GaPFlow 1.0.0rc4

Gap-averaged flow simulations with Gaussian Process regression.

GaPFlow

Gap-averaged flow simulations with Gaussian Process regression.

This code implements the solution of time-dependent lubrication problems as described in:

• Holey, H. et al., Tribology Letters 70 (2022)

The extension to atomistic-continuum multiscale simulations with Gaussian process (GP) surrogate models has been described in:

• Holey, H. et al., Science Advances 11, eadx4546 (2025)

The code uses µGrid for handling macroscale fields and tinygp as GP library. Molecular dynamics (MD) simulations run with LAMMPS through its Python interface. Elastic deformation is computed using ContactMechanics.

Installation

pip install GaPFlow

Building from source

When building from source follow these steps:

0. Make sure you have MPI installed, e.g. on Debian-based systems openmpi-bin and libopenmpi-dev should be installed on your system.

1. The multiscale framework depends on LAMMPS which is contained as a Git submodule in this repository. After cloning the repository initialize the submodule with

git submodule update --init

2. Install LAMMPS and mpi4py. We provide a script to build LAMMPS via cmake and install the Python package in your local environment.

bash install_lammps.sh

Alternatively, follow the equivalent steps in the LAMMPS documentation with a complete list of build options. Make sure that you have the optional LAMMPS packages MANYBODY, MOLECULES and ÈXTRA-FIX installed. To make sure that everything is correctly installed run python .check_lammps.py. The last three lines should look similar to these:

MPI:  True
mpi4py:  True
Installed packages: ['EXTRA-FIX', 'MANYBODY', 'MOLECULE']

3. Build µGrid's Python bindings

pip install -v --force-reinstall --no-cache --no-binary muGrid muGrid

and make sure MPI and PnetCDF get detected. For manual installations of PnetCDF (recommended), you may need to tell pkg_config where to find it, e.g.

export PKG_CONFIG_PATH=$HOME/.local/lib/pkgconfig:$HOME/.local/lib64/pkgconfig:$PKG_CONFIG_PATH

for instalations under $HOME/.local/.

4. Finally, install the package with its remaining dependencies and testing capabilities

pip install -e .[test]

5. Make sure that everything works by running the tests with pytest.

Minimal example

Simulation inputs are commonly provided in YAML files. A typical input file might look like this:

# examples/journal.yaml
options:
    output: data/journal
    write_freq: 10
grid:
    dx: 1.e-5
    dy: 1.
    Nx: 100
    Ny: 1
    xE: ['D', 'N', 'N']
    xW: ['D', 'N', 'N']
    yS: ['P', 'P', 'P']
    yN: ['P', 'P', 'P']
    xE_D: 877.7007
    xW_D: 877.7007
geometry:
    type: journal
    CR: 1.e-2
    eps: 0.7
    U: 0.1
    V: 0.
numerics:
    tol: 1e-9
    dt: 1e-10
    max_it: 200
properties:
    shear: 0.0794
    bulk: 0.
    EOS: DH
    P0: 101325
    rho0: 877.7007
    T0: 323.15
    C1: 3.5e10
    C2: 1.23

Note that this example uses fixed-form constitutive laws without GP surrogate models or MD data. More example input files can be found in the examples directory.

The input files can be used to start a simulation from the command line

python -m GaPFlow -i my_input_file.yaml

or from a Python script

from GaPFlow.problem import Problem

myProblem = Problem.from_yaml('my_input_file.yaml')
myProblem.run()

Simulation output is stored under the location specified in the input file. After successful completion, you should find the following files.

• config.yml: A sanitized version of your simulation input.
• gap.nc: NetCDF file containing the gap height and gradients.
• sol.nc: NetCDF file containing the solution and stress fields.
• history.csv: Contains the time series of scalar quantities (step, Ekin, residual, ...)
• gp_[xz,yz,zz].csv (Optional): Contains the time series of GP hyperparameters, database size, etc.
• Xtrain.npy (Optional): Training data inputs
• Ytrain.npy (Optional): Training data observations
• Ytrain_err.npy (Optional): Training data observation error

The code comes with a few handy command line tools for visualizations like this one

which shows the transient solution of a 1D journal bearing with active learning of the constitutive behavior.

Documentation

A Sphinx-generated documentation can be built locally with

cd doc
sphinx-apidoc -o . ../GaPFlow
make html

Funding

This work received funding from the German Research Foundation (DFG) through GRK 2450 and from the Alexander von Humboldt Foundation through a Feodor Lynen Fellowship.