Computes an approximate Freidlin-Wentzell quasi-potential between two points \(x_0\) and \(x_1\) by minimizing the FW action functional over discretized paths.
FW_quasipotential(
x0,
x1,
drift,
T = 200,
dt = 0.01,
niter = 200,
stepsize = 0.1
)A list with:
path: matrix of size \(T \times d\)
action: FW action of the optimized path
Starting point (numeric vector).
Target point (numeric vector).
Drift function \(b(x)\).
Number of time steps.
Time step.
Number of gradient descent iterations.
Gradient descent step size.
The algorithm:
Initializes a straight-line path between \(x_0\) and \(x_1\).
Performs simple gradient descent on the FW action.
This is a naive but effective illustrative method for low-dimensional systems. More advanced solvers (string method, MAM, etc.) can be plugged in.