8. Gaussian process regression with MD data

8. Gaussian process regression with MD data#

Lennard-Jones fluid#

Finally, we replace the mock MD data with actual simulation data. To generate a dataset, we run a similar active learning simulation than in the previous tutorial. The YAML input for this simulation looks like this:

options:
    output: data/parabolic_lj_md
    write_freq: 100
    use_tstamp: True
grid:
    Lx: 1470.
    Ly: 1.
    Nx: 200
    Ny: 1
    xE: ['D', 'N', 'N']
    xW: ['D', 'N', 'N']
    yS: ['P', 'P', 'P']
    yN: ['P', 'P', 'P']
    xE_D: 0.8
    xW_D: 0.8
geometry:
    type: parabolic
    hmin: 12.
    hmax: 60.
    U: 0.12
    V: 0.
numerics:
    CFL: 0.5
    adaptive: 1
    tol: 1e-8
    dt: 0.05
    max_it: 50_000
properties:
    shear: 2.15
    bulk: 0.
    EOS: DH
    T: 1.0
    rho0: 0.8
gp:
    press:
        fix_noise: True
        atol: 1.5
        rtol: 0.
        obs_stddev: 2.e-2
        max_steps: 10
    shear:
        fix_noise: True
        atol: 1.5
        rtol: 0.
        obs_stddev: 4.e-3
        max_steps: 10
db:
    dtool: True
    dtool_path: data/gapflow_training_lj 
    init_size: 5
    init_method: rand
md:
    system: lj                     # Lennard-Jones system
    ncpu: 10                       # Max. number of CPUs
    atoms_per_cpu: 1000            # Min. number of atoms per CPU
    infile: lmp/lj/in.lmp          # Location of the LAMMPS input file
    wallfile: lmp/lj/wall.lmp      # Location of the LAMMPS file that contains the coordinates of the wall atoms
    vWall: 0.12                    # Sliding velocity of the lower wall (LJ units)
    cutoff: 2.5                    # Cutoff radius of LJ interactions
    temp: 1.0                      # Temperature
    tsample: 100000                # Sampling time

Here, the md section of the YAML file configures the MD runs.

We ran the simulation from the command line using

mpirun -n 1 python GaPFlow -i parabolic_1d_lj_gp_lammps.yaml

Note that we start the run on a single processor (mpirun -n 1). The number of MPI processes for the LAMMPS simulations are configured in the YAML, and spawned from the parent process. The active learning simulation generated 24 MD simulations over the course of a run which took approximately 3.5 hours. We now want to use this dataset in a subsequent simulation with active learning turned off. The training dataset has been uploaded to Zenodo.

We now download the dataset to our local machine and test it there:

!wget -O- https://zenodo.org/records/18761223/files/gapflow_training_lj.tar.gz | tar -xz -C data
--2026-05-14 14:20:36--  https://zenodo.org/records/18761223/files/gapflow_training_lj.tar.gz
Resolving zenodo.org (zenodo.org)...
137.138.52.235, 188.185.48.75, 188.185.43.153, ...
Connecting to zenodo.org (zenodo.org)|137.138.52.235|:443...
connected.
HTTP request sent, awaiting response...
200 OK
Length: 70537865 (67M) [application/octet-stream]
Saving to: ‘STDOUT’

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The input file looks exactly the same, but we turn active learning off. We also have to make sure that GaPFlow looks for the training dataset in the right location.

lj_gp_input = """
options:
    output: data/parabolic_lj_md
    write_freq: 100
    use_tstamp: True
grid:
    Lx: 1470.
    Ly: 1.
    Nx: 200
    Ny: 1
    xE: ['D', 'N', 'N']
    xW: ['D', 'N', 'N']
    yS: ['P', 'P', 'P']
    yN: ['P', 'P', 'P']
    xE_D: 0.8
    xW_D: 0.8
geometry:
    type: parabolic
    hmin: 12.
    hmax: 60.
    U: 0.12
    V: 0.
numerics:
    CFL: 0.5
    adaptive: 1
    tol: 1e-8
    dt: 0.05
    max_it: 50_000
properties:
    shear: 2.15
    bulk: 0.
    EOS: DH
    T: 1.0
    rho0: 0.8
gp:
    press:
        fix_noise: True
        atol: 1.5
        rtol: 0.
        max_steps: 10
        active_learning: False  # AL turned off, so no new MD data is generated
    shear:
        fix_noise: True
        atol: 1.5
        rtol: 0.
        max_steps: 10
        active_learning: False  # AL turned off, so no new MD data is generated
db:
    dtool: True
    dtool_path: data/gapflow_training_lj  # downloaded from Zenodo
    init_size: 5
    init_method: rand
    init_width: 0.01 # default (for density)
md:
    system: lj
    ncpu: 10
    atoms_per_cpu: 1000 
    infile: lmp/lj/in.lmp
    wallfile: lmp/lj/wall.lmp
    vWall: 0.12
    cutoff: 2.5
    temp: 1.0
    tsample: 100000
"""
from GaPFlow import Problem
lj_problem = Problem.from_string(lj_gp_input)
*************************************************************
*                       PROBLEM SETUP                       *
*************************************************************
- options:
  - output                   : data/parabolic_lj_md
  - write_freq               : 100
  - use_tstamp               : True
  - silent                   : False
- grid:
  - Nx                       : 200
  - Lx                       : 1470.0
  - dx                       : 7.35
  - Ny                       : 1
  - Ly                       : 1.0
  - dy                       : 1.0
  - dim                      : 1
  - bc_xE_P                  : [False, False, False]
  - bc_xE_D                  : [True, False, False]
  - bc_xE_N                  : [False, True, True]
  - bc_xW_P                  : [False, False, False]
  - bc_xW_D                  : [True, False, False]
  - bc_xW_N                  : [False, True, True]
  - bc_xE_D_val              : 0.8
  - bc_xW_D_val              : 0.8
  - bc_yS_P                  : [True, True, True]
  - bc_yS_D                  : [False, False, False]
  - bc_yS_N                  : [False, False, False]
  - bc_yN_P                  : [True, True, True]
  - bc_yN_D                  : [False, False, False]
  - bc_yN_N                  : [False, False, False]
- geometry:
  - U                        : 0.12
  - V                        : 0.0
  - type                     : parabolic
  - flip                     : False
  - hmin                     : 12.0
  - hmax                     : 60.0
- numerics:
  - tol                      : 1e-08
  - max_it                   : 50000
  - dt                       : 0.05
  - adaptive                 : True
  - CFL                      : 0.5
  - MC_order                 : 1
- properties:
  - shear                    : 2.15
  - bulk                     : 0.0
  - EOS                      : DH
  - rho0                     : 0.8
  - P0                       : 101325.0
  - C1                       : 35000000000.0
  - C2                       : 1.23
  - elastic:
    - enabled                : False
- gp:
  - press_gp                 : True
  - shear_gp                 : True
  - press:
    - tol                    : delta
    - atol                   : 1.5
    - rtol                   : 0.0
    - obs_stddev             : 0.0
    - fix_noise              : True
    - max_steps              : 10
    - pause_steps            : 100
    - active_learning        : False
    - similarity_check       : True
    - allowed_skips          : 0
    - perturb_target         : False
    - pause_on_high_residual : False
    - active_dims            : [0, 3]
  - shear:
    - tol                    : delta
    - atol                   : 1.5
    - rtol                   : 0.0
    - obs_stddev             : 0.0
    - fix_noise              : True
    - max_steps              : 10
    - pause_steps            : 100
    - active_learning        : False
    - similarity_check       : True
    - allowed_skips          : 0
    - perturb_target         : False
    - pause_on_high_residual : False
    - active_dims_x          : [0, 1, 3]
    - active_dims_y          : [0, 2, 3]
- db:
  - dtool_path               : data/gapflow_training_lj
  - init_size                : 5
  - init_method              : rand
  - init_width               : 0.01
  - init_seed                : 0
  - normalizer_X             : minmax
  - normalizer_Y             : standard
- md:
  - system                   : lj
  - ncpu                     : 10
  - atoms_per_cpu            : 1000
  - infile                   : lmp/lj/in.lmp
  - wallfile                 : lmp/lj/wall.lmp
  - vWall                    : 0.12
  - cutoff                   : 2.5
  - temp                     : 1.0
  - tsample                  : 100000
*************************************************************
*                  PROBLEM SETUP COMPLETED                  *
*************************************************************
Loading 24 local datasets in 'data/gapflow_training_lj'.
- a16621f5-af5d-4a75-ad1b-65c603f30955 (20260224_170410_lj-009)
- e08cf49b-671a-407a-9a11-22c4257f9911 (20260224_185838_lj-022)
- f38ad65d-a362-4db6-acd8-6272a2d59345 (20260224_181817_lj-017)
- 261e68d4-e64b-4dc0-ae1c-cfbba8344d28 (20260224_173203_lj-012)
- 76d4caaa-2631-438b-9f59-96788645c084 (20260224_185038_lj-021)
- cd8a7e57-fadc-41b2-9b8b-76e0551b20eb (20260224_180933_lj-016)
- 15152602-5c66-49f5-83fd-451124c4124d (20260224_175053_lj-014)
- 72ffa906-4a7a-4d4b-8c4d-78856c000ab7 (20260224_172232_lj-011)
- 75a567f8-044e-42b4-ad4d-03b9ecface92 (20260224_182647_lj-018)
- efa4acb4-afb7-4d64-9362-0681462786ad (20260224_161608_lj-003)
- 8429bfe6-72e9-48ed-a59f-cae66f88171b (20260224_190623_lj-023)
- 8cb5599d-a5db-4c53-bb8f-e819f05d89e1 (20260224_183412_lj-019)
- 7d473ab6-d124-4053-9fa3-78956ba7047c (20260224_184224_lj-020)
- 136f2017-079c-4fe3-954f-43df34d14a78 (20260224_155922_lj-001)
- 6dc20674-c40c-4e80-baa7-10072d04ab10 (20260224_160819_lj-002)
- 36d17b6a-a918-4f26-a598-9ca1bf6571b5 (20260224_163134_lj-005)
- e5ddd7d7-2b60-479a-b1f4-3d385580c2d0 (20260224_163858_lj-006)
- 2ccccd7a-04ab-4d78-be3d-cb3adbb186ac (20260224_164826_lj-007)
- 811e2b05-eff1-4054-acba-e0beff87ec3c (20260224_165442_lj-008)
- f9886de7-bf1a-4207-90b5-ed8f555de8bd (20260224_180027_lj-015)
- 339d8f5c-6674-4d38-9442-0142412347c2 (20260224_174137_lj-013)
- 9efd81b7-69f6-4b25-997d-4014b1245d9f (20260224_191508_lj-024)
- 3cb97a66-ff04-4c0a-87c2-c957aeba9bf8 (20260224_162410_lj-004)
- 78fbb59f-b0ba-4f7c-b81e-52576dacd430 (20260224_171301_lj-010)
                                                             
 Writing output into: data/2026-05-14_142126_parabolic_lj_md

We see that the downloaded training simulations have been recognized. Thus, we are ready to run the simulation.

lj_problem.run()
#-----------------GP TRAINING (ZZ)-----------------
# Timestep     : 0
# Reason       : DB
# Database size: 24
# Objective    : -5.1033
# Hyperparam   : 
# - Log scale  : 1.85187 1.74605
# - Log amp    : 4.16391
# - Log noise  : -4.28893
#--------------------------------------------------
#-----------------GP TRAINING (XZ)-----------------
# Timestep     : 0
# Reason       : DB
# Database size: 24
# Objective    : 43.765
# Hyperparam   : 
# - Log scale  : 3.24342 -0.24961 0.37362
# - Log amp    : 0.98870
# - Log noise  : -1.38213
#--------------------------------------------------
-------------------------------------------------------------
Step   Timestep   Time       CFL        Residual
-------------------------------------------------------------
0      1.1084e-01 0.0000e+00 5.0000e-01 1.0000e+00
100    1.1046e-01 1.1064e+01 5.0000e-01 1.4385e-03
200    1.1026e-01 2.2099e+01 5.0000e-01 6.0513e-04
300    1.1021e-01 3.3122e+01 5.0000e-01 1.6131e-04
400    1.1023e-01 4.4144e+01 5.0000e-01 1.9536e-04
500    1.1029e-01 5.5170e+01 5.0000e-01 4.8111e-04
600    1.1035e-01 6.6202e+01 5.0000e-01 6.8646e-04
700    1.1040e-01 7.7239e+01 5.0000e-01 8.0962e-04
800    1.1044e-01 8.8281e+01 5.0000e-01 8.5502e-04
900    1.1046e-01 9.9327e+01 5.0000e-01 8.3209e-04
1000   1.1044e-01 1.1037e+02 5.0000e-01 7.5378e-04
1100   1.1041e-01 1.2141e+02 5.0000e-01 6.3232e-04
1200   1.1039e-01 1.3245e+02 5.0000e-01 4.8060e-04
1300   1.1036e-01 1.4349e+02 5.0000e-01 3.1817e-04
1400   1.1034e-01 1.5453e+02 5.0000e-01 1.6979e-04
1500   1.1031e-01 1.6556e+02 5.0000e-01 5.5989e-05
1600   1.1029e-01 1.7659e+02 5.0000e-01 1.5027e-05
1700   1.1027e-01 1.8762e+02 5.0000e-01 5.0119e-05
1800   1.1024e-01 1.9864e+02 5.0000e-01 6.2902e-05
1900   1.1021e-01 2.0967e+02 5.0000e-01 6.4260e-05
2000   1.1020e-01 2.2069e+02 5.0000e-01 5.9679e-05
2100   1.1018e-01 2.3171e+02 5.0000e-01 5.1620e-05
2200   1.1018e-01 2.4272e+02 5.0000e-01 4.1535e-05
2300   1.1016e-01 2.5374e+02 5.0000e-01 3.0416e-05
2400   1.1016e-01 2.6476e+02 5.0000e-01 1.8923e-05
2500   1.1015e-01 2.7577e+02 5.0000e-01 7.5092e-06
2600   1.1015e-01 2.8679e+02 5.0000e-01 3.3410e-06
2700   1.1015e-01 2.9780e+02 5.0000e-01 1.3081e-05
2800   1.1014e-01 3.0882e+02 5.0000e-01 2.1182e-05
2900   1.1014e-01 3.1983e+02 5.0000e-01 2.7239e-05
3000   1.1014e-01 3.3084e+02 5.0000e-01 3.1054e-05
3100   1.1014e-01 3.4186e+02 5.0000e-01 3.2667e-05
3200   1.1013e-01 3.5287e+02 5.0000e-01 3.2340e-05
3300   1.1013e-01 3.6388e+02 5.0000e-01 3.0477e-05
3400   1.1012e-01 3.7490e+02 5.0000e-01 2.7510e-05
3500   1.1013e-01 3.8591e+02 5.0000e-01 2.3841e-05
3600   1.1012e-01 3.9692e+02 5.0000e-01 1.9813e-05
3700   1.1012e-01 4.0793e+02 5.0000e-01 1.5706e-05
3800   1.1011e-01 4.1895e+02 5.0000e-01 1.1733e-05
3900   1.1011e-01 4.2996e+02 5.0000e-01 8.0465e-06
4000   1.1011e-01 4.4097e+02 5.0000e-01 4.7413e-06
4100   1.1012e-01 4.5198e+02 5.0000e-01 1.8668e-06
4200   1.1012e-01 4.6299e+02 5.0000e-01 5.6247e-07
4300   1.1011e-01 4.7400e+02 5.0000e-01 2.5532e-06
4400   1.1011e-01 4.8501e+02 5.0000e-01 4.1226e-06
4500   1.1011e-01 4.9602e+02 5.0000e-01 5.2903e-06
4600   1.1011e-01 5.0704e+02 5.0000e-01 6.0758e-06
4700   1.1011e-01 5.1805e+02 5.0000e-01 6.5002e-06
4800   1.1012e-01 5.2906e+02 5.0000e-01 6.5906e-06
4900   1.1012e-01 5.4007e+02 5.0000e-01 6.3844e-06
5000   1.1012e-01 5.5108e+02 5.0000e-01 5.9296e-06
5100   1.1011e-01 5.6209e+02 5.0000e-01 5.2837e-06
5200   1.1011e-01 5.7310e+02 5.0000e-01 4.5082e-06
5300   1.1011e-01 5.8412e+02 5.0000e-01 3.6639e-06
5400   1.1011e-01 5.9513e+02 5.0000e-01 2.8064e-06
5500   1.1012e-01 6.0614e+02 5.0000e-01 1.9825e-06
5600   1.1012e-01 6.1715e+02 5.0000e-01 1.2283e-06
5700   1.1012e-01 6.2816e+02 5.0000e-01 5.6885e-07
5800   1.1012e-01 6.3917e+02 5.0000e-01 1.8738e-08
5900   1.1012e-01 6.5019e+02 5.0000e-01 4.1624e-07
6000   1.1012e-01 6.6120e+02 5.0000e-01 7.3747e-07
6100   1.1012e-01 6.7221e+02 5.0000e-01 9.5170e-07
6200   1.1012e-01 6.8322e+02 5.0000e-01 1.0694e-06
6300   1.1012e-01 6.9423e+02 5.0000e-01 1.1034e-06
6400   1.1012e-01 7.0525e+02 5.0000e-01 1.0675e-06
6500   1.1011e-01 7.1626e+02 5.0000e-01 9.7590e-07
6600   1.1011e-01 7.2727e+02 5.0000e-01 8.4257e-07
6700   1.1011e-01 7.3828e+02 5.0000e-01 6.8057e-07
6800   1.1011e-01 7.4929e+02 5.0000e-01 5.0189e-07
6900   1.1012e-01 7.6030e+02 5.0000e-01 3.1719e-07
7000   1.1012e-01 7.7131e+02 5.0000e-01 1.3565e-07
7077   1.1012e-01 7.7979e+02 5.0000e-01 2.8284e-09
=================================
Total walltime   : 0:03:55
(30.03 steps/s)
 - GP train (zz) : 0:00:00
 - GP infer (zz) : 0:00:23
 - GP train (xz) : 0:00:00
 - GP infer (xz) : 0:00:35
=================================
lj_problem.animate()

On a first impression, the results look qualitatively similar to those of the previous example (note that the geometry is slightly different here). The most obvious difference, however, is the small density dip at the inlet while the pressure increases. Since pressure is not only a function of density (but also gap height and mass flux), and since we expect \(\partial p/\partial \rho > 0\), this is most likely an inlet effect captured by the GP model. If we decrease the minimum gap height of parbolic gap profile, more anomalies appear (see Holey et al., Sci. Adv. 11, 2025).

Hexadecane/gold#

The second example with real MD data is the implemented gold/hexadecane system:

options:
    output: data/cosine_mol
    write_freq: 500
    use_tstamp: True
grid:
    Lx: 1918.
    Ly: 1.
    Nx: 100
    Ny: 1
    xE: ['D', 'N', 'N']
    xW: ['D', 'N', 'N']
    yS: ['P', 'P', 'P']
    yN: ['P', 'P', 'P']
    xE_D: 0.51
    xW_D: 0.51
geometry:
    type: journal
    hmin: 30.
    hmax: 60.
    U: 20.e-5
    V: 0.
numerics:
    CFL: 0.5
    adaptive: 1
    tol: 1e-7
    dt: 1.
    max_it: 50_000
properties:
    shear: 2.15
    bulk: 0.
    EOS: BWR
    T: 1.0
    rho0: 0.51
gp:
    press:
        fix_noise: True
        atol: 1.5
        rtol: 0.
        max_steps: 10
    shear:
        fix_noise: True
        atol: 1.5
        rtol: 0.
        max_steps: 10
db:
    dtool: True
    dtool_path: data/gapflow_training_mol
    init_size: 5
    init_method: rand
md:
    system: mol
    rotation: False
    wall_rotation: False
    ncpu: 20
    atoms_per_cpu: 1000     
    wall: eam
    molecule: hexadecane
    fftemplate: lmp/mol/moltemplate_files/trappe1998.lt
    topo: lmp/mol/moltemplate_files/hexadecane.lt
    staticFiles: lmp/mol/static
    nx: 30
    nz: 3
    vWall: 20.  # in m/s
    temperature: 400.
    Ninit: 50_000
    Nsteady: 50_000
    Nsample: 100_000

We will again use a precomputed dataset, generated with:

mpirun -n 1 python GaPFlow -i journal_1d_gold-hexadecane_gp_lammps.yaml

and fetch it from Zenodo.

WARNING: this dataset contains MD trajectories. The unpacked size is approximately 2GB.

!wget -O- https://zenodo.org/records/18761223/files/gapflow_training_mol.tar.gz | tar -xz -C data
--2026-05-14 14:26:04--  https://zenodo.org/records/18761223/files/gapflow_training_mol.tar.gz
Resolving zenodo.org (zenodo.org)...
188.185.43.153, 188.184.98.114, 188.185.48.75, ...
Connecting to zenodo.org (zenodo.org)|188.185.43.153|:443...
connected.
HTTP request sent, awaiting response...
200 OK
Length: 729782870 (696M) [application/octet-stream]
Saving to: ‘STDOUT’

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-                   100%[===================>] 695.97M  38.1MB/s    in 21s     

2026-05-14 14:26:25 (33.9 MB/s) - written to stdout [729782870/729782870]
/usr/lib/python3.12/pty.py:95: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.
  pid, fd = os.forkpty()
mol_gp_input = """
options:
    output: data/cosine_mol
    write_freq: 500
    use_tstamp: True
grid:
    Lx: 1918.
    Ly: 1.
    Nx: 100
    Ny: 1
    xE: ['D', 'N', 'N']
    xW: ['D', 'N', 'N']
    yS: ['P', 'P', 'P']
    yN: ['P', 'P', 'P']
    xE_D: 0.51
    xW_D: 0.51
geometry:
    type: journal
    hmin: 30.
    hmax: 60.
    U: 20.e-5
    V: 0.
numerics:
    CFL: 0.5
    adaptive: 1
    tol: 1e-9
    dt: 1.
    max_it: 20_000
properties:
    shear: 2.15
    bulk: 0.
    EOS: BWR
    T: 1.0
    rho0: 0.51
gp:
    press:
        fix_noise: True
        atol: 1.5
        rtol: 0.
        max_steps: 10
        active_learning: False
    shear:
        fix_noise: True
        atol: 1.5
        rtol: 0.
        max_steps: 10
        active_learning: False
db:
    dtool: True
    dtool_path: data/gapflow_training_mol
    init_size: 5
    init_method: rand
md:
    system: mol
    rotation: False
    wall_rotation: False
    ncpu: 20
    atoms_per_cpu: 1000     
    wall: eam
    molecule: hexadecane
    fftemplate: lmp/mol/moltemplate_files/trappe1998.lt
    topo: lmp/mol/moltemplate_files/hexadecane.lt
    staticFiles: lmp/mol/static
    nx: 30
    nz: 3
    vWall: 20.  # in m/s
    temperature: 400.
    Ninit: 50_000
    Nsteady: 50_000
    Nsample: 100_000
"""
mol_problem = Problem.from_string(mol_gp_input)
*************************************************************
*                       PROBLEM SETUP                       *
*************************************************************
- options:
  - output                   : data/cosine_mol
  - write_freq               : 500
  - use_tstamp               : True
  - silent                   : False
- grid:
  - Nx                       : 100
  - Lx                       : 1918.0
  - dx                       : 19.18
  - Ny                       : 1
  - Ly                       : 1.0
  - dy                       : 1.0
  - dim                      : 1
  - bc_xE_P                  : [False, False, False]
  - bc_xE_D                  : [True, False, False]
  - bc_xE_N                  : [False, True, True]
  - bc_xW_P                  : [False, False, False]
  - bc_xW_D                  : [True, False, False]
  - bc_xW_N                  : [False, True, True]
  - bc_xE_D_val              : 0.51
  - bc_xW_D_val              : 0.51
  - bc_yS_P                  : [True, True, True]
  - bc_yS_D                  : [False, False, False]
  - bc_yS_N                  : [False, False, False]
  - bc_yN_P                  : [True, True, True]
  - bc_yN_D                  : [False, False, False]
  - bc_yN_N                  : [False, False, False]
- geometry:
  - U                        : 0.0002
  - V                        : 0.0
  - type                     : journal
  - flip                     : False
  - hmin                     : 30.0
  - hmax                     : 60.0
- numerics:
  - tol                      : 1e-09
  - max_it                   : 20000
  - dt                       : 1.0
  - adaptive                 : True
  - CFL                      : 0.5
  - MC_order                 : 1
- properties:
  - shear                    : 2.15
  - bulk                     : 0.0
  - EOS                      : BWR
  - T                        : 1.0
  - gamma                    : 3.0
  - rho0                     : 0.51
  - elastic:
    - enabled                : False
- gp:
  - press_gp                 : True
  - shear_gp                 : True
  - press:
    - tol                    : delta
    - atol                   : 1.5
    - rtol                   : 0.0
    - obs_stddev             : 0.0
    - fix_noise              : True
    - max_steps              : 10
    - pause_steps            : 100
    - active_learning        : False
    - similarity_check       : True
    - allowed_skips          : 0
    - perturb_target         : False
    - pause_on_high_residual : False
    - active_dims            : [0, 3]
  - shear:
    - tol                    : delta
    - atol                   : 1.5
    - rtol                   : 0.0
    - obs_stddev             : 0.0
    - fix_noise              : True
    - max_steps              : 10
    - pause_steps            : 100
    - active_learning        : False
    - similarity_check       : True
    - allowed_skips          : 0
    - perturb_target         : False
    - pause_on_high_residual : False
    - active_dims_x          : [0, 1, 3]
    - active_dims_y          : [0, 2, 3]
- db:
  - dtool_path               : data/gapflow_training_mol
  - init_size                : 5
  - init_method              : rand
  - init_width               : 0.01
  - init_seed                : 123
  - normalizer_X             : minmax
  - normalizer_Y             : standard
- md:
  - system                   : mol
  - rotation                 : False
  - wall_rotation            : False
  - ncpu                     : 20
  - atoms_per_cpu            : 1000
  - wall                     : eam
  - molecule                 : hexadecane
  - fftemplate               : lmp/mol/moltemplate_files/trappe1998.lt
  - topo                     : lmp/mol/moltemplate_files/hexadecane.lt
  - staticFiles              : lmp/mol/static
  - nx                       : 30
  - nz                       : 3
  - vWall                    : 20.0
  - temperature              : 400.0
  - Ninit                    : 50000
  - Nsteady                  : 50000
  - Nsample                  : 100000
*************************************************************
*                  PROBLEM SETUP COMPLETED                  *
*************************************************************
Loading 33 local datasets in 'data/gapflow_training_mol'.
- e51c1376-04cf-4495-b6d6-2b30650fc68a (20260225_124045_mol-027)
- 47a2bb5b-fbba-4ad9-911c-4a2367ba6a43 (20260225_122910_mol-026)
- cee1e0c4-f2d8-42ba-a392-c5d25babe071 (20260225_131646_mol-030)
- 2cb28059-829c-4a61-8f83-3dffe781dc86 (20260225_102029_mol-015)
- 10d0c211-e876-440f-85bb-37740b47cdf9 (20260224_184134_mol-001)
- fa361852-3166-4c34-a67a-6be28eec73ea (20260224_185318_mol-002)
- eec69799-a72b-4fc4-87a8-21416679164e (20260224_193706_mol-006)
- ed7895e4-a14d-4e10-b716-e9fdbad2104a (20260225_120651_mol-024)
- 8e4df19c-06e7-4597-9eb8-3053661d095f (20260225_093351_mol-011)
- f19f06f0-47d3-45b0-ad34-d0b491b448fa (20260225_113025_mol-021)
- 0c2ffa8a-3559-4bb3-a5d8-a92ba66a78e4 (20260225_100714_mol-014)
- 77fc90af-8332-484c-b6f9-a17264d14868 (20260225_115443_mol-023)
- 7cbc21e7-f6fb-429d-bdec-2f1914319bf3 (20260225_125359_mol-028)
- d46cddb7-b220-4788-b261-ae7231c6b311 (20260225_094419_mol-012)
- 04d36f06-b80d-4d58-ac5b-ecb3b08c5d2f (20260225_110652_mol-019)
- 0c674cdf-2c59-418a-88a8-f9f5847ac3e8 (20260224_202805_mol-010)
- 031a01d1-acd8-4be0-bf56-4d75a9e7e9c8 (20260225_104343_mol-017)
- e1535166-b734-4945-8bf8-c1c662ef939c (20260224_201448_mol-009)
- 8f98e359-42e8-4944-8e57-b3f83193fb55 (20260224_191548_mol-004)
- a7aaef16-236c-457d-b4a8-40521c4d218b (20260225_111822_mol-020)
- 16776e0d-0dd1-4628-9921-6a5b8ebda83e (20260225_105606_mol-018)
- 9a1be5fa-973e-4077-aa70-9330096c846f (20260225_135517_mol-033)
- a0218d18-9f74-4804-b714-8a29a8a305c5 (20260224_200352_mol-008)
- 40b160fc-fd31-45cb-ac69-24148b0c1c1a (20260225_114140_mol-022)
- d12193e7-a048-4b64-9b5a-ffa1bacfd316 (20260225_133042_mol-031)
- 26afc521-130e-4a4d-85cc-075b6252469a (20260224_192655_mol-005)
- c6bb355b-c1b5-45fe-98cd-c90ac59199bd (20260224_195034_mol-007)
- 14931755-9607-42d4-a88c-6722bcad945f (20260224_190538_mol-003)
- 08eed622-2932-40ae-bd4d-89f7f79a2bbb (20260225_095649_mol-013)
- e16853d7-d429-43dc-a82d-50d8e80f0614 (20260225_103111_mol-016)
- 19169224-a53d-45d2-b0fb-29f6c700b7fb (20260225_121727_mol-025)
- 3adb390c-3fb1-4aaf-82f6-060c583c9ec4 (20260225_134301_mol-032)
- 4bc51e82-b605-4780-88d3-3a018eb61e6d (20260225_130434_mol-029)
                                                            
   Writing output into: data/2026-05-14_142628_cosine_mol
mol_problem.run()
#-----------------GP TRAINING (ZZ)-----------------
# Timestep     : 0
# Reason       : DB
# Database size: 33
# Objective    : -12.894
# Hyperparam   : 
# - Log scale  : 2.73037 2.37563
# - Log amp    : 5.96638
# - Log noise  : -5.28286
#--------------------------------------------------
#-----------------GP TRAINING (XZ)-----------------
# Timestep     : 0
# Reason       : DB
# Database size: 33
# Objective    : 53.694
# Hyperparam   : 
# - Log scale  : 0.13991 -0.25637 0.16889
# - Log amp    : 0.24145
# - Log noise  : -2.42967
#--------------------------------------------------
-------------------------------------------------------------
Step   Timestep   Time       CFL        Residual
-------------------------------------------------------------
0      2.9533e+01 0.0000e+00 5.0000e-01 1.0000e+00
500    2.9224e+01 1.4684e+04 5.0000e-01 4.4158e-05
1000   2.9018e+01 2.9239e+04 5.0000e-01 4.0145e-05
1500   2.8927e+01 4.3721e+04 5.0000e-01 3.7212e-05
2000   2.8907e+01 5.8178e+04 5.0000e-01 3.4681e-05
2500   2.8904e+01 7.2631e+04 5.0000e-01 3.2577e-05
3000   2.8903e+01 8.7082e+04 5.0000e-01 3.0865e-05
3500   2.8861e+01 1.0152e+05 5.0000e-01 2.9295e-05
4000   2.8857e+01 1.1595e+05 5.0000e-01 2.7793e-05
4500   2.8875e+01 1.3038e+05 5.0000e-01 2.6250e-05
5000   2.8898e+01 1.4483e+05 5.0000e-01 2.4569e-05
5500   2.8900e+01 1.5928e+05 5.0000e-01 2.2659e-05
6000   2.8899e+01 1.7373e+05 5.0000e-01 2.0511e-05
6500   2.8899e+01 1.8818e+05 5.0000e-01 1.8169e-05
7000   2.8899e+01 2.0263e+05 5.0000e-01 1.5713e-05
7500   2.8897e+01 2.1708e+05 5.0000e-01 1.3239e-05
8000   2.8897e+01 2.3152e+05 5.0000e-01 1.0846e-05
8500   2.8897e+01 2.4597e+05 5.0000e-01 8.6089e-06
9000   2.8898e+01 2.6042e+05 5.0000e-01 6.5772e-06
9500   2.8898e+01 2.7487e+05 5.0000e-01 4.7746e-06
10000  2.8896e+01 2.8932e+05 5.0000e-01 3.2071e-06
10500  2.8895e+01 3.0377e+05 5.0000e-01 1.8711e-06
11000  2.8895e+01 3.1821e+05 5.0000e-01 7.5117e-07
11500  2.8896e+01 3.3266e+05 5.0000e-01 1.7734e-07
12000  2.8899e+01 3.4711e+05 5.0000e-01 9.4185e-07
12500  2.8897e+01 3.6156e+05 5.0000e-01 1.5683e-06
13000  2.8895e+01 3.7601e+05 5.0000e-01 2.0794e-06
13500  2.8895e+01 3.9045e+05 5.0000e-01 2.4948e-06
14000  2.8897e+01 4.0490e+05 5.0000e-01 2.8305e-06
14500  2.8900e+01 4.1935e+05 5.0000e-01 3.0997e-06
15000  2.8905e+01 4.3380e+05 5.0000e-01 3.3132e-06
15500  2.8903e+01 4.4826e+05 5.0000e-01 3.4794e-06
16000  2.8901e+01 4.6271e+05 5.0000e-01 3.6068e-06
16500  2.8902e+01 4.7716e+05 5.0000e-01 3.7023e-06
17000  2.8906e+01 4.9161e+05 5.0000e-01 3.7712e-06
17500  2.8911e+01 5.0606e+05 5.0000e-01 3.8176e-06
18000  2.8917e+01 5.2052e+05 5.0000e-01 3.8450e-06
18500  2.8921e+01 5.3498e+05 5.0000e-01 3.8559e-06
19000  2.8919e+01 5.4944e+05 5.0000e-01 3.8520e-06
19500  2.8919e+01 5.6390e+05 5.0000e-01 3.8368e-06
20000  2.8921e+01 5.7836e+05 5.0000e-01 3.8121e-06
=================================
Total walltime   : 0:10:33
(31.59 steps/s)
 - GP train (zz) : 0:00:00
 - GP infer (zz) : 0:01:03
 - GP train (xz) : 0:00:00
 - GP infer (xz) : 0:01:33
=================================

The convergence to a steady state is a bit slow in this case. Thus, we have limited the simulation run to 20000 steps. Feel free to run it for longer!

mol_problem.animate()