### Introduction

This is a package for machine learning (ML) of the potential energy surface (PES) from costly ab initio calculations using the sparse Gaussian process regression (SGPR) algorithm. Ab initio calculations such as structure relaxation, AIMD, NEB, etc. can be substantially accelerated by fast ML models built on-the-fly. Moreover, the ML models built with smaller size of physical systems can be applied for simulations of larger systems which are impossible with direct ab initio methods. In principle, all the calculators supported by the atomic simulation environment (ASE) can be modeled.

### Dependencies

- required:
`numpy`

,`scipy`

,`pytorch`

,`ase`

,`mpi`

- conditional:
`mpi4py`

(see below) - optional:
`pymatgen`

,`spglib`

,`mendeleev`

,`matplotlib`

,`nglview`

,`psutil`

,`LAMMPS`

`mpi4py`

is only required if `pytorch`

is not directly linked
with `mpi`

(i.e. `torch.distributed.is_mpi_available() == False`

).
Note that for coupling `pytorch`

with `mpi`

it should be compiled from the source.
This package is regularly synced with the latest
versions of `ase`

and `pytorch`

.
Additional setting maybe needed for linking
the ab initio calculators (VASP, GAUSSIAN, etc.)
with `ase`

(see this).

### Installation

Clone the source code by

`git clone https://github.com/amirhajibabaei/AutoForce.git`

Go to the source code directory and install by

`pip install .`

### Command line interface

For machine learning accelerated molecular dynamics, structure relaxation, etc (using VASP, GAUSSIAN, etc.) from the command line see theforce/cl/README.md.

### Python API

It wraps ASE calculators:

```
from theforce.calculator.active import ActiveCalculator
# atoms = see ASE docs
# main_calc = see ASE calculators
# kernel = see the proceeding
calc = ActiveCalculator(calculator=main_calc)
atoms.set_calculator(calc)
# proceed with the desired calculations
# ...
```

For detailed information see theforce/calculator/README.md.

### Optional coupling with LAMMPS

For running LAMMPS dynamics, it's python package should be installed. See the examples/LAMMPS folder.

### Examples

For usage examples, see the examples/ folder.

### Practical notes

#### On-the-fly ML

- Ab initio calculations: The ab-initio calculators should be used only for single-point energy and force calculations. If on-the-fly ML fails, first and foremost, check if the underlying ab initio calculations (for the electronic structure) do converge.
- ML models: The default settings are such that ML models are automatically saved and loaded in consecutive simulations. Thus check if the proper model is present in the working directory.
- Initial structure for MD:
Starting MD with a relaxed strucure (forces=0) is not advised.
Either manually disturb the initial structure or use the
`rattle`

mechanism. - Structure optimization: Many structure relaxation algorithms depend on the forces history. With on-the-fly ML, every time the model is updated, forces suddenly change. The force discontinuity, if too large, may corrupt the optimizer. This can be avoided by reseting the optimizer history or training a preliminary model before relaxation.

#### Scalability

- Distributed computing with MPI: The algorithm can use at most N (=number of atoms in the system) processes during MD. Using more processes can only speed-up the ML updates.
- CUDA: Currently no GPU acceleration is implemented.
- Species: Presence of more atomic species makes the simulation slower (often exponentially).

### Citation

```
@article{PhysRevB.103.214102,
title = {Sparse Gaussian process potentials: Application to lithium diffusivity in superionic conducting solid electrolytes},
author = {Hajibabaei, Amir and Myung, Chang Woo and Kim, Kwang S.},
journal = {Phys. Rev. B},
volume = {103},
issue = {21},
pages = {214102},
numpages = {7},
year = {2021},
month = {Jun},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.103.214102},
url = {https://link.aps.org/doi/10.1103/PhysRevB.103.214102}
}
```