Struct PhysicsInformedKernel 

pub struct PhysicsInformedKernel<State = Untrained> { /* private fields */ }

Physics-Informed Kernel

Implements kernel methods that incorporate physical laws and differential equations into the learning process. Useful for solving PDEs and modeling physical systems with sparse data.

Mathematical Background

For a PDE: Nu = 0 (e.g., heat equation, wave equation) The kernel incorporates both data fitting and PDE residual minimization:

Loss = λ_data * ||u - u_data||² + λ_physics * ||N[u]||²

Examples

use sklears_kernel_approximation::scientific_computing_kernels::{
    PhysicsInformedKernel, PhysicsInformedConfig, PhysicalSystem
};
use scirs2_core::ndarray::array;
use sklears_core::traits::{Fit, Transform};

let config = PhysicsInformedConfig {
    system_type: PhysicalSystem::HeatEquation,
    ..Default::default()
};

let pinn = PhysicsInformedKernel::new(config);
let X = array![[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]]; // (x, t) coordinates
let fitted = pinn.fit(&X, &()).unwrap();
let features = fitted.transform(&X).unwrap();

Implementations

impl PhysicsInformedKernel<Untrained>

pub fn new(config: PhysicsInformedConfig) -> Self

Create a new physics-informed kernel

pub fn with_system(system: PhysicalSystem) -> Self

Create with default configuration

pub fn n_components(self, n: usize) -> Self

Set number of components

pub fn physics_weight(self, weight: Float) -> Self

Set physics weight

impl PhysicsInformedKernel<Trained>

pub fn boundary_data(&self) -> &Array2<Float>

Get boundary data

pub fn pde_residual( &self, x: &Array2<Float>, solution: &Array1<Float>, ) -> Result<Array1<Float>>

Evaluate PDE residual for a given system

Trait Implementations

impl<State: Clone> Clone for PhysicsInformedKernel<State>

fn clone(&self) -> PhysicsInformedKernel<State>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<State: Debug> Debug for PhysicsInformedKernel<State>

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

Formats the value using the given formatter.

impl Estimator for PhysicsInformedKernel<Untrained>

type Config = PhysicsInformedConfig

Configuration type for the estimator

type Error = SklearsError

Error type for the estimator

type Float = f64

The numeric type used by this estimator

fn config(&self) -> &Self::Config

Get estimator configuration

fn validate_config(&self) -> Result<(), SklearsError>

Validate estimator configuration with detailed error context

fn check_compatibility( &self, n_samples: usize, n_features: usize, ) -> Result<(), SklearsError>

Check if estimator is compatible with given data dimensions

fn metadata(&self) -> EstimatorMetadata

Get estimator metadata

impl Fit<ArrayBase<OwnedRepr<f64>, Dim<[usize; 2]>>, ()> for PhysicsInformedKernel<Untrained>

type Fitted = PhysicsInformedKernel<Trained>

The fitted model type

fn fit(self, x: &Array2<Float>, _y: &()) -> Result<Self::Fitted>

Fit the model to the provided data with validation

fn fit_with_validation( self, x: &X, y: &Y, _x_val: Option<&X>, _y_val: Option<&Y>, ) -> Result<(Self::Fitted, FitMetrics), SklearsError>

where Self: Sized,

Fit with custom validation and early stopping

impl Transform<ArrayBase<OwnedRepr<f64>, Dim<[usize; 2]>>> for PhysicsInformedKernel<Trained>

fn transform(&self, x: &Array2<Float>) -> Result<Array2<Float>>

Transform the input data