Free Energy Surface Reconstruction from Umbrella Samples Using Gaussian Process Regression

T Stecher and N Bernstein and G Csanyi, JOURNAL OF CHEMICAL THEORY AND COMPUTATION, 10, 4079-4097 (2014).

DOI: 10.1021/ct500438v

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

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