Julia implementations of basic potential energy landscapes for testing sampling, optimization, etc.

This package can be added with the command:

(@v1.XYZ) pkg> add TestLandscapes

Currently, these landscapes are in dimensions one and two, but they allow for exploration of multiple minima, along with energetic and entropic bottlenecks.

These codes do not include derivatives, gradients or Hessians. These can be obtained using ForwardDiff, Zygote, or some other automatic differentiation tool.

This work was supported in part by the US National Science Foundation Grants DMS-1818716 and DMS-2111278.

These landscapes are motivated by the following publications:

• An Automatic Method for Finding the Greatest or Least Value of a Function, Rosenbrock, The Computer Journal, 3(3), 175-184, 1960.
• Reaction Paths on Multidimensional Energy Hypersurfaces, Müller, Angew. Chem. 19(1),1-13, 1980.
• Illustration of transition path theory on a collection of simple examples, Metzner, Schütte, and Vanden-Eijnden, J. Chem. Phys., 125, 084110, 2006.
• Free Energy Computations, Lelièvre, Rousset, and Stoltz, Imperial College Press, 2006.
• Role of Ito’s lemma in sampling pinned diffusion paths in the continuous-time limit, Malsom and Pinski, Phys. Rev. E, 94, 042131, 2016.
• Nonlinear reaction coordinate analysis in the reweighted path ensemble, Lechner, Rogal, Juraszek, Ensing, and Bolhuis, J. Chem. Phys., 133, 174110, 2010.
• Weighted ensemble: Recent mathematical developments, Aristoff, Copperman, Simpson, Webber, and Zuckerman, J. Chem. Phys., 158, 014108 2023.