Free Energy Surface Reconstruction from Umbrella Samples Using Gaussian Process Regression. Stecher, T., Bernstein, N., & Csányi, G. Journal of Chemical Theory and Computation, 10(9):4079--4097, September, 2014. 00002
Free Energy Surface Reconstruction from Umbrella Samples Using Gaussian Process Regression [link]Paper  doi  abstract   bibtex   
We demonstrate how the Gaussian process regression approach can be used to efficiently reconstruct free energy surfaces from umbrella sampling simulations. By making a prior assumption of smoothness and taking account of the sampling noise in a consistent fashion, we achieve a significant improvement in accuracy over the state of the art in two or more dimensions or, equivalently, a significant cost reduction to obtain the free energy surface within a prescribed tolerance in both regimes of spatially sparse data and short sampling trajectories. Stemming from its Bayesian interpretation the method provides meaningful error bars without significant additional computation. A software implementation is made available on www.libatoms.org.
@article{ stecher_free_2014,
  title = {Free {Energy} {Surface} {Reconstruction} from {Umbrella} {Samples} {Using} {Gaussian} {Process} {Regression}},
  volume = {10},
  issn = {1549-9618},
  url = {http://dx.doi.org/10.1021/ct500438v},
  doi = {10.1021/ct500438v},
  abstract = {We demonstrate how the Gaussian process regression approach can be used to efficiently reconstruct free energy surfaces from umbrella sampling simulations. By making a prior assumption of smoothness and taking account of the sampling noise in a consistent fashion, we achieve a significant improvement in accuracy over the state of the art in two or more dimensions or, equivalently, a significant cost reduction to obtain the free energy surface within a prescribed tolerance in both regimes of spatially sparse data and short sampling trajectories. Stemming from its Bayesian interpretation the method provides meaningful error bars without significant additional computation. A software implementation is made available on www.libatoms.org.},
  number = {9},
  urldate = {2015-04-07TZ},
  journal = {Journal of Chemical Theory and Computation},
  author = {Stecher, Thomas and Bernstein, Noam and Csányi, Gábor},
  month = {September},
  year = {2014},
  note = {00002},
  pages = {4079--4097}
}

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