Freidlin–Wentzell Quasi-Potential via Path Minimization

Computes an approximate Freidlin–Wentzell quasi-potential between two points \(x_0\) and \(x_1\) by minimizing the FW action functional over discretized paths.

Usage

FW_quasipotential(
  x0,
  x1,
  drift,
  T = 200,
  dt = 0.01,
  niter = 200,
  stepsize = 0.1
)

Arguments

x0: Starting point (numeric vector).
x1: Target point (numeric vector).
drift: Drift function b(x).
T: Number of time steps.
dt: Time step.
niter: Number of gradient descent iterations.
stepsize: Gradient descent step size.

Value

A list with:

path: matrix of size T × d
action: FW action of the optimized path

Details

The algorithm:

Initializes a straight-line path between x0 and x1.
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.