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learned_free_energy_estimation/README.md
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# Targeted free energy estimation via learned mappings
This repository contains supporting data for our publication
([arXiv](https://arxiv.org/abs/2002.04913)). Here, we provide
- molecular dynamics (MD) datasets underlying the results reported in our paper,
- a LAMMPS input script to generate these datasets, and
- the data plotted in Fig. 5 of our paper to facilitate comparison.
## Abstract
Free energy perturbation (FEP) was proposed by Zwanzig more than six decades ago
as a method to estimate free energy differences, and has since inspired a huge
body of related methods that use it as an integral building block. Being an
importance sampling based estimator, however, FEP suffers from a severe
limitation: the requirement of sufficient overlap between distributions.
One strategy to mitigate this problem, called Targeted Free Energy Perturbation,
uses a high-dimensional mapping in configuration space to increase overlap of
the underlying distributions. Despite its potential, this method has attracted
only limited attention due to the formidable challenge of formulating a
tractable mapping. Here, we cast Targeted FEP as a machine learning problem in
which the mapping is parameterized as a neural network that is optimized so as
to increase overlap. We develop a new model architecture that respects
permutational and periodic symmetries often encountered in atomistic simulations
and test our method on a fully-periodic solvation system. We demonstrate that
our method leads to a substantial variance reduction in free energy estimates
when compared against baselines, without requiring any additional data.
## Dataset
We generated the datasets using the open-source MD package
[LAMMPS](https://lammps.sandia.gov). The prototypical solvation problem of study
consists of a solute particle immersed in a liquid comprising 125 solvent
particles. The solvent-solvent interactions are modelled using a Lennard-Jones
potential and the solute-solvent interactions via a Weeks-Chandler-Andersen
(WCA) potential. Further simulation details can be found in the LAMMPS script
provided (see below) and in our [paper](https://arxiv.org/abs/2002.04913)
(see Sec. 4 and Appendix B).
### Download
You can download the compressed datasets (~3.8GB) using the command:
> wget https://storage.googleapis.com/learned_free_energy_estimation/learned_free_energy_estimation_datasets.tar.bz2
or by copying the above link directly into your browser.
Once the archive `learned_free_energy_estimation_datasets.tar.bz2` is
downloaded, you can extract it with the command:
> tar -xvf learned_free_energy_estimation_datasets.tar.bz2
### Data format
The archive contains a total of 40 files:
- 10 train datasets for ensemble *A* (`ensemble_a_train_<<index>>.dat`),
- 10 train datasets for ensemble *B* (`ensemble_b_train_<<index>>.dat`),
- 10 test datasets for ensemble *A* (`ensemble_a_test_<<index>>.dat`) and
- 10 test datasets for ensemble *B* (`ensemble_b_test_<<index>>.dat`).
Each file is text-based and stored in a LAMMPS compatible format (see [dump command](https://lammps.sandia.gov/doc/dump.html)). Train datasets contain 90k records
each and test datasets contain 10k records, totalling 1M records for each
ensemble.
Each record contains 135 lines and is structured as follows:
- lines 1-9: Header information.
- lines 10-135: A matrix with shape `[126, 5]` containing the
- `id` (column 1),
- `type` (column 2) and
- `x, y, z` coordinates (columns 3-5)
of all particles.
For information on how the data was generated and partitioned into the final
datasets we refer to Sec. 4 and Appendix B of our [paper](https://arxiv.org/abs/2002.04913).
## LAMMPS script
The file `lammps.dat` contains a sample input script to generate data from
ensemble *A*. You can generate data from ensemble *B* by updating the value of
the solute radius, as suggested in the inline comment. For more information on
how the datasets were post-processed and partitioned, we refer to Sec. 4 and
Appendix B of our [paper](https://arxiv.org/abs/2002.04913).
## Figures
The subdirectory `figures` contains 4 files:
- `figure_5a_work_values.dat`: contains data underlying the histogram of work values in Fig. 5a.
- `figure_5b_df_bar.dat`: contains the BAR estimate of dF in Fig. 5b.
- `figure_5b_df_lbar.dat`: contains the LBAR estimate of dF in Fig. 5b.
- `figure_5b_df_mbar.dat`: contains the MBAR estimate of dF in Fig. 5b.
## Reference
If you find this repository helpful for your research, please cite our publication:
```
@article{Wirnsberger2020,
title={Targeted free energy estimation via learned mappings},
author={Wirnsberger, Peter and Ballard, Andrew J and Papamakarios, George and
Abercrombie, Stuart and Racanière, Sébastien and Pritzel, Alexander and
Jimenez Rezende, Danilo and Blundell, Charles}
journal={Journal of Chemical Physics},
vol={153},
year={2020},
doi={10.1063/5.0018903}
}
```
## Disclaimer
This is not an official Google product.
learned_free_energy_estimation/figures/figure_5a_work_values.dat
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# This file contains the free energy difference estimate (dF) obtained with BAR.
# column 1: samples per stage
# column 2: running estimate of dF
# column 3: error estimate of dF
3.600000e+02 3.356145e+01 1.160258e+00
7.200000e+02 3.330670e+01 6.652928e-01
1.080000e+03 3.309202e+01 3.906047e-01
1.440000e+03 3.329708e+01 4.272797e-01
1.800000e+03 3.340741e+01 4.464825e-01
2.160000e+03 3.347179e+01 3.865523e-01
2.520000e+03 3.344130e+01 2.935404e-01
2.880000e+03 3.346065e+01 2.936623e-01
3.240000e+03 3.346843e+01 3.623459e-01
3.600000e+03 3.348440e+01 3.735038e-01
3.960000e+03 3.349923e+01 3.670251e-01
4.320000e+03 3.350323e+01 3.606472e-01
4.680000e+03 3.351892e+01 3.204698e-01
5.040000e+03 3.352921e+01 3.383537e-01
5.400000e+03 3.345833e+01 3.097039e-01
5.760000e+03 3.349099e+01 2.979677e-01
6.120000e+03 3.348305e+01 2.713998e-01
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1.008000e+04 3.345716e+01 1.996589e-01
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# This file contains the free energy difference estimate (dF) obtained with LBAR.
# column 1: samples per stage
# column 2: running estimate of dF
# column 3: error estimate of dF
3.600000e+02 3.349788e+01 1.895375e-01
7.200000e+02 3.350255e+01 1.173658e-01
1.080000e+03 3.345561e+01 8.884246e-02
1.440000e+03 3.346067e+01 1.055573e-01
1.800000e+03 3.346017e+01 6.971400e-02
2.160000e+03 3.346283e+01 5.870146e-02
2.520000e+03 3.345409e+01 6.385113e-02
2.880000e+03 3.345067e+01 5.167651e-02
3.240000e+03 3.344354e+01 4.338535e-02
3.600000e+03 3.344073e+01 5.199348e-02
3.960000e+03 3.344467e+01 4.811212e-02
4.320000e+03 3.344608e+01 4.957572e-02
4.680000e+03 3.345111e+01 4.372126e-02
5.040000e+03 3.344837e+01 4.105537e-02
5.400000e+03 3.344826e+01 3.673295e-02
5.760000e+03 3.345362e+01 3.246598e-02
6.120000e+03 3.345146e+01 2.710875e-02
6.480000e+03 3.345397e+01 2.812333e-02
6.840000e+03 3.345973e+01 2.688819e-02
7.200000e+03 3.345442e+01 2.678559e-02
7.560000e+03 3.345242e+01 2.964878e-02
7.920000e+03 3.345720e+01 3.546160e-02
8.280000e+03 3.345431e+01 3.684802e-02
8.640000e+03 3.345385e+01 3.256461e-02
9.000000e+03 3.344926e+01 3.124246e-02
9.360000e+03 3.345124e+01 2.997602e-02
9.720000e+03 3.345532e+01 3.764838e-02
1.008000e+04 3.345669e+01 3.944818e-02
1.044000e+04 3.345609e+01 4.159643e-02
1.080000e+04 3.345890e+01 4.038244e-02
1.116000e+04 3.345588e+01 3.806132e-02
1.152000e+04 3.345622e+01 3.539648e-02
1.188000e+04 3.345530e+01 3.508175e-02
1.224000e+04 3.345318e+01 3.113125e-02
1.260000e+04 3.345466e+01 3.103770e-02
1.296000e+04 3.345465e+01 2.969564e-02
1.332000e+04 3.345461e+01 2.842129e-02
1.368000e+04 3.345523e+01 2.861964e-02
1.404000e+04 3.345308e+01 2.976752e-02
1.440000e+04 3.345459e+01 2.866483e-02
1.476000e+04 3.345740e+01 2.849421e-02
1.512000e+04 3.345755e+01 2.953191e-02
1.548000e+04 3.345732e+01 2.982905e-02
1.584000e+04 3.345668e+01 2.729995e-02
1.620000e+04 3.345538e+01 2.633044e-02
1.656000e+04 3.345508e+01 2.821412e-02
1.692000e+04 3.345424e+01 2.672319e-02
1.728000e+04 3.345396e+01 2.737178e-02
1.764000e+04 3.345649e+01 2.482744e-02
1.800000e+04 3.345676e+01 2.218114e-02
1.836000e+04 3.345788e+01 2.368290e-02
1.872000e+04 3.345766e+01 2.210998e-02
1.908000e+04 3.345661e+01 2.191125e-02
1.944000e+04 3.345887e+01 2.155311e-02
1.980000e+04 3.345990e+01 2.198394e-02
2.016000e+04 3.345869e+01 2.217097e-02
2.052000e+04 3.345923e+01 2.114518e-02
2.088000e+04 3.345843e+01 1.971882e-02
2.124000e+04 3.345790e+01 1.769456e-02
2.160000e+04 3.345734e+01 1.807510e-02
2.196000e+04 3.345605e+01 1.903102e-02
2.232000e+04 3.345590e+01 1.887765e-02
2.268000e+04 3.345610e+01 1.958672e-02
2.304000e+04 3.345450e+01 1.893310e-02
2.340000e+04 3.345395e+01 1.634889e-02
2.376000e+04 3.345262e+01 1.727471e-02
2.412000e+04 3.345308e+01 1.702726e-02
2.448000e+04 3.345143e+01 1.726969e-02
2.484000e+04 3.345186e+01 1.635990e-02
2.520000e+04 3.345155e+01 1.558564e-02
2.556000e+04 3.345093e+01 1.713004e-02
2.592000e+04 3.345149e+01 1.705798e-02
2.628000e+04 3.345184e+01 1.782475e-02
2.664000e+04 3.345004e+01 1.729369e-02
2.700000e+04 3.345015e+01 1.537575e-02
2.736000e+04 3.344937e+01 1.586798e-02
2.772000e+04 3.344965e+01 1.557332e-02
2.808000e+04 3.344843e+01 1.636389e-02
2.844000e+04 3.344734e+01 1.746362e-02
2.880000e+04 3.344685e+01 1.752052e-02
2.916000e+04 3.344869e+01 1.627432e-02
2.952000e+04 3.344880e+01 1.570771e-02
2.988000e+04 3.344797e+01 1.538384e-02
3.024000e+04 3.344810e+01 1.661807e-02
3.060000e+04 3.344924e+01 1.688930e-02
3.096000e+04 3.345143e+01 1.700617e-02
3.132000e+04 3.345189e+01 1.635848e-02
3.168000e+04 3.345242e+01 1.565976e-02
3.204000e+04 3.345258e+01 1.669652e-02
3.240000e+04 3.345334e+01 1.647089e-02
3.276000e+04 3.345345e+01 1.630553e-02
3.312000e+04 3.345320e+01 1.712725e-02
3.348000e+04 3.345314e+01 1.928316e-02
3.384000e+04 3.345416e+01 1.957835e-02
3.420000e+04 3.345479e+01 1.818534e-02
3.456000e+04 3.345436e+01 1.859291e-02
3.492000e+04 3.345371e+01 1.790069e-02
3.528000e+04 3.345348e+01 1.795681e-02
3.564000e+04 3.345274e+01 1.804278e-02
3.600000e+04 3.345143e+01 1.723724e-02
3.636000e+04 3.345247e+01 1.650927e-02
3.672000e+04 3.345188e+01 1.565446e-02
3.708000e+04 3.345203e+01 1.592539e-02
3.744000e+04 3.345190e+01 1.633893e-02
3.780000e+04 3.345142e+01 1.691888e-02
3.816000e+04 3.345050e+01 1.775923e-02
3.852000e+04 3.345065e+01 1.778553e-02
3.888000e+04 3.345069e+01 1.821726e-02
3.924000e+04 3.345047e+01 1.809353e-02
3.960000e+04 3.345073e+01 1.863572e-02
3.996000e+04 3.344997e+01 1.853360e-02
4.032000e+04 3.344899e+01 1.751741e-02
4.068000e+04 3.344849e+01 1.713530e-02
4.104000e+04 3.344848e+01 1.798550e-02
4.140000e+04 3.344909e+01 1.786074e-02
4.176000e+04 3.344859e+01 1.876743e-02
4.212000e+04 3.344926e+01 1.904277e-02
4.248000e+04 3.345050e+01 1.871265e-02
4.284000e+04 3.345075e+01 1.833487e-02
4.320000e+04 3.345048e+01 1.769999e-02
4.356000e+04 3.344912e+01 1.694893e-02
4.392000e+04 3.344922e+01 1.655425e-02
4.428000e+04 3.344922e+01 1.592833e-02
4.464000e+04 3.344890e+01 1.600801e-02
4.500000e+04 3.344949e+01 1.532098e-02
4.536000e+04 3.344971e+01 1.520954e-02
4.572000e+04 3.345032e+01 1.389949e-02
4.608000e+04 3.345044e+01 1.362274e-02
4.644000e+04 3.344994e+01 1.380415e-02
4.680000e+04 3.345100e+01 1.307876e-02
4.716000e+04 3.345066e+01 1.350675e-02
4.752000e+04 3.345137e+01 1.399953e-02
4.788000e+04 3.345198e+01 1.368733e-02
4.824000e+04 3.345119e+01 1.417560e-02
4.860000e+04 3.345084e+01 1.370177e-02
4.896000e+04 3.345167e+01 1.336129e-02
4.932000e+04 3.345149e+01 1.321620e-02
4.968000e+04 3.345174e+01 1.322723e-02
5.004000e+04 3.345161e+01 1.372314e-02
5.040000e+04 3.345146e+01 1.413769e-02
5.076000e+04 3.345091e+01 1.524773e-02
5.112000e+04 3.345106e+01 1.569305e-02
5.148000e+04 3.345136e+01 1.540788e-02
5.184000e+04 3.345092e+01 1.494903e-02
5.220000e+04 3.345061e+01 1.425892e-02
5.256000e+04 3.345077e+01 1.404698e-02
5.292000e+04 3.345138e+01 1.378148e-02
5.328000e+04 3.345115e+01 1.416820e-02
5.364000e+04 3.345069e+01 1.482320e-02
5.400000e+04 3.345054e+01 1.521984e-02
5.436000e+04 3.345011e+01 1.554475e-02
5.472000e+04 3.344947e+01 1.530901e-02
5.508000e+04 3.344885e+01 1.536937e-02
5.544000e+04 3.344911e+01 1.495125e-02
5.580000e+04 3.344930e+01 1.494363e-02
5.616000e+04 3.344886e+01 1.517101e-02
5.652000e+04 3.344868e+01 1.502119e-02
5.688000e+04 3.344928e+01 1.516857e-02
5.724000e+04 3.344911e+01 1.485791e-02
5.760000e+04 3.344947e+01 1.432502e-02
5.796000e+04 3.344941e+01 1.426034e-02
5.832000e+04 3.344857e+01 1.503905e-02
5.868000e+04 3.344871e+01 1.517237e-02
5.904000e+04 3.344895e+01 1.550907e-02
5.940000e+04 3.344864e+01 1.502987e-02
5.976000e+04 3.344874e+01 1.495937e-02
6.012000e+04 3.344942e+01 1.451461e-02
6.048000e+04 3.345043e+01 1.407457e-02
6.084000e+04 3.345031e+01 1.450419e-02
6.120000e+04 3.345082e+01 1.481870e-02
6.156000e+04 3.345083e+01 1.521320e-02
6.192000e+04 3.345055e+01 1.472360e-02
6.228000e+04 3.345017e+01 1.489866e-02
6.264000e+04 3.344994e+01 1.493294e-02
6.300000e+04 3.344977e+01 1.477639e-02
6.336000e+04 3.344965e+01 1.505030e-02
6.372000e+04 3.345062e+01 1.496573e-02
6.408000e+04 3.345042e+01 1.465139e-02
6.444000e+04 3.345001e+01 1.435557e-02
6.480000e+04 3.345000e+01 1.418506e-02
6.516000e+04 3.345005e+01 1.407812e-02
6.552000e+04 3.344975e+01 1.394085e-02
6.588000e+04 3.344994e+01 1.455162e-02
6.624000e+04 3.345040e+01 1.462324e-02
6.660000e+04 3.345056e+01 1.473854e-02
6.696000e+04 3.345044e+01 1.506232e-02
6.732000e+04 3.345034e+01 1.484131e-02
6.768000e+04 3.345075e+01 1.463086e-02
6.804000e+04 3.345098e+01 1.397270e-02
6.840000e+04 3.345135e+01 1.382335e-02
6.876000e+04 3.345141e+01 1.406288e-02
6.912000e+04 3.345150e+01 1.434701e-02
6.948000e+04 3.345141e+01 1.370572e-02
6.984000e+04 3.345131e+01 1.405650e-02
7.020000e+04 3.345139e+01 1.450708e-02
7.056000e+04 3.345112e+01 1.449040e-02
7.092000e+04 3.345141e+01 1.478461e-02
7.128000e+04 3.345147e+01 1.470006e-02
7.164000e+04 3.345156e+01 1.517971e-02
7.200000e+04 3.345179e+01 1.461807e-02
7.236000e+04 3.345251e+01 1.461843e-02
7.272000e+04 3.345274e+01 1.504138e-02
7.308000e+04 3.345280e+01 1.475233e-02
7.344000e+04 3.345247e+01 1.526317e-02
7.380000e+04 3.345238e+01 1.501225e-02
7.416000e+04 3.345252e+01 1.533020e-02
7.452000e+04 3.345258e+01 1.564110e-02
7.488000e+04 3.345313e+01 1.567644e-02
7.524000e+04 3.345369e+01 1.556450e-02
7.560000e+04 3.345396e+01 1.598915e-02
7.596000e+04 3.345348e+01 1.602431e-02
7.632000e+04 3.345362e+01 1.552658e-02
7.668000e+04 3.345405e+01 1.536915e-02
7.704000e+04 3.345419e+01 1.495454e-02
7.740000e+04 3.345443e+01 1.486716e-02
7.776000e+04 3.345475e+01 1.473523e-02
7.812000e+04 3.345488e+01 1.417810e-02
7.848000e+04 3.345509e+01 1.430072e-02
7.884000e+04 3.345531e+01 1.411477e-02
7.920000e+04 3.345526e+01 1.390596e-02
7.956000e+04 3.345539e+01 1.350224e-02
7.992000e+04 3.345552e+01 1.375998e-02
8.028000e+04 3.345549e+01 1.387193e-02
8.064000e+04 3.345488e+01 1.355985e-02
8.100000e+04 3.345495e+01 1.344556e-02
8.136000e+04 3.345518e+01 1.325654e-02
8.172000e+04 3.345509e+01 1.305198e-02
8.208000e+04 3.345463e+01 1.307672e-02
8.244000e+04 3.345433e+01 1.296584e-02
8.280000e+04 3.345417e+01 1.302655e-02
8.316000e+04 3.345433e+01 1.271783e-02
8.352000e+04 3.345443e+01 1.278077e-02
8.388000e+04 3.345503e+01 1.292941e-02
8.424000e+04 3.345511e+01 1.341828e-02
8.460000e+04 3.345484e+01 1.368871e-02
8.496000e+04 3.345486e+01 1.341405e-02
8.532000e+04 3.345503e+01 1.316640e-02
8.568000e+04 3.345545e+01 1.287838e-02
8.604000e+04 3.345567e+01 1.300123e-02
8.640000e+04 3.345592e+01 1.334809e-02
8.676000e+04 3.345590e+01 1.348339e-02
8.712000e+04 3.345572e+01 1.350306e-02
8.748000e+04 3.345582e+01 1.334966e-02
8.784000e+04 3.345550e+01 1.334321e-02
8.820000e+04 3.345530e+01 1.302465e-02
8.856000e+04 3.345507e+01 1.284108e-02
8.892000e+04 3.345513e+01 1.246001e-02
8.928000e+04 3.345517e+01 1.253922e-02
8.964000e+04 3.345517e+01 1.248138e-02
9.000000e+04 3.345504e+01 1.250002e-02
learned_free_energy_estimation/figures/figure_5b_df_mbar.dat
+184
View File
@@ -0,0 +1,184 @@
# This file contains the free energy difference estimate (dF) obtained with MBAR.
# column 1: samples per stage
# column 2: running estimate of dF
# column 3: error estimate of dF
5.000000e+02 3.348947e+01 6.862397e-02
1.000000e+03 3.347387e+01 4.854148e-02
1.500000e+03 3.347623e+01 3.967133e-02
2.000000e+03 3.348673e+01 3.439447e-02
2.500000e+03 3.347544e+01 3.075069e-02
3.000000e+03 3.348640e+01 2.809994e-02
3.500000e+03 3.347364e+01 2.599614e-02
4.000000e+03 3.346986e+01 2.431905e-02
4.500000e+03 3.346961e+01 2.291930e-02
5.000000e+03 3.346484e+01 2.173656e-02
5.500000e+03 3.346934e+01 2.072029e-02
6.000000e+03 3.346451e+01 1.984469e-02
6.500000e+03 3.346112e+01 1.906542e-02
7.000000e+03 3.346448e+01 1.837210e-02
7.500000e+03 3.345465e+01 1.775237e-02
8.000000e+03 3.345397e+01 1.718846e-02
8.500000e+03 3.345652e+01 1.667432e-02
9.000000e+03 3.345805e+01 1.620102e-02
9.500000e+03 3.346146e+01 1.577490e-02
1.000000e+04 3.346144e+01 1.537617e-02
1.050000e+04 3.345814e+01 1.500688e-02
1.100000e+04 3.345771e+01 1.466039e-02
1.150000e+04 3.346071e+01 1.433827e-02
1.200000e+04 3.346027e+01 1.403640e-02
1.250000e+04 3.345883e+01 1.375421e-02
1.300000e+04 3.345853e+01 1.348973e-02
1.350000e+04 3.346009e+01 1.323468e-02
1.400000e+04 3.346103e+01 1.299762e-02
1.450000e+04 3.345552e+01 1.276921e-02
1.500000e+04 3.345334e+01 1.255442e-02
1.550000e+04 3.345482e+01 1.235281e-02
1.600000e+04 3.345732e+01 1.215894e-02
1.650000e+04 3.345797e+01 1.197288e-02
1.700000e+04 3.345815e+01 1.179542e-02
1.750000e+04 3.345590e+01 1.162467e-02
1.800000e+04 3.345629e+01 1.146072e-02
1.850000e+04 3.345542e+01 1.130306e-02
1.900000e+04 3.345807e+01 1.115385e-02
1.950000e+04 3.345522e+01 1.101022e-02
2.000000e+04 3.345209e+01 1.087127e-02
2.050000e+04 3.345170e+01 1.073895e-02
2.100000e+04 3.345297e+01 1.061029e-02
2.150000e+04 3.345232e+01 1.048628e-02
2.200000e+04 3.345287e+01 1.036741e-02
2.250000e+04 3.345100e+01 1.025204e-02
2.300000e+04 3.345211e+01 1.014036e-02
2.350000e+04 3.345150e+01 1.003258e-02
2.400000e+04 3.345267e+01 9.927045e-03
2.450000e+04 3.345188e+01 9.824914e-03
2.500000e+04 3.344938e+01 9.725246e-03
2.550000e+04 3.345166e+01 9.629378e-03
2.600000e+04 3.345270e+01 9.535662e-03
2.650000e+04 3.345214e+01 9.445890e-03
2.700000e+04 3.345417e+01 9.358481e-03
2.750000e+04 3.345247e+01 9.272714e-03
2.800000e+04 3.345346e+01 9.188538e-03
2.850000e+04 3.345430e+01 9.108273e-03
2.900000e+04 3.345416e+01 9.029007e-03
2.950000e+04 3.345309e+01 8.952522e-03
3.000000e+04 3.345190e+01 8.878327e-03
3.050000e+04 3.344897e+01 8.805188e-03
3.100000e+04 3.344964e+01 8.732210e-03
3.150000e+04 3.344939e+01 8.663034e-03
3.200000e+04 3.344794e+01 8.594927e-03
3.250000e+04 3.344955e+01 8.528876e-03
3.300000e+04 3.345027e+01 8.463777e-03
3.350000e+04 3.344999e+01 8.400015e-03
3.400000e+04 3.344984e+01 8.338387e-03
3.450000e+04 3.345104e+01 8.277393e-03
3.500000e+04 3.344932e+01 8.218733e-03
3.550000e+04 3.344877e+01 8.160845e-03
3.600000e+04 3.344790e+01 8.104316e-03
3.650000e+04 3.344738e+01 8.048099e-03
3.700000e+04 3.344686e+01 7.993584e-03
3.750000e+04 3.344745e+01 7.940271e-03
3.800000e+04 3.344820e+01 7.888244e-03
3.850000e+04 3.344765e+01 7.836854e-03
3.900000e+04 3.344642e+01 7.786979e-03
3.950000e+04 3.344496e+01 7.737392e-03
4.000000e+04 3.344476e+01 7.688966e-03
4.050000e+04 3.344575e+01 7.641278e-03
4.100000e+04 3.344529e+01 7.594414e-03
4.150000e+04 3.344507e+01 7.548341e-03
4.200000e+04 3.344515e+01 7.503361e-03
4.250000e+04 3.344542e+01 7.458615e-03
4.300000e+04 3.344475e+01 7.415060e-03
4.350000e+04 3.344495e+01 7.372151e-03
4.400000e+04 3.344539e+01 7.330419e-03
4.450000e+04 3.344489e+01 7.289283e-03
4.500000e+04 3.344518e+01 7.248814e-03
4.550000e+04 3.344483e+01 7.208634e-03
4.600000e+04 3.344505e+01 7.169400e-03
4.650000e+04 3.344549e+01 7.130802e-03
4.700000e+04 3.344656e+01 7.092623e-03
4.750000e+04 3.344620e+01 7.055154e-03
4.800000e+04 3.344553e+01 7.017677e-03
4.850000e+04 3.344510e+01 6.981500e-03
4.900000e+04 3.344430e+01 6.945682e-03
4.950000e+04 3.344375e+01 6.910502e-03
5.000000e+04 3.344317e+01 6.875701e-03
5.050000e+04 3.344380e+01 6.841235e-03
5.100000e+04 3.344336e+01 6.807528e-03
5.150000e+04 3.344314e+01 6.774260e-03
5.200000e+04 3.344290e+01 6.741623e-03
5.250000e+04 3.344230e+01 6.709539e-03
5.300000e+04 3.344314e+01 6.678291e-03
5.350000e+04 3.344342e+01 6.647072e-03
5.400000e+04 3.344318e+01 6.616171e-03
5.450000e+04 3.344379e+01 6.585470e-03
5.500000e+04 3.344381e+01 6.555845e-03
5.550000e+04 3.344434e+01 6.526642e-03
5.600000e+04 3.344501e+01 6.497285e-03
5.650000e+04 3.344619e+01 6.468459e-03
5.700000e+04 3.344623e+01 6.439974e-03
5.750000e+04 3.344664e+01 6.412096e-03
5.800000e+04 3.344615e+01 6.384088e-03
5.850000e+04 3.344599e+01 6.356764e-03
5.900000e+04 3.344632e+01 6.330156e-03
5.950000e+04 3.344659e+01 6.303682e-03
6.000000e+04 3.344593e+01 6.277147e-03
6.050000e+04 3.344578e+01 6.251312e-03
6.100000e+04 3.344642e+01 6.225851e-03
6.150000e+04 3.344603e+01 6.200300e-03
6.200000e+04 3.344555e+01 6.175259e-03
6.250000e+04 3.344555e+01 6.150557e-03
6.300000e+04 3.344542e+01 6.126220e-03
6.350000e+04 3.344515e+01 6.101949e-03
6.400000e+04 3.344525e+01 6.077983e-03
6.450000e+04 3.344496e+01 6.054339e-03
6.500000e+04 3.344501e+01 6.030827e-03
6.550000e+04 3.344471e+01 6.007627e-03
6.600000e+04 3.344506e+01 5.984742e-03
6.650000e+04 3.344514e+01 5.962256e-03
6.700000e+04 3.344494e+01 5.940045e-03
6.750000e+04 3.344566e+01 5.917884e-03
6.800000e+04 3.344522e+01 5.895819e-03
6.850000e+04 3.344488e+01 5.874460e-03
6.900000e+04 3.344457e+01 5.853076e-03
6.950000e+04 3.344488e+01 5.831963e-03
7.000000e+04 3.344486e+01 5.811116e-03
7.050000e+04 3.344525e+01 5.790804e-03
7.100000e+04 3.344566e+01 5.770541e-03
7.150000e+04 3.344601e+01 5.750545e-03
7.200000e+04 3.344603e+01 5.730280e-03
7.250000e+04 3.344619e+01 5.710471e-03
7.300000e+04 3.344545e+01 5.690757e-03
7.350000e+04 3.344417e+01 5.671172e-03
7.400000e+04 3.344337e+01 5.651868e-03
7.450000e+04 3.344334e+01 5.632921e-03
7.500000e+04 3.344244e+01 5.613913e-03
7.550000e+04 3.344261e+01 5.595240e-03
7.600000e+04 3.344314e+01 5.576832e-03
7.650000e+04 3.344388e+01 5.558491e-03
7.700000e+04 3.344386e+01 5.540588e-03
7.750000e+04 3.344375e+01 5.522747e-03
7.800000e+04 3.344326e+01 5.505254e-03
7.850000e+04 3.344329e+01 5.487653e-03
7.900000e+04 3.344302e+01 5.470438e-03
7.950000e+04 3.344398e+01 5.453349e-03
8.000000e+04 3.344413e+01 5.436500e-03
8.050000e+04 3.344421e+01 5.419629e-03
8.100000e+04 3.344489e+01 5.402948e-03
8.150000e+04 3.344496e+01 5.386430e-03
8.200000e+04 3.344543e+01 5.369879e-03
8.250000e+04 3.344561e+01 5.353712e-03
8.300000e+04 3.344542e+01 5.337605e-03
8.350000e+04 3.344541e+01 5.321604e-03
8.400000e+04 3.344607e+01 5.305934e-03
8.450000e+04 3.344640e+01 5.290176e-03
8.500000e+04 3.344655e+01 5.274630e-03
8.550000e+04 3.344652e+01 5.259196e-03
8.600000e+04 3.344677e+01 5.243956e-03
8.650000e+04 3.344692e+01 5.228882e-03
8.700000e+04 3.344680e+01 5.213822e-03
8.750000e+04 3.344745e+01 5.198685e-03
8.800000e+04 3.344757e+01 5.183810e-03
8.850000e+04 3.344768e+01 5.169171e-03
8.900000e+04 3.344788e+01 5.154574e-03
8.950000e+04 3.344715e+01 5.140136e-03
9.000000e+04 3.344682e+01 5.125559e-03
learned_free_energy_estimation/lammps.dat
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# Simulate a WCA solute particle immersed into a Lennard-Jones solvent.
#
# We first generate an initial configuration of particles located at random
# positions. We then minimise the system and equilibrate it to the target
# temperature. During the production run, we sample configurations at regular
# intervals.
################################################################################
# Specify input parameters.
################################################################################
# We use the same box dimensions and temperature as in Jarzynski (2002),
# Phys. Rev. E 65, 046122, but convert these quantities to reduced units.
# T=300 K, eps=0.1854 kcal/mol, k_boltzmann=0.001987204 kcal/mol/K.
variable solute_radius equal 9.2/3.542
variable box_length equal 22.28/3.542
variable temperature_reference equal 300*0.001987204/0.1854
variable temperature_damp equal 0.5
variable seed equal 1234
variable num_solvent_particles equal 125
variable dump_frequency equal 5000
variable timestep equal 0.002
variable runtime_equi equal 50000
variable runtime_prod equal 500000
variable steps_equilibration equal floor(${runtime_equi}/${timestep})
variable steps_production equal floor(${runtime_prod}/${timestep})
################################################################################
# Create solvent particles at random positions and place solute at the origin.
################################################################################
units lj
atom_style atomic
dimension 3
boundary p p p
variable box_length_half equal ${box_length}/2.0
region domain block -${box_length_half} ${box_length_half} &
-${box_length_half} ${box_length_half} &
-${box_length_half} ${box_length_half} &
units box
create_box 2 domain
create_atoms 2 random 1 ${seed} domain
create_atoms 1 random ${num_solvent_particles} ${seed} domain
set type 2 x 0.0 y 0.0 z 0.0
group solute type 2
group solvent type 1
# Initialise particle masses.
mass 1 1
mass 2 10000000
################################################################################
# Define pair-style.
################################################################################
variable sigma_solute equal ${solute_radius}
variable radius_cutoff_solute equal 1.12246*${sigma_solute}
variable radius_cutoff equal ${box_length}/2.0
pair_style lj/cut ${radius_cutoff}
# Lennard-Jones interaction between solvent particles.
pair_coeff 1 1 1.0 1.0
# WCA interaction between solute and solvent particles.
pair_coeff 1 2 1.0 ${sigma_solute} ${radius_cutoff_solute}
# No interaction between solute particles.
pair_coeff 2 2 0.0 0.0
# Shift energies to be zero at the cutoff and update neighbor list settings.
pair_modify shift yes
neighbor 0.3 bin
neigh_modify delay 5
################################################################################
# Perform minimisation.
################################################################################
fix freeze solute setforce 0.0 0.0 0.0
minimize 1.0e-4 1.0e-6 100 1000
################################################################################
# Perform equilibration run.
################################################################################
reset_timestep 0
compute temperature_solvent solvent temp
compute kinetic_energy all ke
compute potential_energy all pe
variable total_energy equal c_kinetic_energy+c_potential_energy
# Compute centre-of-mass velocity and solute position for monitoring.
variable vcmx equal "vcm(all,x)"
variable vcmy equal "vcm(all,y)"
variable vcmz equal "vcm(all,z)"
variable vcm2 equal v_vcmx*v_vcmx+v_vcmy*v_vcmy+v_vcmz*v_vcmz
compute position_solute solute com
# Specify terminal output.
thermo_style custom step temp c_temperature_solvent c_potential_energy &
c_kinetic_energy v_total_energy press v_vcm2 &
c_position_solute[1] c_position_solute[2] c_position_solute[3]
thermo_modify norm no
thermo 1000
# Specify integration timestep.
timestep ${timestep}
# Apply Langevin thermostat to solvent particles.
fix flangevin solvent langevin ${temperature_reference} &
${temperature_reference} ${temperature_damp} ${seed} zero yes
fix fnve all nve
run ${steps_equilibration}
################################################################################
# Production run.
################################################################################
reset_timestep 0
dump fDumpTrajectory all custom ${dump_frequency} &
trajectory.dat id type x y z
dump_modify fDumpTrajectory sort id format float %.8g
fix fDumpEnergy all ave/time ${dump_frequency} 1 ${dump_frequency} &
c_potential_energy file energy.dat format %.8g
run ${steps_production}