Struct WassersteinGradientFlow 

pub struct WassersteinGradientFlow {
    pub tau: f64,
    pub positions: Vec<f64>,
    pub n_particles: usize,
    pub potential_alpha: f64,
}

Wasserstein gradient flow simulation using the JKO (Jordan-Kinderlehrer-Otto) minimising movement scheme.

Evolves a discrete probability measure ρ = (x_i, w_i) under the gradient flow of the free energy F[ρ] = ∫ ρ log ρ dx + ∫ V ρ dx (Fokker-Planck).

Fields

tau: f64

JKO time step τ.

positions: Vec<f64>

Current particle positions x_i.

n_particles: usize

Equal weights w_i = 1/N.

potential_alpha: f64

Potential V(x) = α x² / 2 (quadratic confining potential), coefficient α.

Implementations

impl WassersteinGradientFlow

pub fn new(n_particles: usize, tau: f64, potential_alpha: f64) -> Self

Initialise with N Gaussian-distributed particles.

pub fn step(&mut self)

Perform one JKO step: move particles to minimise τ F[ρ] + W_2²(ρ^n, ρ) / 2 via a proximal operator. For the quadratic potential V = α x²/2 the JKO update has the closed-form shrinkage: x_i^{n+1} = x_i^n / (1 + τ α).

pub fn run(&mut self, n_steps: usize)

Run n_steps JKO steps.

pub fn mean(&self) -> f64

Compute the empirical mean of the particle cloud.

pub fn variance(&self) -> f64

Compute the empirical variance of the particle cloud.

pub fn steady_state_variance(&self) -> f64

Steady-state variance: σ² = 1/(τ α N) · N = 1/α (Gaussian with covariance 1/α).

Trait Implementations

impl Clone for WassersteinGradientFlow

fn clone(&self) -> WassersteinGradientFlow

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for WassersteinGradientFlow

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.