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@ -0,0 +1,329 @@
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(pypolymlp-interface)=
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# Force constants calculation using pypolymlp (machine learning potential)
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**This is an experimental feature.**
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With the `--pypolymlp` option, phono3py can interface with the polynomial
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machine learning potential (MLP) code,
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[pypolymlp](https://github.com/sekocha/pypolymlp), to perform training and
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evaluation tasks of MLPs. This feature aims to reduce the computational cost of
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anharmonic force constant calculations by using MLPs as an intermediary layer,
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efficiently representing atomic interactions.
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The training process involves using a dataset consisting of supercell
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displacements, forces, and energies. The trained MLPs are then employed to
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compute forces for supercells with specific displacements.
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For more details on the methodology, refer to <u>A. Togo and A. Seko, J. Chem. Phys.
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**160**, 211001 (2024)</u> [[doi](https://doi.org/10.1063/5.0211296)].
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An example of its usage can be found in the `example/NaCl-pypolymlp` directory
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in the distribution from GitHub or PyPI.
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## Requirement
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- [pypolymlp](https://github.com/sekocha/pypolymlp)
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- [symfc](https://github.com/symfc/symfc)
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## Workflow
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1. Generate random displacements in supercells. Use {ref}`--rd
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<random_displacements_option>` option.
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2. Calculate corresponding forces and energies in supercells. Use of VASP
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interface is recommended for {ref}`--sp <sp_option>` option is supported.
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3. Prepare dataset composed of displacements, forces, and energies in
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supercells. The dataset must be stored in a phono3py-yaml-like file, e.g.,
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`phono3py_params.yaml`. Use {ref}`--cf3 <cf3_option>` and {ref}`--sp
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<sp_option>` option simultaneously.
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4. Develop MLPs. At this step `phono3py.pmlp` is saved.
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5. Generate displacements in supercells either systematic or random displacements.
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6. Evaluate MLPs for forces of the supercells generated in step 5.
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7. Calculate force constants from displacement-force dataset from steps 5 and 6.
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The steps 4-7 are executed in running phono3py with `--pypolymlp`
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option.
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### Steps 1-3: Dataset preparation
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For the training, the following supercell data are required in the phono3py
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setting to use pypolymlp:
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- Displacements
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- Forces
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- Total energies
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These data must be stored in phono3py.yaml-like file.
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The supercells with displacements are generated by
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```
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% phono3py --pa auto --rd 100 -c POSCAR-unitcell --dim 2 2 2
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_ _____
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_ __ | |__ ___ _ __ ___|___ / _ __ _ _
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| '_ \| '_ \ / _ \| '_ \ / _ \ |_ \| '_ \| | | |
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| |_) | | | | (_) | | | | (_) |__) | |_) | |_| |
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| .__/|_| |_|\___/|_| |_|\___/____/| .__/ \__, |
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|_| |_| |___/
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3.5.0
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-------------------------[time 2024-09-19 14:40:00]-------------------------
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Compiled with OpenMP support (max 10 threads).
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Python version 3.12.4
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Spglib version 2.5.0
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Unit cell was read from "POSCAR-unitcell".
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-------------------------------- unit cell ---------------------------------
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Lattice vectors:
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a 5.603287477054753 0.000000000000000 0.000000000000000
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b 0.000000000000000 5.603287477054753 0.000000000000000
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c 0.000000000000000 0.000000000000000 5.603287477054753
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Atomic positions (fractional):
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1 Na 0.00000000000000 0.00000000000000 0.00000000000000 22.990
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2 Na 0.00000000000000 0.50000000000000 0.50000000000000 22.990
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3 Na 0.50000000000000 0.00000000000000 0.50000000000000 22.990
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4 Na 0.50000000000000 0.50000000000000 0.00000000000000 22.990
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5 Cl 0.50000000000000 0.50000000000000 0.50000000000000 35.453
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6 Cl 0.50000000000000 0.00000000000000 0.00000000000000 35.453
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7 Cl 0.00000000000000 0.50000000000000 0.00000000000000 35.453
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8 Cl 0.00000000000000 0.00000000000000 0.50000000000000 35.453
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----------------------------------------------------------------------------
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Supercell (dim): [2 2 2]
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Primitive matrix:
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[0. 0.5 0.5]
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[0.5 0. 0.5]
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[0.5 0.5 0. ]
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Displacement distance: 0.03
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Number of displacements: 100
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NAC parameters were read from "BORN".
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Spacegroup: Fm-3m (225)
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Displacement dataset was written in "phono3py_disp.yaml".
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-------------------------[time 2024-09-19 14:40:00]-------------------------
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_
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___ _ __ __| |
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/ _ \ '_ \ / _` |
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\___|_| |_|\__,_|
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```
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For the generated supercells, forces and energies are calculated. Here it is
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assumed to use the VASP code. Once the calculations are complete, the data
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(forces and energies) can be extracted using the following command:
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```bash
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% phono3py --sp --cf3 vasprun_xmls/vasprun-{00001..00100}.xml
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```
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This command extracts the necessary data and stores it in the
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`phono3py_params.yaml` file. For more details, refer to the description of the
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{ref}`--sp <sp_option>` option. Currently, supercell energy extraction from
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calculator outputs is only supported when using the VASP interface.
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``````{note}
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A set of the VASP calculation results is placed in `example/NaCl-rd`. It is
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obtained by
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```bash
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% tar xvfa ../NaCl-rd/vasprun_xmls.tar.xz
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```
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``````
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### Steps 4-7: Force constants calculation (systematic displacements in step 5)
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After developing MLPs, displacements are generated systematically considering
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crystal symmetry.
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Having `phono3py_params.yaml`, phono3py is executed with `--pypolymlp` option,
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```
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% phono3py-load --pypolymlp phono3py_params.yaml
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_ _____
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_ __ | |__ ___ _ __ ___|___ / _ __ _ _
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| '_ \| '_ \ / _ \| '_ \ / _ \ |_ \| '_ \| | | |
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| |_) | | | | (_) | | | | (_) |__) | |_) | |_| |
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| .__/|_| |_|\___/|_| |_|\___/____/| .__/ \__, |
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|_| |_| |___/
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3.5.0
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-------------------------[time 2024-09-19 15:20:27]-------------------------
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Compiled with OpenMP support (max 10 threads).
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Running in phono3py.load mode.
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Python version 3.12.6
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Spglib version 2.5.0
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----------------------------- General settings -----------------------------
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HDF5 data compression filter: gzip
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Crystal structure was read from "phono3py_params.yaml".
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Supercell (dim): [2 2 2]
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Primitive matrix:
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[0. 0.5 0.5]
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[0.5 0. 0.5]
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[0.5 0.5 0. ]
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Spacegroup: Fm-3m (225)
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Use -v option to watch primitive cell, unit cell, and supercell structures.
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NAC parameters were read from "phono3py_params.yaml".
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----------------------------- Force constants ------------------------------
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Displacement dataset for fc3 was read from "phono3py_params.yaml".
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----------------------------- pypolymlp start ------------------------------
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Pypolymlp is a generator of polynomial machine learning potentials.
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Please cite the paper: A. Seko, J. Appl. Phys. 133, 011101 (2023).
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Pypolymlp is developed at https://github.com/sekocha/pypolymlp.
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Developing MLPs by pypolymlp...
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Regression: cholesky decomposition ...
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- alpha: 0.001
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- alpha: 0.01
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- alpha: 0.1
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- alpha: 1.0
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- alpha: 10.0
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Clear training X.T @ X
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Calculate X.T @ X for test data
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Clear test X.T @ X
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Regression: model selection ...
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- alpha = 1.000e-03 : rmse (train, test) = 9.39542e+14 9.39543e+14
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- alpha = 1.000e-02 : rmse (train, test) = 9.39542e+14 9.39543e+14
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- alpha = 1.000e-01 : rmse (train, test) = 0.03738 0.04961
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- alpha = 1.000e+00 : rmse (train, test) = 0.03900 0.04742
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- alpha = 1.000e+01 : rmse (train, test) = 0.04058 0.04584
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MLPs were written into "phono3py.pmlp"
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------------------------------ pypolymlp end -------------------------------
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Generate displacements
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Displacement distance: 0.001
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Evaluate forces in 292 supercells by pypolymlp
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Computing fc3[ 1, x, x ] using numpy.linalg.pinv.
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Displacements (in Angstrom):
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[ 0.0010 0.0000 0.0000]
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[-0.0010 0.0000 0.0000]
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Computing fc3[ 33, x, x ] using numpy.linalg.pinv.
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Displacements (in Angstrom):
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[ 0.0010 0.0000 0.0000]
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[-0.0010 0.0000 0.0000]
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Expanding fc3.
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fc3 was symmetrized.
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fc2 was symmetrized.
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Max drift of fc3: -0.000000 (zzz) -0.000000 (zzz) -0.000000 (zzz)
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Max drift of fc2: -0.000000 (zz) -0.000000 (zz)
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fc3 was written into "fc3.hdf5".
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fc2 was written into "fc2.hdf5".
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----------- None of ph-ph interaction calculation was performed. -----------
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Dataset generated using MMLPs was written in "phono3py_mlp_eval_dataset.yaml".
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Summary of calculation was written in "phono3py.yaml".
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-------------------------[time 2024-09-19 15:21:41]-------------------------
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_
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___ _ __ __| |
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/ _ \ '_ \ / _` |
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| __/ | | | (_| |
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\___|_| |_|\__,_|
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```
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Information about the development of MLPs using pypolymlp is provided between
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the `pypolymlp start` and `pypolymlp end` sections. The polynomial MLPs are
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saved in the `phono3py.pmlp` file, which can be reused in subsequent phono3py
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executions with the `--pypolymlp` option when only displacements (and no forces)
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are provided.
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After the MLPs are developed, systematic displacements, such as those involving
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the displacement of one or two atoms in supercells, are generated with a
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displacement distance of 0.001 Angstrom. The forces for these supercells are
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then evaluated using pypolymlp. Both the generated displacements and the
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corresponding forces are stored in the `phono3py_mlp_eval_dataset` file.
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### Steps 4-6: Force constants calculation (random displacements in step 5)
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After developing MLPs, random displacements are generated by specifying
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{ref}`--rd <random_displacements_option>` option. To compute force constants
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with random displacements, an external force constants calculator is necessary.
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For this, symfc is used which is invoked by `--symfc` option.
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Having `phono3py_params.yaml`, phono3py is executed with `--pypolymlp` option,
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```
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% phono3py-load --pypolymlp --rd 200 --symfc phono3py_params.yaml
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_ _____
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_ __ | |__ ___ _ __ ___|___ / _ __ _ _
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| '_ \| '_ \ / _ \| '_ \ / _ \ |_ \| '_ \| | | |
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| |_) | | | | (_) | | | | (_) |__) | |_) | |_| |
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| .__/|_| |_|\___/|_| |_|\___/____/| .__/ \__, |
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|_| |_| |___/
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3.5.0-dev22+g575c4107
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-------------------------[time 2024-09-19 15:33:23]-------------------------
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Compiled with OpenMP support (max 10 threads).
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Running in phono3py.load mode.
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Python version 3.12.6
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Spglib version 2.5.0
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----------------------------- General settings -----------------------------
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HDF5 data compression filter: gzip
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Crystal structure was read from "phono3py_params.yaml".
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Supercell (dim): [2 2 2]
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Primitive matrix:
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[0. 0.5 0.5]
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[0.5 0. 0.5]
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[0.5 0.5 0. ]
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Spacegroup: Fm-3m (225)
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Use -v option to watch primitive cell, unit cell, and supercell structures.
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NAC parameters were read from "phono3py_params.yaml".
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----------------------------- Force constants ------------------------------
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Displacement dataset for fc3 was read from "phono3py_params.yaml".
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----------------------------- pypolymlp start ------------------------------
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Pypolymlp is a generator of polynomial machine learning potentials.
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Please cite the paper: A. Seko, J. Appl. Phys. 133, 011101 (2023).
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Pypolymlp is developed at https://github.com/sekocha/pypolymlp.
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Developing MLPs by pypolymlp...
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Regression: cholesky decomposition ...
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- alpha: 0.001
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- alpha: 0.01
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- alpha: 0.1
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- alpha: 1.0
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- alpha: 10.0
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Clear training X.T @ X
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Calculate X.T @ X for test data
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Clear test X.T @ X
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Regression: model selection ...
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- alpha = 1.000e-03 : rmse (train, test) = 9.39542e+14 9.39543e+14
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- alpha = 1.000e-02 : rmse (train, test) = 9.39542e+14 9.39543e+14
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- alpha = 1.000e-01 : rmse (train, test) = 0.03738 0.04961
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- alpha = 1.000e+00 : rmse (train, test) = 0.03900 0.04742
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- alpha = 1.000e+01 : rmse (train, test) = 0.04058 0.04584
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MLPs were written into "phono3py.pmlp"
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------------------------------ pypolymlp end -------------------------------
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Generate random displacements
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Twice of number of snapshots will be generated for plus-minus displacements.
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Displacement distance: 0.001
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Evaluate forces in 400 supercells by pypolymlp
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-------------------------------- Symfc start -------------------------------
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Symfc is a non-trivial force constants calculator. Please cite the paper:
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A. Seko and A. Togo, arXiv:2403.03588.
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Symfc is developed at https://github.com/symfc/symfc.
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Computing [2, 3] order force constants.
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Increase log-level to watch detailed symfc log.
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--------------------------------- Symfc end --------------------------------
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-------------------------------- Symfc start -------------------------------
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Symfc is a non-trivial force constants calculator. Please cite the paper:
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A. Seko and A. Togo, arXiv:2403.03588.
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Symfc is developed at https://github.com/symfc/symfc.
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Computing [2] order force constants.
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Increase log-level to watch detailed symfc log.
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--------------------------------- Symfc end --------------------------------
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Max drift of fc3: -0.000000 (xyx) 0.000000 (zyy) -0.000000 (xyx)
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Max drift of fc2: 0.000000 (xx) 0.000000 (xx)
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fc3 was written into "fc3.hdf5".
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fc2 was written into "fc2.hdf5".
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----------- None of ph-ph interaction calculation was performed. -----------
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Dataset generated using MMLPs was written in "phono3py_mlp_eval_dataset.yaml".
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Summary of calculation was written in "phono3py.yaml".
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-------------------------[time 2024-09-19 15:34:41]-------------------------
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_
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___ _ __ __| |
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/ _ \ '_ \ / _` |
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| __/ | | | (_| |
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\___|_| |_|\__,_|
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```
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The development of MLPs follows the same procedure as described for the
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systematic displacements (in step 5) above.
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After the MLPs are developed, 200 supercells with random directional
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displacements are generated. These displacements are then inverted, resulting in
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an additional 200 supercells. In total, 400 supercells are created. The forces
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for these supercells are then evaluated. Finally, the force constants are
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calculated using symfc.
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Atsushi Togo