numra-spde

Stochastic partial differential equation solvers for the Numra workspace — Method of Lines with SDE time stepping, white and colored noise sources.

Solves SPDEs ∂u/∂t = L[u] + σ(u) ξ(x,t) by discretizing the spatial operator L with finite differences (sharing numra-pde's discretization machinery) and time-stepping the resulting SDE system with numra-sde's steppers. Supports additive and multiplicative noise, ensemble runs, and adaptive time control.

Example

use numra_pde::Grid1D;
use numra_spde::{SpdeSystem};

// Stochastic heat equation: ∂T/∂t = α ∂²T/∂x² + σ ξ(x,t)
struct StochasticHeat { alpha: f64, sigma: f64 }

impl SpdeSystem<f64> for StochasticHeat {
    fn dim(&self) -> usize { 1 }
    fn drift(&self, _t: f64, u: &[f64], du: &mut [f64], grid: &Grid1D<f64>) {
        let dx = grid.dx_uniform();
        let n = u.len();
        for i in 0..n {
            let l = if i == 0 { 0.0 } else { u[i - 1] };
            let r = if i == n - 1 { 0.0 } else { u[i + 1] };
            du[i] = self.alpha * (l - 2.0 * u[i] + r) / (dx * dx);
        }
    }
    fn diffusion(&self, _t: f64, u: &[f64], sigma: &mut [f64], _grid: &Grid1D<f64>) {
        for s in sigma.iter_mut() { *s = self.sigma; }
    }
}

What's in this crate

• SpdeSystem trait — drift, diffusion, optional noise-correlation hooks
• MolSdeSolver — Method-of-Lines stepper composing numra-pde discretizations with numra-sde time integrators
• SpdeEnsemble — Rayon-parallel Monte Carlo over realizations
• SpdeOptions / SpdeResult / SpdeStats — configuration and diagnostics
• SpdeMethod — selectable underlying SDE stepper
• Noise sources: WhiteNoise, ColoredNoise, ColoredNoiseGenerator, SpaceTimeNoise, NoiseCorrelation

Composes with

• numra-pde — provides spatial grids and finite-difference operators
• numra-sde — provides the time-stepping schemes underneath MOL
• numra-stats — ensemble mean / std / percentile across realizations
• numra-interp — post-hoc resampling of fields onto common grids

See cross-formalism tests for the SPDE = PDE + SDE composition check.

Install

[dependencies]
numra-spde = "0.1"

Or via the umbrella crate:

[dependencies]
numra = "0.1"

Documentation

• API: https://docs.rs/numra-spde
• Book: Stochastic PDEs
• Source: https://github.com/moussaoutlook/numra-rs/tree/main/numra-spde

License

Numra Academic & Research License (Non-Commercial). Academic and research use is free; commercial use requires a separate license — contact contact@spectralautomata.com. See LICENSE.