Simulates samples from the double-well potential \(U(x) = (x^2 - 1)^2\)
using Euler-Maruyama integration of the overdamped Langevin equation
\(dX_t = -U'(X_t) dt + \sqrt{2\beta^{-1}} dW_t\).
Samples are wrapped as a StateTransitionData with a
PotentialGroundTruth recording the known well locations,
barrier position, and barrier height.
Usage
synthetic_potential_control(
n = 100L,
beta = 2,
n_steps = 5000L,
dt = 0.01,
seed = 42L
)
Arguments
- n
integer number of samples to collect
- beta
numeric inverse temperature (higher = sharper wells, default 2)
- n_steps
integer Euler-Maruyama steps per sample (default 5000)
- dt
numeric step size (default 0.01)
- seed
integer RNG seed
Value
StateTransitionData with PotentialGroundTruth and
metadata()$potential_control carrying generating parameters.
The single experiment "coords" has one feature row: the simulated x values.
colData carries x_coord and well ("left"/"right").
Details
The ground truth for this potential:
Wells at x = ±1 (minima of U)
Barrier at x = 0 (maximum of U between wells)
Barrier height = U(0) - U(1) = 1