2D Landscapes

This is the entropic switch or, alternatively, the three well potential. It has the feature that, for a diffusion, the preferred pathway from the lower left well to the lower right well is sensitive to the temperature. From Metzner et al. (2006).

using Plots
using TestLandscapes

xx = LinRange(-2, 2, 100)
yy = LinRange(-1.0, 2.0, 100)
contourf(xx, yy, [EntropicSwitch([x_, y_]) for y_ in yy, x_ in xx], cbar=false)
xlabel!("x")
ylabel!("y")

From Lelièvre et al. (2006).

using Plots
using TestLandscapes

xx = LinRange(-1.1, 1.1, 100)
yy = LinRange(-1.0, 1.0, 100)
contourf(xx, yy, [SymmetricTwoChannel([x_, y_]) for y_ in yy, x_ in xx], cbar=false)
xlabel!("x")
ylabel!("y")

This is the Muller, sometimes Muller-Brown, potential, which is regularly used as a test problem for sampling, optimization, and related computations. From Müller (1980).

using Plots
using TestLandscapes

xx = LinRange(-1.5, 1., 100)
yy = LinRange(-0.5, 2.0, 100)
contourf(xx, yy, [Muller([x_, y_]) for y_ in yy, x_ in xx], cbar=false,levels=-150:10:120)
xlabel!("x")
ylabel!("y")

The banana shaped Rosenbrock energy landscape, originally appearing in Rosenbrock (1960).

using Plots
using TestLandscapes

xx = LinRange(-1, 1, 100)
yy = LinRange(-1, 1, 100)
contourf(xx, yy, [Rosenbrock([x_, y_]) for y_ in yy, x_ in xx],levels=[0:10:40|>collect; 50:50:500|>collect],  cbar=false)
xlabel!("x")
ylabel!("y")

This a Z shaped potential that requires backtracking to transition between the two minima. This potential appeared in Lechner et al. (2010).

using Plots
using TestLandscapes

xx = LinRange(-15, 15, 200);yy = LinRange(-15, 15, 200);contourf(xx, yy, [Zpotential([x_, y_]) for y_ in yy, x_ in xx], cbar=false)
xlabel!("x")
ylabel!("y")

This is the potential appearing in Αristoff et al. (2023).

using Plots
using TestLandscapes

xx = LinRange(0, 1, 100)
yy = LinRange(0, 1, 100)
contourf(xx, yy, [EntropicBox([x_, y_]) for y_ in yy, x_ in xx],cbar=false)
xlabel!("x")
ylabel!("y")