This repository contains supporting data for our publication (journal, arXiv). 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.

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.

We generated the datasets using the open-source MD package LAMMPS. 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 (see Sec. 4 and Appendix B).

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

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). 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.

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.

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.

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={J. Chem. Phys.},
  volume={153},
  number={14},
  pages={144112},
  year={2020},
  doi={10.1063/5.0018903}
}

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