) – stress format, default to “VASP”

static from_config(param_file, coeff_file, **kwargs)

Initialize potentials with parameters file and coefficient file.

• Parameters
  • param_file (str) – The file storing the configuration of potentials.
  • coeff_file (str) – The file storing the coefficients of potentials.
• Returns SNAPotential.

pair_coeff(_ = ‘pair_coeff * * {coeff_file} {param_file} {elements}_ )

pair_style(_ = ‘pair_style snap_ )

train(train_structures, train_energies, train_forces, train_stresses=None, include_stress=False, stress_format=’VASP’, **kwargs)

Training data with models.

• Parameters
  • train_structures ([Structure]) – The list of Pymatgen Structure object. energies ([float]): The list of total energies of each structure in structures list.
  • train_energies ([float]) – List of total energies of each structure in structures list.
  • train_forces ([np.array]) – List of (m, 3) forces array of each structure with m atoms in structures list. m can be varied with each single structure case.
  • train_stresses (list) – List of (6, ) virial stresses of each structure in structures list.
  • include_stress (bool) – Whether to include stress components.
  • stress_format (string) – stress format, default to VASP

write_param()

Write parameter and coefficient file to perform lammps calculation.

class maml.apps.pes.SpectralNeighborAnalysis(rcutfac, twojmax, element_profile, quadratic=False, **kwargs)

Bases: LMPStaticCalculator

Calculator for bispectrum components to characterize the local neighborhood of each atom in a general way.

Usage:

[(b, db, e)] = sna.calculate([Structure])
b: 2d NumPy array with shape (N, n_bs) containing bispectrum

> coefficients, where N is the No. of atoms in structure and
> n_bs is the No. of bispectrum components.

db: 2d NumPy array with shape (N, 3 \* n_bs \* n_elements)

    containing the first order derivatives of bispectrum
    coefficients with respect to atomic coordinates,
    where n_elements is the No. of elements in element_profile.

e: 2d NumPy array with shape (N, 1) containing the element of

    each atom.

CMDS( = [‘pair_style lj/cut 10’, ‘pair_coeff * * 1 1’, ‘compute sna all sna/atom ‘, ‘compute snad all snad/atom ‘, ‘compute snav all snav/atom ‘, ‘dump 1 all custom 1 dump.element element’, ‘dump_modify 1 sort id’, ‘dump 2 all custom 1 dump.sna c_sna[*]’, ‘dump_modify 2 sort id’, ‘dump 3 all custom 1 dump.snad c_snad[*]’, ‘dump_modify 3 sort id’, ‘dump 4 all custom 1 dump.snav c_snav[*]’, ‘dump_modify 4 sort id’_ )

_parse()

Parse results from dump files.

_sanity_check(structure)

Check if the structure is valid for this calculation.

_setup()

Setup a calculation, writing input files, etc.

static get_bs_subscripts(twojmax)

Method to list the subscripts 2j1, 2j2, 2j of bispectrum components.

• Parameters twojmax (int) – Band limit for bispectrum components.
• Returns List of all subscripts [2j1, 2j2, 2j].

property n_bs()

Returns No. of bispectrum components to be calculated.

maml.apps.pes.get_default_lmp_exe()

Get lammps executable Returns: Lammps executable name.

maml.apps.pes._base module

Base classes for potentials.

class maml.apps.pes._base.Potential(model, describer: BaseDescriber | None = None, **kwargs)

Bases: PotentialMixin, BaseModel

Potential models that can be used to fit structure-[energy, force, stress] pairs.

class maml.apps.pes._base.PotentialMixin()

Bases: object

Abstract base class for a Interatomic Potential.

abstract evaluate(test_structures, test_energies, test_forces, test_stresses)

Evaluate energies, forces and stresses of structures with trained interatomic potentials.

• Parameters
  • test_structures (list) – List of Pymatgen Structure Objects.
  • test_energies (list) – List of DFT-calculated total energies of each structure in structures list.
  • test_forces (list) – List of DFT-calculated (m, 3) forces of each structure with m atoms in structures list. m can be varied with each single structure case.
  • test_stresses (list) – List of DFT-calculated (6, ) viriral stresses of each structure in structures list.

abstract from_config(**kwargs)

Initialize potentials with parameters file.

abstract predict_efs(structure)

Predict energy, forces and stresses of the structure.

• Parameters structure (Structure) – Pymatgen Structure object.
• Returns energy, forces, stress

abstract train(train_structures, train_energies, train_forces, train_stresses, **kwargs)

Train interatomic potentials with energies, forces ann stresses corresponding

to structures.

• Parameters
  • train_structures (list) – List of Pymatgen Structure objects.
  • train_energies (list) – List of DFT-calculated total energies of each structure in structures list.
  • train_forces (list) – List of DFT-calculated (m, 3) forces of each structure with m atoms in structures list. m can be varied with each single structure case.
  • train_stresses (list) – List of DFT-calculated (6, ) virial stresses of each structure in structures list.

abstract write_param()

Write optimized weights file to perform energy and force prediction via lammps calculation.

maml.apps.pes._gap module

This module provides SOAP-GAP interatomic potential class.

class maml.apps.pes._gap.GAPotential(name=None, param=None)

Bases: LammpsPotential

This class implements Smooth Overlap of Atomic Position potentials.

abc_impl( = <_abc.abc_data object )

static _line_up(structure, energy, forces, virial_stress)

Convert input structure, energy, forces, virial_stress to proper configuration format for MLIP usage.

• Parameters
  • structure (Structure) – Pymatgen Structure object.
  • energy (float) – DFT-calculated energy of the system.
  • forces (list) – The forces should have dimension (num_atoms, 3).
  • virial_stress (list) – stress should has 6 distinct elements arranged in order [xx, yy, zz, xy, yz, xz].

Returns:

evaluate(test_structures, test_energies, test_forces, test_stresses=None, predict_energies=True, predict_forces=True, predict_stress=False)

Evaluate energies, forces and stresses of structures with trained interatomic potentials.

• Parameters
  • test_structures ([Structure]) – List of Pymatgen Structure Objects.
  • test_energies ([float]) – List of DFT-calculated total energies of each structure in structures list.
  • test_forces ([np.array]) – List of DFT-calculated (m, 3) forces of each structure with m atoms in structures list. m can be varied with each single structure case.
  • test_stresses (list) – List of DFT-calculated (6, ) viriral stresses of each structure in structures list.
  • predict_energies (bool) – Whether to predict energies of configurations.
  • predict_forces (bool) – Whether to predict forces of configurations.
  • predict_stress (bool) – Whether to predict virial stress of configurations.

static from_config(filename)

Initialize potentials with parameters file.

• Parameters filename (str) – The file storing parameters of potentials, filename should ends with “.xml”.
• Returns GAPotential.

pair_coeff(_ = ‘pair_coeff * * {} {} {}_ )

pair_style(_ = ‘pair_style quip_ )

static read_cfgs(filename, predict=False)

Read the configuration file.

• Parameters filename (str) – The configuration file to be read.

save(filename=’param.yaml’)

Save parameters of the potentials.

• Parameters filename (str) – The file to store parameters of potentials.
• Returns (str)

train(train_structures, train_energies, train_forces, train_stresses=None, default_sigma=(0.0005, 0.1, 0.05, 0.01), use_energies=True, use_forces=True, use_stress=False, **kwargs)

Training data with gaussian process regression.

• Parameters
  • train_structures ([Structure]) – The list of Pymatgen Structure object. energies ([float]): The list of total energies of each structure in structures list.
  • train_energies ([float]) – List of total energies of each structure in structures list.
  • train_forces ([np.array]) – List of (m, 3) forces array of each structure with m atoms in structures list. m can be varied with each single structure case.
  • train_stresses (list) – List of (6, ) virial stresses of each structure in structures list.
  • default_sigma (list) – Error criteria in energies, forces, stress and hessian. Should have 4 numbers.
  • use_energies (bool) – Whether to use dft total energies for training. Default to True.
  • use_forces (bool) – Whether to use dft atomic forces for training. Default to True.
  • use_stress (bool) – Whether to use dft virial stress for training. Default to False.
  • kwargs – l_max (int): Parameter to configure GAP. The band limit of

spherical harmonics basis function. Default to 12.

n_max (int): Parameter to configure GAP. The number of radial basis

  function. Default to 10.

atom_sigma (float): Parameter to configure GAP. The width of gaussian

  atomic density. Default to 0.5.

zeta (float): Present when covariance function type is do product.

  Default to 4.

cutoff (float): Parameter to configure GAP. The cutoff radius.

  Default to 4.0.

cutoff_transition_width (float): Parameter to configure GAP.

  The transition width of cutoff radial. Default to 0.5.

delta (float): Parameter to configure Sparsification.

  The signal variance of noise. Default to 1.

f0 (float): Parameter to configure Sparsification.

  The signal mean of noise. Default to 0.0.

n_sparse (int): Parameter to configure Sparsification.

  Number of sparse points.

covariance_type (str): Parameter to configure Sparsification.

  The type of convariance function. Default to dot_product.

sparse_method (str): Method to perform clustering in sparsification.

  Default to ‘cur_points’.

sparse_jitter (float): Intrisic error of atomic/bond energy,

  used to regularise the sparse covariance matrix.
  Default to 1e-8.

e0 (float): Atomic energy value to be subtracted from energies

  before fitting. Default to 0.0.

e0_offset (float): Offset of baseline. If zero, the offset is

  the average atomic energy of the input data or the e0
  specified manually. Default to 0.0.

write_cfgs(filename, cfg_pool)

Write the formatted configuration file.

• Parameters
  • filename (str) – The filename to be written.
  • cfg_pool (list) – The configuration pool contains structure and energy/forces properties.

write_param(xml_filename=’gap.2020.01.xml’)

Write xml file to perform lammps calculation.

• Parameters xml_filename (str) – Filename to store xml formatted parameters.

maml.apps.pes._lammps module

This module provides basic LAMMPS calculator classes.

class maml.apps.pes._lammps.DefectFormation(ff_settings, specie, lattice, alat, **kwargs)

Bases: LMPStaticCalculator

Defect formation energy calculator.

_parse()

Parse results from dump files.

_sanity_check(structure)

Check if the structure is valid for this calculation.

_setup()

Setup a calculation, writing input files, etc.

calculate()

Calculate the vacancy formation given Potential class.

static get_unit_cell(specie, lattice, alat)

Get the unit cell from specie, lattice type and lattice constant.

• Parameters
  • specie (str) – Name of specie.
  • lattice (str) – The lattice type of structure. e.g. bcc or diamond.
  • alat (float) – The lattice constant of specific lattice and specie.

class maml.apps.pes._lammps.ElasticConstant(ff_settings, potential_type=’external’, deformation_size=1e-06, jiggle=1e-05, maxiter=400, maxeval=1000, full_matrix=False, **kwargs)

Bases: LMPStaticCalculator

Elastic constant calculator.

RESTART_CONFIG( = {‘external’: {‘read_command’: ‘read_restart’, ‘restart_file’: ‘restart.equil’, ‘write_command’: ‘write_restart’}, ‘internal’: {‘read_command’: ‘read_restart’, ‘restart_file’: ‘restart.equil’, ‘write_command’: ‘write_restart’}_ )

_parse()

Parse results from dump files.

_sanity_check(structure)

Check if the structure is valid for this calculation.

_setup()

Setup a calculation, writing input files, etc.

class maml.apps.pes._lammps.EnergyForceStress(ff_settings, **kwargs)

Bases: LMPStaticCalculator

Calculate energy, forces and virial stress of structures.

_parse()

Parse results from dump files.

static _rotate_force_stress(structure, forces, stresses)

_sanity_check(structure)

Check if the structure is valid for this calculation.

_setup()

Setup a calculation, writing input files, etc.

calculate(structures)

Calculate the energy, forces and stresses of structures. Proper rotation of the results are applied when the structure is triclinic.

• Parameters structures (list) – a list of structures

Returns: list of (energy, forces, stresses) tuple

class maml.apps.pes._lammps.LMPRelaxationCalculator(ff_settings, box_relax=True, box_relax_keywords=’aniso 0.0 vmax 0.001’, box_triclinic=False, min_style=’cg’, etol=1e-15, ftol=1e-15, maxiter=5000, maxeval=5000, **kwargs)

Bases: LMPStaticCalculator

Structural Relaxation Calculator.

_parse()

Parse results from dump files.

_sanity_check(structure)

Check if the structure is valid for this calculation.

_setup()

Setup a calculation, writing input files, etc.

class maml.apps.pes._lammps.LMPStaticCalculator(**kwargs)

Bases: object

Abstract class to perform static structure property calculation using LAMMPS.

COMMON_CMDS( = [‘units metal’, ‘atom_style charge’, ‘box tilt large’, ‘read_data data.static’, ‘run 0’_ )

abstract _parse()

Parse results from dump files.

abstract _sanity_check(structure)

Check if the structure is valid for this calculation.

abstract _setup()

Setup a calculation, writing input files, etc.

allowed_kwargs(_ = [‘lmp_exe’_ )

calculate(structures)

Perform the calculation on a series of structures.

• Parameters structures – Input structures in a list.
• Returns List of computed data corresponding to each structure, varies with different subclasses.

set_lmp_exe(lmp_exe: str)

Set lammps executable for the instance.

• Parameters lmp_exe (str) – lammps executable path

Returns:

class maml.apps.pes._lammps.LammpsPotential(model, describer: BaseDescriber | None = None, **kwargs)

Bases: Potential, ABC

Lammps compatible potentials that call lammps executable for energy/force/stress calculations.

abc_impl( = <_abc.abc_data object )

predict_efs(structure)

Predict energy, forces and stresses of the structure.

• Parameters structure (Structure) – Pymatgen Structure object.
• Returns energy, forces, stress

class maml.apps.pes._lammps.LatticeConstant(ff_settings, box_relax=True, box_relax_keywords=’aniso 0.0 vmax 0.001’, box_triclinic=False, min_style=’cg’, etol=1e-15, ftol=1e-15, maxiter=5000, maxeval=5000, **kwargs)

Bases: LMPRelaxationCalculator

Lattice Constant Relaxation Calculator.

calculate(structures)

Calculate the relaxed lattice parameters of a list of structures.

• Parameters structures ([Structure]) – Input structures in a list.
• Returns List of relaxed lattice constants (a, b, c in Å) of the input structures.

class maml.apps.pes._lammps.NudgedElasticBand(ff_settings, specie, lattice, alat, num_replicas=7, **kwargs)

Bases: LMPStaticCalculator

NudgedElasticBand migration energy calculator.

_parse()

Parse results from dump files.

_sanity_check(structure)

Check if the structure is valid for this calculation.

_setup()

Setup a calculation, writing input files, etc.

calculate()

Calculate the NEB barrier given Potential class.

static get_unit_cell(specie, lattice, alat)

Get the unit cell from specie, lattice type and lattice constant.

• Parameters
  • specie (str) – Name of specie.
  • lattice (str) – The lattice type of structure. e.g. bcc or diamond.
  • alat (float) – The lattice constant of specific lattice and specie.

class maml.apps.pes._lammps.SpectralNeighborAnalysis(rcutfac, twojmax, element_profile, quadratic=False, **kwargs)

Bases: LMPStaticCalculator

Calculator for bispectrum components to characterize the local neighborhood of each atom in a general way.

Usage:

[(b, db, e)] = sna.calculate([Structure])
b: 2d NumPy array with shape (N, n_bs) containing bispectrum

> coefficients, where N is the No. of atoms in structure and
> n_bs is the No. of bispectrum components.

db: 2d NumPy array with shape (N, 3 \* n_bs \* n_elements)

    containing the first order derivatives of bispectrum
    coefficients with respect to atomic coordinates,
    where n_elements is the No. of elements in element_profile.

e: 2d NumPy array with shape (N, 1) containing the element of

    each atom.

CMDS( = [‘pair_style lj/cut 10’, ‘pair_coeff * * 1 1’, ‘compute sna all sna/atom ‘, ‘compute snad all snad/atom ‘, ‘compute snav all snav/atom ‘, ‘dump 1 all custom 1 dump.element element’, ‘dump_modify 1 sort id’, ‘dump 2 all custom 1 dump.sna c_sna[*]’, ‘dump_modify 2 sort id’, ‘dump 3 all custom 1 dump.snad c_snad[*]’, ‘dump_modify 3 sort id’, ‘dump 4 all custom 1 dump.snav c_snav[*]’, ‘dump_modify 4 sort id’_ )

_parse()

Parse results from dump files.

_sanity_check(structure)

Check if the structure is valid for this calculation.

_setup()

Setup a calculation, writing input files, etc.

static get_bs_subscripts(twojmax)

Method to list the subscripts 2j1, 2j2, 2j of bispectrum components.

• Parameters twojmax (int) – Band limit for bispectrum components.
• Returns List of all subscripts [2j1, 2j2, 2j].

property n_bs()

Returns No. of bispectrum components to be calculated.

class maml.apps.pes._lammps.SurfaceEnergy(ff_settings, bulk_structure, miller_indexes, min_slab_size=15, min_vacuum_size=15, lll_reduce=False, center_slab=False, in_unit_planes=False, primitive=True, max_normal_search=None, reorient_lattice=True, box_relax=False, **kwargs)

Bases: LMPRelaxationCalculator

Surface energy Calculator.

This calculator generate and calculate surface energies of slab structures based on inputs of bulk_structure and miller_indexes with the SlabGenerator in pymatgen: https://pymatgen.org/pymatgen.core.surface.html

calculate()

Calculate surface energies with the formula: E(Surface) = (E(Slab) - E(bulk)) / Area(surface). (J/m^2).

• Returns List of miller_indexes with their respective relaxed slab structures and surface energies in J/m^2.

maml.apps.pes._lammps._pretty_input(lines)

maml.apps.pes._lammps.read_dump(file_name, dtype=’float’)

maml.apps.pes._lammps.get_default_lmp_exe()

Get lammps executable Returns: Lammps executable name.

maml.apps.pes._mtp module

This module provides MTP interatomic potential class.

class maml.apps.pes._mtp.MTPotential(name=None, param=None, version=None)

Bases: LammpsPotential

This class implements moment tensor potentials. Installation of the mlip package is needed. Please refer to https://mlip.skoltech.ru.

abc_impl( = <_abc.abc_data object )

_line_up(structure, energy, forces, virial_stress)

Convert input structure, energy, forces, virial_stress to proper configuration format for mlip usage.

• Parameters
  • structure (Structure) – Pymatgen Structure object.
  • energy (float) – DFT-calculated energy of the system.
  • forces (list) – The forces should have dimension (num_atoms, 3).
  • virial_stress (list) – stress should has 6 distinct elements arranged in order [xx, yy, zz, yz, xz, xy].

evaluate(test_structures, test_energies, test_forces, test_stresses=None, **kwargs)

Evaluate energies, forces and stresses of structures with trained interatomic potentials.

• Parameters
  • test_structures ([Structure]) – List of Pymatgen Structure Objects.
  • test_energies ([float]) – List of DFT-calculated total energies of each structure in structures list.
  • test_forces ([np.array]) – List of DFT-calculated (m, 3) forces of each structure with m atoms in structures list. m can be varied with each single structure case.
  • test_stresses (list) – List of DFT-calculated (6, ) viriral stresses of each structure in structures list.
  • kwargs – Parameters of write_param method.

static from_config(filename, elements)

Initialize potentials with parameters file.

• Parameters
  • filename (str) – The file storing parameters of potentials, filename should ends with “.mtp”.
  • elements (list) – The list of elements.
• Returns MTPotential

pair_coeff(_ = ‘pair_coeff * *_ )

pair_style(_ = ‘pair_style mlip {}_ )

read_cfgs(filename)

• Parameters filename (str) – The configuration file to be read.

train(train_structures, train_energies, train_forces, train_stresses, unfitted_mtp=’08g.mtp’, max_dist=5, radial_basis_size=8, max_iter=1000, energy_weight=1, force_weight=0.01, stress_weight=0.001, init_params=’same’, scale_by_force=0, bfgs_conv_tol=0.001, weighting=’vibration’)

Training data with moment tensor method.

• Parameters
  • train_structures ([Structure]) – The list of Pymatgen Structure object. energies ([float]): The list of total energies of each structure in structures list.
  • train_energies ([float]) – List of total energies of each structure in structures list.
  • train_forces ([np.array]) – List of (m, 3) forces array of each structure with m atoms in structures list. m can be varied with each single structure case.
  • train_stresses (list) – List of (6, ) virial stresses of each structure in structures list.
  • unfitted_mtp (str) – Define the initial mtp file. Default to the mtp file stored in .params directory.
  • max_dist (float) – The actual radial cutoff.
  • radial_basis_size (int) – Relevant to number of radial basis function.
  • max_iter (int) – The number of maximum iteration.
  • energy_weight (float) – The weight of energy.
  • force_weight (float) – The weight of forces.
  • stress_weight (float) – The weight of stresses. Zero-weight can be assigned.
  • init_params (str) – How to initialize parameters if a potential was not pre-fitted. Choose from “same” and “random”.
  • scale_by_force (float) – Default=0. If >0 then configurations near equilibrium (with roughly force < scale_by_force) get more weight.
  • bfgs_conv_tol (float) – Stop training if error dropped by a factor smaller than this over 50 BFGS iterations.
  • weighting (str) – How to weight configuration with different sizes relative to each other. Choose from “vibrations”, “molecules” and “structures”.

write_cfg(filename, cfg_pool)

Write configurations to file :param filename: filename :type filename: str :param cfg_pool: list of configurations. :type cfg_pool: list

Returns:

write_ini(mtp_filename=’fitted.mtp’, select=False, **kwargs)

Write mlip.ini file for mlip packages of version mlip-2 or mlip-dev. Supported keyword arguments are parallel with options stated in the mlip manuals. mlip-2 is recommended, as it is the only officially supported version by mlip. Please refer to https://mlip.skoltech.ru.

• Parameters
  • mlip-2 – mtp_filename (str): Name of file with MTP to be loaded. write_cfgs (str): Name of file for mlp processed configurations to be written to. write_cfgs_skip (int): Skipped number of processed configurations before writing. select (bool): activates or deactivates calculation of extrapolation grades and

optionally writing configurations with high extrapolation grades. False is recommended for large-scale MD run.

select_save_selected (str): Name of file for saving configurations with grade

  exceeding select_threshold.

select_threshold (float): Configurations with extrapolation grade exceeding the

  value will be saved to the specified file.

select_threshold_break (float): The mlip execution will be interrupted if the

  extrapolation grade exceeds this value.

select_load_state (str): Name of file for loading the active learning state,

  typically created by the mlp calc-grade command.

select_log (str): Name of file (or standard output stream stdout/stderr) for

  writing a log of the configuration selection process.

* **mlip-dev** – Abinitio (int): Defines Ab-initio models. Default to 1.

0: If Ab-initio models is not required. 1: Used if driver provides EFS data with configurations. 2: Use embedded Lennard-Jones pair potentials.

r_min (float): Distance to minimum of pair function (in Angstroms).

Default to 2.0.

scale (float): Value of pair function in minimum (in eV).

Default to 1.0.

cutoff (float): Cutoff radius (in Angstroms). Default to 5.0. 3: Use DFT models by VASP. Linking via files exchange. POSCAR (str): Relative path of POSCAR file. OUTCAR (str): Relative path of OUTCAR file. Start_command (str): Relative path of command file. 4: Use potentials calculating by LAMMPS. Linking via files exchange. Input_file (str): File with configuration to be read by lammps. Output_file (str): File with configuration and EFS data to be read by MLIP. Start_command (str): Relative path of command file. 5: Use MTP as Ab-initio potentials. MTP_filename (str): MTP file name.

MLIP (str): MTP.

load_from (str): Potential filename. Cacluate_EFS (bool): Whether to perform EFS calculation by MTP. Fit (bool): Whether to perform MTP learning.

Save (str): Output MTP file name (for trained MTP). Energy_equation_weight (float): Weight for energy equation in

fitting procedure. Default to 1.0. Forces_equation_weight (float): Weight for forces equations in

fitting procedure. Default to 0.001.

Stress_equation_weight (float): Weight for stresses equations in

fitting procedure.  Default to 0.1.

Relative_forces_weight (float): If greater than zero, large forces

will be fitted less accurate than small. Default to 0.0.

Fit_log (str): File to write fitting log. No logging if not specified.

Default to None.

Select (bool): Whether to activate active learning. Default to False. Site_E_weight (float): Weight for site energy equations in

selection procedure. Default to 1.0.

Energy_weight (float): Weight for energy equation in

selection procedure. Default to 0.0.

Forces_weight (float): Weight for forces equations in

selection procedure. Default to 0.0.

Stress_weight (float): Weight for stresses equations in

selection procedure. Default to 0.0.

Threshold_slct (float): Selection threshold - maximum

allowed extrapolation level. Default to 0.1.

Save_TS (str): Filename where selected configurations

will be saved. No configuration saving if not specified.
Default to None.

Save_state (str): Filename where state of the selection

will be saved. No saving if not specified. Default to None.

Load_state (str): Filename where state of the selection

will be loaded. No saving if not specified. Default to None.

Select_log (str): File to write fitting log. No logging

if not specified. Default to None.

LOFT (bool): Whether to perform learning on the fly. Default to False EFSviaMTP (bool): Works only on LOFT regime. If True,

only MTP-calculated EFS will be passed to driver, else
pass to driver ab-initio EFS while LOTF when learning occurs.

Log (str): Filename to write log of learning on the fly process.

No logging if not specified. Default to None.

Check_errors (bool): If True, comparison and accumulation of

error statistics for EFS calculated by ab-initio models and MTP.
Default to False.

Log (str): Filename to write log of learning on the fly process.

    No logging if not specified. Default to None.

Write_cfgs (bool): File for writing all processed configurations.

No configuration recording if not specified. Default to None.

Skip_N (int): The number of configurations to skip while writing.

    Default to 0.

Log (str): Filename to write MLIP log. No logging if not specified.

Default to None.

Driver (int): Defines the configuration driver. Default to 1.

0: No driver or external MD driver. 1: Read configurations from database file.

Database_filename (str): Configuration file name. Max_count (int): Maximal number of configurations to read. Log (str): Filename to write reading log. No logging

if not specified. Default to None. 2: Embedded algorithm for relaxation. Pressure (float): External pressure (in GPa).

If not zero enthalpy is minimized. Default to 0.0.

Iteration_limit (int): Maximal number of iteration of

the relaxation process. Default to 500.

Min_dist (float): Minimal interatomic distance constraint

(in Angstroms). Default to 1.0.

Forces_tolerance (float): Forces on atoms in relaxed

configuration should be smaller than this value
(in eV/Angstroms). Default to 0.0001.

Stress_tolerance (float): Stresses in relaxed configuration

should be smaller than this value (in GPa). Default to 0.001.

Max_step (float): Maximal allowed displacement of atoms and

lattice vectors in Cartesian coordinates (in Angstroms).
Default to 0.5.

Min_step (float): Minimal displacement of atoms and

lattice vectors in Cartesian coordinates (in Angstroms).
Default to 1.0e-8.

BFGS_Wolfe_C1 (float): Wolfe condition constant on the function

decrease (linesearch stopping criterea). Default to 1.0e-3.

BFGS_Wolfe_C2 (float): Wolfe condition constant on the gradient

decrease (linesearch stopping criterea). Default to 0.7.

Save_relaxed (str): Filename for output results of relaxation.

No configuration will be saved if not specified.
Default to None.

Log (str): Filename to write relaxation log. No logging

if not specified. Default to None.

write_param(fitted_mtp=’fitted.mtp’, **kwargs)

Write fitted mtp parameter file to perform lammps calculation.

• Parameters fitted_mtp (str) – Filename to store xml formatted parameters.

maml.apps.pes._mtp.feed(attribute, kwargs, dictionary, tab=’\t’)

• Parameters
  • attribute (str) – Attribute to be operated.
  • kwargs (dict) – Generic parameters.
  • dictionary (dict) – The default parameters dictionary.
  • tab (str) – ‘t’ or ‘tt’, depend on orders of attribute.
• Returns (str).

maml.apps.pes._nnp module

This module provides NNP interatomic potential class.

class maml.apps.pes._nnp.NNPotential(name=None, param=None, weight_param=None, scaling_param=None)

Bases: LammpsPotential

This class implements Neural Network Potential.

abc_impl( = <_abc.abc_data object )

_line_up(structure, energy, forces, virial_stress)

Convert input structure, energy, forces, virial_stress to proper configuration format for n2p2 usage. Note that n2p2 takes bohr as length unit and Hartree as energy unit.

• Parameters
  • structure (Structure) – Pymatgen Structure object.
  • energy (float) – DFT-calculated energy of the system.
  • forces (list) – The forces should have dimension (num_atoms, 3).
  • virial_stress (list) – stress should has 6 distinct elements arranged in order [xx, yy, zz, xy, yz, xz].

bohr_to_angstrom(_ = 0.52917721090_ )

eV_to_Ha(_ = 0.03674932217565_ )

evaluate(test_structures, test_energies, test_forces, test_stresses=None)

Evaluate energies, forces and stresses of structures with trained interatomic potentials.

• Parameters
  • test_structures ([Structure]) – List of Pymatgen Structure Objects.
  • test_energies ([float]) – List of DFT-calculated total energies of each structure in structures list.
  • test_forces ([np.array]) – List of DFT-calculated (m, 3) forces of each structure with m atoms in structures list. m can be varied with each single structure case.
  • test_stresses (list) – List of DFT-calculated (6, ) viriral stresses of each structure in structures list.

static from_config(input_filename, scaling_filename, weights_filenames)

Initialize potentials with parameters file.

• Parameters
  • input_filename (str) – The file storing the input configuration of Neural Network Potential.
  • scaling_filename (str) – The file storing scaling info of Neural Network Potential.
  • weights_filenames (list) – List of files storing weights of each specie in Neural Network Potential.

load_input(filename=’input.nn’)

Load input file from trained Neural Network Potential.

• Parameters filename (str) – The input filename.

load_scaler(scaling_filename)

Load scaling info of trained Neural Network Potential.

• Parameters scaling_filename (str) – The scaling file.

load_weights(weights_filename, specie)

Load weights file of trained Neural Network Potential.

• Parameters
  • weights_filename (str) – The weights file.
  • specie (str) – The name of specie.

pair_coeff(_ = ‘pair_coeff * * {}_ )

pair_style(_ = ‘pair_style nnp dir “./” showew no showewsum 0 maxew 10000000 resetew yes cflength 1.8897261328 cfenergy 0.0367493254_ )

read_cfgs(filename=’output.data’)

Read the configuration file.

• Parameters filename (str) – The configuration file to be read.

train(train_structures, train_energies, train_forces, train_stresses=None, **kwargs)

Training data with moment tensor method.

• Parameters
  • train_structures ([Structure]) – The list of Pymatgen Structure object. energies ([float]): The list of total energies of each structure in structures list.
  • train_energies ([float]) – List of total energies of each structure in structures list.
  • train_forces ([np.array]) – List of (m, 3) forces array of each structure with m atoms in structures list. m can be varied with each single structure case.
  • train_stresses (list) – List of (6, ) virial stresses of each structure in structures list.
  • kwargs – Parameters in write_input method.

write_cfgs(filename, cfg_pool)

Write the formatted configuration file.

• Parameters
  • filename (str) – The filename to be written.
  • cfg_pool (list) – The configuration pool contains structure and energy/forces properties.

write_input(**kwargs)

Write input.nn file to train the Neural Network Potential.

• Parameters
  • atom_energy (float) – Atomic reference energy.
  • kwargs – General nnp settings:

atom_energy (dict): Free atom reference energy for each specie. cutoff_type (int): Type of cutoff function. Default to 1

(i.e., cosine function).

scale_features (int): Determine the method to scale the

  symmetry function.
  0: no scaling.
  1: scale_symmetry_functions.
  2: center_symmetry_functions.
  3. scale_symmetry_functions_sigma.

scale_min_short (float): Minimum value for scaling.

  Default to 0.0.

scale_max_short (float): Maximum value for scaling.

  Default to 1.

hidden_layers (list): List of the numbers of

  nodes in each hidden layer.

activations (str): Activation function for each hidden layer.

  ’t’: tanh, ‘s’: logistic, ‘p’: softplus.

normalize_nodes (boolean): Whether to normalize input of nodes.

Additional settings for training:

  epoch (int): Number of training epochs.
  updater_type (int): Weight update method

  > 0: gradient Descent, 1: Kalman filter.

  parallel_mode (int): Training parallelization used.

      Default to serial mode.

  jacobian_mode (int): Jacobian computation mode.

      0: Summation to single gradient,
      1: Per-task summed gradient,
      2: Full Jacobian.

  update_strategy (int): Update strategy.

      0: combined, 1: per-element.

  selection_mode (int): Update candidate selection mode.

      0: random, 1: sort, 2: threshold

  task_batch_size_energy (int): Number of energy update

      candidates prepared per task for each update.

  task_batch_size_force (int): Number of force update

      candidates prepared per task for each update.

  test_fraction (float): Fraction of structures kept for

      testing.

  force_weight (float): Weight of force updates relative

      to energy updates. Default to 10.0

  short_energy_fraction (float): Fraction of energy updates

      per epoch. Default to 1.0.

  short_force_fraction (float): Fraction of force updates

      per epoch. Default to 0.02315.

  short_energy_error_threshold (float): RMSE threshold for

      energy update candidates. Default to 0.0.

  short_force_error_threshold (float): RMSE threshold for

      force update candidates. Default to 1.0.

  rmse_threshold_trials (int): Maximum number of RMSE

      threshold trials. Default to 3.

  weights_min (float): Minimum value for initial random

      weights. Default to -1.

  weights_max (float): Maximum value for initial random

      weights. Default to 1.

  write_trainpoints (int): Write energy comparison every

      this many epochs. Default to 1.

  write_trainforces (int): Write force comparison every

      this many epochs. Default to 1.

  write_weights_epoch (int): Write weights every this many

      epochs. Default to 1.

  write_neuronstats (int): Write neuron statistics every

      this many epochs. Default to 1.

  # Kalman Filter
  kalman_type (int): Kalman filter type. Default to 0.
  kalman_epsilon (float): General Kalman filter parameter

  > epsilon. Default to 0.01.

  kalman_q0 (float): General Kalman filter parameter q0.

      Default to 0.01.

  kalman_qtau (float): General Kalman filter parameter

      qtau. Default to 2.302.

  kalman_qmin (float): General Kalman filter parameter qmin.

      Default to 1e-6.

  kalman_eta (float): Standard Kalman filter parameter eta.

      Default to 0.01.

  kalman_etatau (float): Standard Kalman filter parameter

      etatau. Defaults to 2.302.

  kalman_etamax (float): Standard Kalman filter parameter

      etamax. Default to 1.0.

Symmetry functions:

  r_cut (float): Cutoff distance (unit: Å).
  r_etas (numpy.array): η in radial function.
  r_shift (numpy.array): Rs in radial function.
  a_etas (numpy.array): η in angular function.
  zetas (numpy.array): ζ in angular function.
  lambdas (numpy.array): λ in angular function. Default to (1, -1).

write_param()

Write optimized weights file to perform energy and force prediction.

maml.apps.pes._snap module

This module provides SNAP interatomic potential class.

class maml.apps.pes._snap.SNAPotential(model, name=None)

Bases: LammpsPotential

This class implements Spectral Neighbor Analysis Potential.

abc_impl( = <_abc.abc_data object )

evaluate(test_structures, test_energies, test_forces, test_stresses=None, include_stress=False, stress_format=’VASP’)

Evaluate energies, forces and stresses of structures with trained machinea learning potentials.

• Parameters
  • test_structures ([Structure]) – List of Pymatgen Structure Objects.
  • test_energies ([float]) – List of DFT-calculated total energies of each structure in structures list.
  • test_forces ([np.array]) – List of DFT-calculated (m, 3) forces of each structure with m atoms in structures list. m can be varied with each single structure case.
  • test_stresses (list) – List of DFT-calculated (6, ) viriral stresses of each structure in structures list.
  • include_stress (bool) – Whether to include stress components.
  • stress_format (str) – stress format, default to “VASP”

static from_config(param_file, coeff_file, **kwargs)

Initialize potentials with parameters file and coefficient file.

• Parameters
  • param_file (str) – The file storing the configuration of potentials.
  • coeff_file (str) – The file storing the coefficients of potentials.
• Returns SNAPotential.

pair_coeff(_ = ‘pair_coeff * * {coeff_file} {param_file} {elements}_ )

pair_style(_ = ‘pair_style snap_ )

train(train_structures, train_energies, train_forces, train_stresses=None, include_stress=False, stress_format=’VASP’, **kwargs)

Training data with models.

• Parameters
  • train_structures ([Structure]) – The list of Pymatgen Structure object. energies ([float]): The list of total energies of each structure in structures list.
  • train_energies ([float]) – List of total energies of each structure in structures list.
  • train_forces ([np.array]) – List of (m, 3) forces array of each structure with m atoms in structures list. m can be varied with each single structure case.
  • train_stresses (list) – List of (6, ) virial stresses of each structure in structures list.
  • include_stress (bool) – Whether to include stress components.
  • stress_format (string) – stress format, default to VASP

write_param()

Write parameter and coefficient file to perform lammps calculation.