Struct PhysicsInformedInterp 

pub struct PhysicsInformedInterp { /* private fields */ }

Physics-informed RBF interpolator.

Enforces a PDE constraint at a grid of collocation points by augmenting the standard RBF least-squares system with additional penalty rows.

Example

use scirs2_interpolate::physics_interp::{
    PhysicsInformedInterp, PhysicsInterpConfig, LaplaceResidual,
};

let config = PhysicsInterpConfig {
    pde_weight: 0.5,
    n_collocation: 9,
    rbf_epsilon: 2.0,
    ..PhysicsInterpConfig::default()
};
let mut interp = PhysicsInformedInterp::new(config);

let points = vec![[0.0_f64, 0.0], [1.0, 0.0], [0.5, 1.0]];
let values = vec![0.0, 1.0, 0.5];
let pde = LaplaceResidual { f: 0.0 };

interp.fit(&points, &values, &pde).expect("fit should succeed");
let out = interp.evaluate(&points).expect("evaluate should succeed");

Implementations

impl PhysicsInformedInterp

pub fn new(config: PhysicsInterpConfig) -> Self

Create a new interpolator with the given configuration.

pub fn fit<P: PdeResidual>( &mut self, points: &[[f64; 2]], values: &[f64], pde: &P, ) -> Result<(), InterpolateError>

Fit the physics-informed RBF to points / values with PDE pde.

Internally, collocation points are placed on a regular grid inside the bounding box of the data. The combined least-squares system is solved via normal equations (Φᵀ Φ w = Φᵀ y) using Gaussian elimination.

pub fn evaluate( &self, query_points: &[[f64; 2]], ) -> Result<Vec<f64>, InterpolateError>

Evaluate the fitted interpolant at query_points.

pub fn pde_residual_norm<P: PdeResidual>(&self, pde: &P) -> f64

Compute the RMS PDE residual norm at the collocation points.

Returns 0.0 if no collocation points exist or the interpolant is not fitted.

pub fn total_loss<P: PdeResidual>(&self, pde: &P) -> f64

Total loss = data_fit_mse + pde_weight * pde_residual_mse.

Trait Implementations

impl Debug for PhysicsInformedInterp

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

Formats the value using the given formatter.