Modified single sweep method for reconstructing free-energy landscapes

Two modifications of the recently developed single sweep method to efficiently reconstruct free-energy landscapes in several dimensions are proposed. In single sweep, the free energy is estimated as a linear combination of radial basis functions whose parameters are optimised by minimising an appropriate objective function. In this work, the single variance Gaussian radial basis usually employed in single sweep when non-periodic collective variables are used is generalised to a basis of multivariate Gaussians whose covariance matrix can change with the location of the basis function on the landscape. A new objective function, aimed at a more accurate reconstruction of the landscape in the vicinity of stationary points, is also introduced. The performance of the modified single sweep is compared to that of the standard method in the reconstruction of a model benchmark potential and of the free-energy profile of a physically relevant example. The results of these comparisons show that employing the new objective function can result in an improvement of the efficiency and accuracy of the reconstruction.