A toolbox for constructing potential landscapes for dynamical systems using Monte Carlo simulation. The method is based on the potential landscape definition by Wang et al. (2008) (also see Zhou & Li, 2016, for further mathematical discussions) and can be used for a large variety of models.

simlandr can help to:

1. Run batch simulations for different parameter values;
2. Store large simulation outputs into hard drive by the reusable hash_big_matrix class, and perform out-of-memory calculation;
3. Check convergence of the simulations;
4. Construct 2d, 3d, 4d potential landscapes based on the simulation outputs;
5. Calculate the minimal energy path and barrier height for transitions between states.

## Installation

You can install the released version of simlandr from CRAN with:

install.packages("simlandr")

And you can install the development version from GitHub with:

install.packages("devtools")
devtools::install_github("Sciurus365/simlandr")
devtools::install_github("Sciurus365/simlandr", build_vignettes = TRUE) # Use this command if you want to build vignettes

## Example

library(simlandr)

# Simulation

## Single simulation

## Batch simulation: simulate a set of models with different parameter values
arg_name = "parameter", ele_name = "a",
start = -6, end = -1, by = 1
)
default_list = list(
initial = list(x = 0, y = 0),
parameter = list(a = -4, b = 0, c = 0, sigmasq = 1)
),
length = 1e4,
seed = 1614,
bigmemory = FALSE
)

#> Output(s) from 6 simulations.
# Construct landscapes

## Example 1. 2D (x, y as U) landscape
plot(l_single_grad_2d)


### To make the landscape smoother
make_2d_static(single_output_grad, x = "x", adjust = 5) %>% plot()


## Example 2. 3D (x, y, color as U) landscape
plot(l_single_grad_3d, 2)


### plot(l_single_grad_3d) # to show the landscape in 3D (x, y, z)

## Example 3. 4D (x, y, z, color as U) landscape
set.seed(1614)
single_output_grad <- matrix(runif(nrow(single_output_grad), min = 0, max = 5), ncol = 1, dimnames = list(NULL, "z")) %>% cbind(single_output_grad)
l_single_grad_4d <- make_4d_static(single_output_grad, x = "x", y = "y", z = "z", n = 50)
### plot(l_single_grad_4d) # to show the landscape in 4D (x, y, z, color as U)

## Example 4. 2D (x, y as U) matrix (by a)
plot(l_batch_grad_2d)


## Example 5. 3D (x, y, color as U) matrix (by a)
l_batch_grad_3d <- make_3d_matrix(batch_output_grad, x = "x", y = "y", cols = "a")
plot(l_batch_grad_3d)


## Example 6. 3D (x, y, z/color as U) animation (by a)
l_batch_grad_3d_animation <- make_3d_animation(batch_output_grad, x = "x", y = "y", fr = "a")
### plot(l_batch_grad_3d_animation) # to show the landscape animation in 3D (x, y, z as U)
### plot(l_batch_grad_3d_animation, 2) # to show the landscape animation in 3D (x, y, color as U)
# Calculate energy barriers
## Example 1. Energy barrier for the 2D landscape
start_location_value = -1, end_location_value = 1,
start_r = 0.3, end_r = 0.3
)
#> delta_U_start   delta_U_end
#>      2.896270      2.806378

plot(l_single_grad_2d) + autolayer(b_single_grad_2d)


## Example 2. Energy barrier for the 3D landscape
start_location_value = c(-1, -1), end_location_value = c(1, 1),
start_r = 0.3, end_r = 0.3
)
#> delta_U_start   delta_U_end
#>      3.491516      3.360399
plot(l_single_grad_3d, 2) + autolayer(b_single_grad_3d)


## Example 3. Energy barrier for many 2D landscapes
start_location_value = -1, end_location_value = 1,
start_r = 0.3, end_r = 0.3
)
#> # A tibble: 6 × 9
#>     <dbl>   <dbl> <dbl>  <dbl>    <dbl>    <dbl> <dbl>         <dbl>       <dbl>
#> 1  -1.21    1.56  1.21  -0.332  -0.171     7.10     -6         5.54       7.43
#> 2  -1.08    0.243 1.08   0.348   0.0418    4.65     -5         4.40       4.30
#> 3  -0.957   0.355 0.977  0.454   0.0418    2.87     -4         2.52       2.42
#> 4  -0.808   0.530 0.807  0.572   0.0205    1.62     -3         1.09       1.05
#> 5  -0.702   0.710 0.700  0.659   0.0205    0.884    -2         0.174      0.225
#> 6  -0.702   0.895 0.700  0.834  -0.702     0.895    -1         0          0.0613
plot(l_batch_grad_2d) + autolayer(b_batch_grad_2d)


## Example 4. Energy barrier for many 3D landscapes
start_location_value = c(-1, -1), end_location_value = c(1, 1),
start_r = 0.3, end_r = 0.3
)
#> # A tibble: 6 × 12
plot(l_batch_grad_3d) + autolayer(b_batch_grad_3d)
See the vignettes of this package (browseVignettes("simlandr") or https://psyarxiv.com/pzva3/) for more examples and explanations. Also see https://doi.org/10.1080/00273171.2022.2119927 for our recent work using simlandr.