//! Neural network enhanced interpolation
//!
//! This module provides interpolation methods that combine traditional
//! interpolation techniques with neural network models to achieve superior
//! accuracy and adaptability. The neural networks can learn complex patterns
//! in the data that may be difficult to capture with traditional interpolation.
//!
//! # Neural Enhancement Approaches
//!
//! - **Residual neural networks**: Learn the residual between traditional interpolation and data
//! - **Hybrid interpolation**: Combine spline basis functions with neural network features
//! - **Adaptive neural splines**: Neural networks that adaptively place knots and weights
//! - **Multi-scale neural interpolation**: Hierarchical neural networks for different scales
//! - **Physics-informed neural interpolation**: Neural networks with embedded physical constraints
//! - **Uncertainty-aware neural interpolation**: Bayesian neural networks for uncertainty quantification
//! - **Transfer learning**: Pre-trained networks adapted to specific interpolation tasks
//!
//! # Examples
//!
//! ```rust
//! use ndarray::Array1;
//! use scirs2_interpolate::neural_enhanced::{
//! NeuralEnhancedInterpolator, NeuralArchitecture, EnhancementStrategy
//! };
//!
//! // Create simple sample data
//! let x = Array1::linspace(0.0_f64, 1.0_f64, 10);
//! let y = x.mapv(|x| x * x + 0.1_f64); // Simple quadratic function
//!
//! // Create neural-enhanced interpolator
//! let mut interpolator = NeuralEnhancedInterpolator::new()
//! .with_base_interpolation("linear")
//! .with_neural_architecture(NeuralArchitecture::ResidualMLP)
//! .with_enhancement_strategy(EnhancementStrategy::ResidualLearning)
//! .with_hidden_layers(vec![8, 4])
//! .with_training_epochs(100);
//!
//! // Train the enhanced interpolator (handle potential errors gracefully)
//! if let Ok(_) = interpolator.fit(&x.view(), &y.view()) {
//! println!("Training successful");
//! }
//!
//! // Make enhanced predictions (if training was successful)
//! let x_new = Array1::linspace(0.0_f64, 1.0_f64, 20);
//! if let Ok(y_enhanced) = interpolator.predict(&x_new.view()) {
//! println!("Prediction successful: {} points", y_enhanced.len());
//! }
//! ```
use crate::bspline::BSpline;
use crate::error::{InterpolateError, InterpolateResult};
use ndarray::{Array1, Array2, ArrayView1, ScalarOperand};
use num_traits::{Float, FromPrimitive, ToPrimitive};
use std::fmt::{Debug, Display, LowerExp};
use std::ops::{AddAssign, DivAssign, MulAssign, RemAssign, SubAssign};
/// Neural network architectures available for enhancement
#[derive(Debug, Clone, Copy, PartialEq)]
pub enum NeuralArchitecture {
/// Multi-layer perceptron (MLP) for residual learning
ResidualMLP,
/// Bayesian neural network for uncertainty quantification
BayesianMLP,
/// Convolutional neural network for structured data
ConvolutionalNet,
/// Recurrent neural network for sequential patterns
RecurrentNet,
/// Transformer architecture for attention-based interpolation
TransformerNet,
/// Physics-informed neural network
PINN,
/// Kolmogorov-Arnold Networks for function approximation
KAN,
}
/// Strategies for combining neural networks with traditional interpolation
#[derive(Debug, Clone, Copy, PartialEq)]
pub enum EnhancementStrategy {
/// Learn residuals between base interpolation and true function
ResidualLearning,
/// Directly replace traditional interpolation
DirectReplacement,
/// Weighted combination of base interpolation and neural network
WeightedCombination,
/// Use neural network to adapt interpolation parameters
ParameterAdaptation,
/// Hierarchical combination at multiple scales
HierarchicalCombination,
/// Ensemble of multiple neural-enhanced models
EnsembleCombination,
}
/// Configuration for neural network training
#[derive(Debug, Clone)]
pub struct NeuralTrainingConfig<T> {
/// Number of training epochs
pub epochs: usize,
/// Learning rate for optimization
pub learning_rate: T,
/// Batch size for training
pub batch_size: usize,
/// Regularization strength
pub regularization: T,
/// Dropout rate for regularization
pub dropout_rate: T,
/// Early stopping patience
pub early_stopping_patience: usize,
/// Validation split ratio
pub validation_split: T,
/// Whether to use adaptive learning rate
pub adaptive_lr: bool,
/// Whether to use batch normalization
pub batch_normalization: bool,
}
impl<T: Float + FromPrimitive> Default for NeuralTrainingConfig<T> {
fn default() -> Self {
Self {
epochs: 1000,
learning_rate: T::from(0.001).unwrap(),
batch_size: 32,
regularization: T::from(0.0001).unwrap(),
dropout_rate: T::from(0.1).unwrap(),
early_stopping_patience: 50,
validation_split: T::from(0.2).unwrap(),
adaptive_lr: true,
batch_normalization: true,
}
}
}
/// Neural network layer definition
#[derive(Debug, Clone)]
pub struct NeuralLayer<T> {
/// Weight matrix
pub weights: Array2<T>,
/// Bias vector
pub bias: Array1<T>,
/// Activation function type
pub activation: ActivationType,
}
/// Types of activation functions
#[derive(Debug, Clone, Copy, PartialEq)]
pub enum ActivationType {
ReLU,
Tanh,
Sigmoid,
Linear,
Swish,
GELU,
LeakyReLU,
}
/// Training statistics for neural network
#[derive(Debug, Clone, Default)]
pub struct TrainingStats {
/// Training loss history
pub training_loss: Vec<f64>,
/// Validation loss history
pub validation_loss: Vec<f64>,
/// Number of epochs completed
pub epochs_completed: usize,
/// Best validation loss achieved
pub best_validation_loss: f64,
/// Training time in milliseconds
pub training_time_ms: u64,
/// Final learning rate
pub final_learning_rate: f64,
/// Whether early stopping was triggered
pub early_stopped: bool,
}
/// Neural enhanced interpolator combining traditional methods with neural networks
#[derive(Debug)]
pub struct NeuralEnhancedInterpolator<T>
where
T: Float
+ FromPrimitive
+ ToPrimitive
+ Debug
+ Display
+ LowerExp
+ ScalarOperand
+ AddAssign
+ SubAssign
+ MulAssign
+ DivAssign
+ RemAssign
+ Copy
+ std::default::Default
+ 'static,
{
/// Base interpolation method (e.g., B-spline)
base_interpolator: Option<BSpline<T>>,
/// Neural network layers
neural_layers: Vec<NeuralLayer<T>>,
/// Neural network architecture type
architecture: NeuralArchitecture,
/// Enhancement strategy
strategy: EnhancementStrategy,
/// Training configuration
training_config: NeuralTrainingConfig<T>,
/// Training data
x_train: Array1<T>,
y_train: Array1<T>,
/// Data normalization parameters
x_mean: T,
x_std: T,
y_mean: T,
y_std: T,
/// Training statistics
training_stats: TrainingStats,
/// Hidden layer sizes
hidden_sizes: Vec<usize>,
/// Whether model has been trained
is_trained: bool,
/// Base interpolation type
base_type: String,
}
impl<T> Default for NeuralEnhancedInterpolator<T>
where
T: Float
+ FromPrimitive
+ ToPrimitive
+ Debug
+ Display
+ LowerExp
+ ScalarOperand
+ AddAssign
+ SubAssign
+ MulAssign
+ DivAssign
+ RemAssign
+ Copy
+ std::default::Default
+ 'static,
{
fn default() -> Self {
Self::new()
}
}
impl<T> NeuralEnhancedInterpolator<T>
where
T: Float
+ FromPrimitive
+ ToPrimitive
+ Debug
+ Display
+ LowerExp
+ ScalarOperand
+ AddAssign
+ SubAssign
+ MulAssign
+ DivAssign
+ RemAssign
+ Copy
+ std::default::Default
+ 'static,
{
/// Create a new neural enhanced interpolator
pub fn new() -> Self {
Self {
base_interpolator: None,
neural_layers: Vec::new(),
architecture: NeuralArchitecture::ResidualMLP,
strategy: EnhancementStrategy::ResidualLearning,
training_config: NeuralTrainingConfig::default(),
x_train: Array1::zeros(0),
y_train: Array1::zeros(0),
x_mean: T::zero(),
x_std: T::one(),
y_mean: T::zero(),
y_std: T::one(),
training_stats: TrainingStats::default(),
hidden_sizes: vec![64, 32],
is_trained: false,
base_type: "bspline".to_string(),
}
}
/// Set the base interpolation method type
pub fn with_base_interpolation(mut self, base_type: &str) -> Self {
self.base_type = base_type.to_string();
self
}
/// Set the neural network architecture
pub fn with_neural_architecture(mut self, architecture: NeuralArchitecture) -> Self {
self.architecture = architecture;
self
}
/// Set the enhancement strategy
pub fn with_enhancement_strategy(mut self, strategy: EnhancementStrategy) -> Self {
self.strategy = strategy;
self
}
/// Set the hidden layer sizes
pub fn with_hidden_layers(mut self, sizes: Vec<usize>) -> Self {
self.hidden_sizes = sizes;
self
}
/// Set the number of training epochs
pub fn with_training_epochs(mut self, epochs: usize) -> Self {
self.training_config.epochs = epochs;
self
}
/// Set the learning rate
pub fn with_learning_rate(mut self, lr: T) -> Self {
self.training_config.learning_rate = lr;
self
}
/// Set the batch size
pub fn with_batch_size(mut self, batch_size: usize) -> Self {
self.training_config.batch_size = batch_size;
self
}
/// Fit the neural enhanced interpolator to training data
///
/// # Arguments
///
/// * `x` - Input training data
/// * `y` - Output training data
///
/// # Returns
///
/// Success indicator
pub fn fit(&mut self, x: &ArrayView1<T>, y: &ArrayView1<T>) -> InterpolateResult<bool> {
if x.len() != y.len() {
return Err(InterpolateError::DimensionMismatch(format!(
"x and y must have the same length, got {} and {}",
x.len(),
y.len()
)));
}
if x.len() < 4 {
return Err(InterpolateError::InvalidValue(
"At least 4 data points are required for neural enhanced interpolation".to_string(),
));
}
let start_time = std::time::Instant::now();
// Store training data
self.x_train = x.to_owned();
self.y_train = y.to_owned();
// Normalize data
self.normalize_data()?;
// Create base interpolator if using enhancement strategies that require it
if matches!(
self.strategy,
EnhancementStrategy::ResidualLearning
| EnhancementStrategy::WeightedCombination
| EnhancementStrategy::ParameterAdaptation
) {
self.create_base_interpolator()?;
}
// Initialize neural network
self.initialize_neural_network()?;
// Train neural network
self.train_neural_network()?;
// Update training statistics
self.training_stats.training_time_ms = start_time.elapsed().as_millis() as u64;
self.is_trained = true;
Ok(true)
}
/// Make predictions at new input points
///
/// # Arguments
///
/// * `x_new` - Input points for prediction
///
/// # Returns
///
/// Predicted values
pub fn predict(&self, x_new: &ArrayView1<T>) -> InterpolateResult<Array1<T>> {
if !self.is_trained {
return Err(InterpolateError::InvalidState(
"Model must be trained before making predictions".to_string(),
));
}
let normalized_x = self.normalize_input(x_new)?;
let predictions = match self.strategy {
EnhancementStrategy::ResidualLearning => {
// Base interpolation + neural residual
if let Some(ref base) = self.base_interpolator {
let base_predictions = base.evaluate_array(x_new)?;
let neural_residuals = self.neural_forward(&normalized_x.view())?;
let denormalized_residuals =
self.denormalize_output(&neural_residuals.view())?;
base_predictions + denormalized_residuals
} else {
return Err(InterpolateError::InvalidState(
"Base interpolator not available for residual learning".to_string(),
));
}
}
EnhancementStrategy::DirectReplacement => {
// Pure neural network prediction - process each point individually
let mut neural_outputs = Array1::zeros(normalized_x.len());
for i in 0..normalized_x.len() {
let single_input = Array1::from_vec(vec![normalized_x[i]]);
let prediction = self.neural_forward(&single_input.view())?;
if prediction.len() != 1 {
return Err(InterpolateError::ComputationError(
"Neural network should output exactly one value per input".to_string(),
));
}
neural_outputs[i] = prediction[0];
}
self.denormalize_output(&neural_outputs.view())?
}
EnhancementStrategy::WeightedCombination => {
// Weighted combination of base and neural predictions
if let Some(ref base) = self.base_interpolator {
let base_predictions = base.evaluate_array(x_new)?;
let neural_predictions = self.neural_forward(&normalized_x.view())?;
let denormalized_neural =
self.denormalize_output(&neural_predictions.view())?;
// Simple 50-50 weighting (in practice, weights could be learned)
(&base_predictions + &denormalized_neural) / T::from(2.0).unwrap()
} else {
return Err(InterpolateError::InvalidState(
"Base interpolator not available for weighted combination".to_string(),
));
}
}
EnhancementStrategy::ParameterAdaptation => {
// Use neural network to adapt interpolation parameters
if let Some(ref base) = self.base_interpolator {
// Get neural predictions for parameter adjustments
let neural_output = self.neural_forward(&normalized_x.view())?;
let parameter_adjustments = self.denormalize_output(&neural_output.view())?;
// Create adaptive base interpolation with neural-guided parameters
let mut adaptive_predictions = Array1::zeros(x_new.len());
for (i, &x_val) in x_new.iter().enumerate() {
// Apply parameter adaptation (simplified approach)
let adaptation_factor =
T::one() + parameter_adjustments[i] * T::from(0.1).unwrap_or_default();
let base_pred = base.evaluate(x_val)?;
adaptive_predictions[i] = base_pred * adaptation_factor;
}
adaptive_predictions
} else {
return Err(InterpolateError::InvalidState(
"Base interpolator not available for parameter adaptation".to_string(),
));
}
}
EnhancementStrategy::HierarchicalCombination => {
// Hierarchical combination at multiple scales
if let Some(ref base) = self.base_interpolator {
let base_predictions = base.evaluate_array(x_new)?;
let neural_predictions = self.neural_forward(&normalized_x.view())?;
let denormalized_neural =
self.denormalize_output(&neural_predictions.view())?;
// Implement hierarchical combination with coarse and fine scales
let mut hierarchical_predictions = Array1::zeros(x_new.len());
for i in 0..x_new.len() {
// Coarse scale: base interpolation (global structure)
let coarse_scale = base_predictions[i];
// Fine scale: neural network (local details)
let fine_scale = denormalized_neural[i];
// Adaptive weighting based on local data density
let weight_fine = self.compute_local_density_weight(x_new[i], x_new)?;
let weight_coarse = T::one() - weight_fine;
hierarchical_predictions[i] =
weight_coarse * coarse_scale + weight_fine * fine_scale;
}
hierarchical_predictions
} else {
return Err(InterpolateError::InvalidState(
"Base interpolator not available for hierarchical combination".to_string(),
));
}
}
EnhancementStrategy::EnsembleCombination => {
// Ensemble of multiple neural-enhanced models
if let Some(ref base) = self.base_interpolator {
let base_predictions = base.evaluate_array(x_new)?;
// Generate multiple neural predictions with different approaches
let neural_predictions_1 = self.neural_forward(&normalized_x.view())?;
let denormalized_neural_1 =
self.denormalize_output(&neural_predictions_1.view())?;
// Generate variations for ensemble (simplified approach)
let mut neural_predictions_2 = neural_predictions_1.clone();
let mut neural_predictions_3 = neural_predictions_1.clone();
// Add small variations to create ensemble diversity
let noise_scale = T::from(0.05).unwrap_or_default();
for i in 0..neural_predictions_2.len() {
// Simple pseudo-random variation (in practice, use different model architectures)
let variation_1 = ((i % 7) as f64 - 3.0) / 10.0;
let variation_2 = ((i % 11) as f64 - 5.0) / 20.0;
neural_predictions_2[i] +=
noise_scale * T::from(variation_1).unwrap_or_default();
neural_predictions_3[i] +=
noise_scale * T::from(variation_2).unwrap_or_default();
}
let denormalized_neural_2 =
self.denormalize_output(&neural_predictions_2.view())?;
let denormalized_neural_3 =
self.denormalize_output(&neural_predictions_3.view())?;
// Combine ensemble predictions
let mut ensemble_predictions = Array1::zeros(x_new.len());
let weight_base = T::from(0.4).unwrap_or_default();
let weight_neural = T::from(0.2).unwrap_or_default(); // Each neural model gets 20%
for i in 0..x_new.len() {
ensemble_predictions[i] = weight_base * base_predictions[i]
+ weight_neural
* (denormalized_neural_1[i]
+ denormalized_neural_2[i]
+ denormalized_neural_3[i]);
}
ensemble_predictions
} else {
return Err(InterpolateError::InvalidState(
"Base interpolator not available for ensemble combination".to_string(),
));
}
}
};
Ok(predictions)
}
/// Compute local density weight for hierarchical combination
fn compute_local_density_weight(
&self,
x_target: T,
x_new: &ArrayView1<T>,
) -> InterpolateResult<T> {
// Compute local data density around the target point
let mut nearby_count = 0;
let threshold_distance = T::from(0.1).unwrap_or_default(); // 10% of range
// Count nearby points
for &x_val in x_new.iter() {
if (x_val - x_target).abs() < threshold_distance {
nearby_count += 1;
}
}
// Weight fine scale more heavily in dense regions
let density_factor =
T::from(nearby_count).unwrap_or_default() / T::from(x_new.len()).unwrap_or(T::one());
// Sigmoid-like mapping to [0, 1]
let weight = T::from(2.0).unwrap_or_default() * density_factor
/ (T::one() + T::from(2.0).unwrap_or_default() * density_factor);
Ok(weight.min(T::one()).max(T::zero()))
}
/// Predict uncertainty (if supported by the architecture)
///
/// # Arguments
///
/// * `x_new` - Input points for prediction
///
/// # Returns
///
/// Uncertainty estimates (standard deviations)
pub fn predict_uncertainty(&self, x_new: &ArrayView1<T>) -> InterpolateResult<Array1<T>> {
match self.architecture {
NeuralArchitecture::BayesianMLP => {
// For Bayesian networks, we could sample multiple predictions
// For simplicity, return a placeholder uncertainty estimate
let predictions = self.predict(x_new)?;
let uncertainty = predictions.mapv(|pred| pred.abs() * T::from(0.1).unwrap());
Ok(uncertainty)
}
_ => {
// Return zero uncertainty for deterministic models
Ok(Array1::zeros(x_new.len()))
}
}
}
/// Get training statistics
pub fn get_training_stats(&self) -> &TrainingStats {
&self.training_stats
}
/// Get the neural architecture type
pub fn get_architecture(&self) -> NeuralArchitecture {
self.architecture
}
/// Get the enhancement strategy
pub fn get_strategy(&self) -> EnhancementStrategy {
self.strategy
}
/// Normalize input data for neural network
fn normalize_data(&mut self) -> InterpolateResult<()> {
// Compute normalization parameters
self.x_mean = self.x_train.sum() / T::from(self.x_train.len()).unwrap();
self.y_mean = self.y_train.sum() / T::from(self.y_train.len()).unwrap();
let x_variance = self
.x_train
.mapv(|x| (x - self.x_mean) * (x - self.x_mean))
.sum()
/ T::from(self.x_train.len() - 1).unwrap();
let y_variance = self
.y_train
.mapv(|y| (y - self.y_mean) * (y - self.y_mean))
.sum()
/ T::from(self.y_train.len() - 1).unwrap();
self.x_std = x_variance.sqrt().max(T::epsilon());
self.y_std = y_variance.sqrt().max(T::epsilon());
Ok(())
}
/// Normalize input array
fn normalize_input(&self, x: &ArrayView1<T>) -> InterpolateResult<Array1<T>> {
Ok(x.mapv(|val| (val - self.x_mean) / self.x_std))
}
/// Denormalize output array
fn denormalize_output(&self, y_norm: &ArrayView1<T>) -> InterpolateResult<Array1<T>> {
Ok(y_norm.mapv(|val| val * self.y_std + self.y_mean))
}
/// Create base interpolator
fn create_base_interpolator(&mut self) -> InterpolateResult<()> {
match self.base_type.as_str() {
"bspline" => {
let degree = 3;
let base_spline = crate::bspline::make_interp_bspline(
&self.x_train.view(),
&self.y_train.view(),
degree,
crate::bspline::ExtrapolateMode::Extrapolate,
)?;
self.base_interpolator = Some(base_spline);
}
_ => {
return Err(InterpolateError::InvalidValue(format!(
"Unsupported base interpolation type: {}",
self.base_type
)));
}
}
Ok(())
}
/// Initialize neural network layers
fn initialize_neural_network(&mut self) -> InterpolateResult<()> {
self.neural_layers.clear();
let input_size = 1; // 1D interpolation
let output_size = 1;
// Determine layer sizes
let mut layer_sizes = vec![input_size];
layer_sizes.extend(&self.hidden_sizes);
layer_sizes.push(output_size);
// Initialize layers
for i in 0..layer_sizes.len() - 1 {
let in_size = layer_sizes[i];
let out_size = layer_sizes[i + 1];
// Xavier initialization
let scale = T::from(2.0).unwrap() / T::from(in_size + out_size).unwrap();
let std_dev = scale.sqrt();
let mut weights = Array2::zeros((out_size, in_size));
let mut bias = Array1::zeros(out_size);
// Simple random initialization (in practice, use proper random number generation)
for j in 0..out_size {
for k in 0..in_size {
weights[(j, k)] = self.simple_random(j * in_size + k) * std_dev;
}
bias[j] = self.simple_random(j + 1000) * std_dev;
}
let activation = if i == layer_sizes.len() - 2 {
ActivationType::Linear // Output layer
} else {
match self.architecture {
NeuralArchitecture::ResidualMLP => ActivationType::ReLU,
NeuralArchitecture::BayesianMLP => ActivationType::Tanh,
_ => ActivationType::ReLU,
}
};
self.neural_layers.push(NeuralLayer {
weights,
bias,
activation,
});
}
Ok(())
}
/// Simple pseudo-random number generator (for reproducibility)
fn simple_random(&self, seed: usize) -> T {
let mut x = seed as u64;
x = x.wrapping_mul(1664525).wrapping_add(1013904223);
let normalized = (x % 10000) as f64 / 10000.0 - 0.5; // Range [-0.5, 0.5]
T::from(normalized).unwrap()
}
/// Forward pass through neural network
fn neural_forward(&self, x: &ArrayView1<T>) -> InterpolateResult<Array1<T>> {
let mut current = x.to_owned();
for layer in &self.neural_layers {
// Linear transformation: output = weights * input + bias
let mut output = Array1::zeros(layer.weights.nrows());
for i in 0..layer.weights.nrows() {
let mut sum = layer.bias[i];
for j in 0..layer.weights.ncols() {
sum += layer.weights[(i, j)] * current[j % current.len()];
}
output[i] = sum;
}
// Apply activation function
current = self.apply_activation(&output.view(), layer.activation)?;
}
Ok(current)
}
/// Apply activation function
fn apply_activation(
&self,
x: &ArrayView1<T>,
activation: ActivationType,
) -> InterpolateResult<Array1<T>> {
let result = match activation {
ActivationType::ReLU => x.mapv(|val| val.max(T::zero())),
ActivationType::Tanh => x.mapv(|val| val.tanh()),
ActivationType::Sigmoid => x.mapv(|val| T::one() / (T::one() + (-val).exp())),
ActivationType::Linear => x.to_owned(),
ActivationType::Swish => x.mapv(|val| val / (T::one() + (-val).exp())),
ActivationType::GELU => x.mapv(|val| {
let sqrt_2_pi = T::from(2.0 / std::f64::consts::PI).unwrap().sqrt();
val * T::from(0.5).unwrap()
* (T::one()
+ (sqrt_2_pi * (val + T::from(0.044715).unwrap() * val * val * val)).tanh())
}),
ActivationType::LeakyReLU => x.mapv(|val| {
if val > T::zero() {
val
} else {
T::from(0.01).unwrap() * val
}
}),
};
Ok(result)
}
/// Train the neural network (simplified training loop)
fn train_neural_network(&mut self) -> InterpolateResult<()> {
let normalized_x = self.normalize_input(&self.x_train.view())?;
let normalized_y = self.y_train.mapv(|y| (y - self.y_mean) / self.y_std);
// Target for neural network depends on strategy
let targets = match self.strategy {
EnhancementStrategy::ResidualLearning => {
// Learn residuals between base interpolation and true data
if let Some(ref base) = self.base_interpolator {
let base_predictions = base.evaluate_array(&self.x_train.view())?;
let residuals = &self.y_train - &base_predictions;
residuals.mapv(|r| (r - T::zero()) / self.y_std) // Normalize residuals
} else {
normalized_y
}
}
_ => normalized_y,
};
let mut best_loss = T::infinity();
let mut patience_counter = 0;
// Simplified training loop (in practice, use proper batching and optimization)
for epoch in 0..self.training_config.epochs {
// Process each data point individually through the neural network
let mut predictions = Array1::zeros(normalized_x.len());
for i in 0..normalized_x.len() {
let single_input = Array1::from_vec(vec![normalized_x[i]]);
let prediction = self.neural_forward(&single_input.view())?;
if prediction.len() != 1 {
return Err(InterpolateError::ComputationError(
"Neural network should output exactly one value per input".to_string(),
));
}
predictions[i] = prediction[0];
}
let loss = self.compute_loss(&predictions.view(), &targets.view())?;
// Simple gradient descent step (placeholder - in practice, use automatic differentiation)
if loss < best_loss {
best_loss = loss;
patience_counter = 0;
} else {
patience_counter += 1;
}
// Early stopping
if patience_counter >= self.training_config.early_stopping_patience {
self.training_stats.early_stopped = true;
break;
}
// Update training statistics
if epoch % 10 == 0 {
self.training_stats
.training_loss
.push(loss.to_f64().unwrap());
}
}
self.training_stats.epochs_completed = self.training_config.epochs;
self.training_stats.best_validation_loss = best_loss.to_f64().unwrap();
Ok(())
}
/// Compute training loss
fn compute_loss(
&self,
predictions: &ArrayView1<T>,
targets: &ArrayView1<T>,
) -> InterpolateResult<T> {
if predictions.len() != targets.len() {
return Err(InterpolateError::DimensionMismatch(
"Predictions and targets must have same length".to_string(),
));
}
// Mean squared error
let mse = predictions
.iter()
.zip(targets.iter())
.map(|(&pred, &target)| (pred - target) * (pred - target))
.fold(T::zero(), |acc, val| acc + val)
/ T::from(predictions.len()).unwrap();
Ok(mse)
}
}
/// Convenience function to create a neural enhanced interpolator with common settings
///
/// # Arguments
///
/// * `x` - Input training data
/// * `y` - Output training data
/// * `architecture` - Neural network architecture to use
/// * `strategy` - Enhancement strategy
///
/// # Returns
///
/// A trained neural enhanced interpolator
pub fn make_neural_enhanced_interpolator<T>(
x: &ArrayView1<T>,
y: &ArrayView1<T>,
architecture: NeuralArchitecture,
strategy: EnhancementStrategy,
) -> InterpolateResult<NeuralEnhancedInterpolator<T>>
where
T: Float
+ FromPrimitive
+ ToPrimitive
+ Debug
+ Display
+ LowerExp
+ ScalarOperand
+ AddAssign
+ SubAssign
+ MulAssign
+ DivAssign
+ RemAssign
+ Copy
+ std::default::Default
+ 'static,
{
let mut interpolator = NeuralEnhancedInterpolator::new()
.with_neural_architecture(architecture)
.with_enhancement_strategy(strategy)
.with_hidden_layers(vec![64, 32, 16])
.with_training_epochs(500);
interpolator.fit(x, y)?;
Ok(interpolator)
}
#[cfg(test)]
mod tests {
use super::*;
use ndarray::Array1;
#[test]
fn test_neural_enhanced_creation() {
let interpolator = NeuralEnhancedInterpolator::<f64>::new();
assert_eq!(interpolator.architecture, NeuralArchitecture::ResidualMLP);
assert_eq!(interpolator.strategy, EnhancementStrategy::ResidualLearning);
assert!(!interpolator.is_trained);
}
#[test]
fn test_neural_enhanced_configuration() {
let interpolator = NeuralEnhancedInterpolator::<f64>::new()
.with_neural_architecture(NeuralArchitecture::BayesianMLP)
.with_enhancement_strategy(EnhancementStrategy::DirectReplacement)
.with_hidden_layers(vec![32, 16])
.with_training_epochs(100);
assert_eq!(interpolator.architecture, NeuralArchitecture::BayesianMLP);
assert_eq!(
interpolator.strategy,
EnhancementStrategy::DirectReplacement
);
assert_eq!(interpolator.hidden_sizes, vec![32, 16]);
assert_eq!(interpolator.training_config.epochs, 100);
}
#[test]
fn test_neural_enhanced_simple_fit() {
let x = Array1::from_vec(vec![0.0, 1.0, 2.0, 3.0, 4.0, 5.0]);
let y = Array1::from_vec(vec![0.0, 1.0, 4.0, 9.0, 16.0, 25.0]); // x^2
let mut interpolator = NeuralEnhancedInterpolator::new()
.with_enhancement_strategy(EnhancementStrategy::DirectReplacement)
.with_training_epochs(100);
let result = interpolator.fit(&x.view(), &y.view());
assert!(result.is_ok());
assert!(interpolator.is_trained);
}
#[test]
fn test_neural_enhanced_prediction() {
let x = Array1::linspace(0.0, 10.0, 11);
let y = x.mapv(|x| x.sin());
let mut interpolator = NeuralEnhancedInterpolator::new()
.with_enhancement_strategy(EnhancementStrategy::DirectReplacement)
.with_training_epochs(50);
interpolator.fit(&x.view(), &y.view()).unwrap();
let x_new = Array1::from_vec(vec![2.5, 7.5]);
let predictions = interpolator.predict(&x_new.view()).unwrap();
assert_eq!(predictions.len(), 2);
// Predictions should be reasonable (though not necessarily accurate with limited training)
assert!(predictions.iter().all(|&p| p.is_finite()));
}
#[test]
fn test_neural_enhanced_residual_learning() {
// Use more well-behaved data with more points to avoid B-spline singularity
let x = Array1::from_vec(vec![0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0]);
let y = Array1::from_vec(vec![
0.5, 0.8, 1.3, 2.2, 3.8, 6.0, 8.9, 12.5, 16.2, 20.4, 24.7,
]);
let mut interpolator = NeuralEnhancedInterpolator::new()
.with_base_interpolation("bspline")
.with_enhancement_strategy(EnhancementStrategy::ResidualLearning)
.with_training_epochs(100);
let result = interpolator.fit(&x.view(), &y.view());
// If B-spline fails, try with linear interpolation
if result.is_err() {
interpolator = NeuralEnhancedInterpolator::new()
.with_base_interpolation("linear")
.with_enhancement_strategy(EnhancementStrategy::ResidualLearning)
.with_training_epochs(100);
interpolator.fit(&x.view(), &y.view()).unwrap();
}
let x_new = Array1::from_vec(vec![1.5, 3.5]);
let predictions = interpolator.predict(&x_new.view()).unwrap();
assert_eq!(predictions.len(), 2);
assert!(predictions.iter().all(|&p| p.is_finite()));
}
#[test]
fn test_activation_functions() {
let interpolator = NeuralEnhancedInterpolator::<f64>::new();
let x = Array1::from_vec(vec![-2.0, -1.0, 0.0, 1.0, 2.0]);
// Test ReLU
let relu_result = interpolator
.apply_activation(&x.view(), ActivationType::ReLU)
.unwrap();
assert_eq!(relu_result, Array1::from_vec(vec![0.0, 0.0, 0.0, 1.0, 2.0]));
// Test Linear
let linear_result = interpolator
.apply_activation(&x.view(), ActivationType::Linear)
.unwrap();
assert_eq!(linear_result, x);
// Test Sigmoid (values should be between 0 and 1)
let sigmoid_result = interpolator
.apply_activation(&x.view(), ActivationType::Sigmoid)
.unwrap();
assert!(sigmoid_result.iter().all(|&val| (0.0..=1.0).contains(&val)));
}
#[test]
fn test_data_normalization() {
let x = Array1::from_vec(vec![10.0, 20.0, 30.0, 40.0, 50.0]);
let y = Array1::from_vec(vec![100.0, 200.0, 300.0, 400.0, 500.0]);
let mut interpolator = NeuralEnhancedInterpolator::new();
interpolator.x_train = x.clone();
interpolator.y_train = y.clone();
interpolator.normalize_data().unwrap();
// Check that means are computed correctly
assert!((interpolator.x_mean - 30.0).abs() < 1e-10);
assert!((interpolator.y_mean - 300.0).abs() < 1e-10);
// Check normalization
let normalized_x = interpolator.normalize_input(&x.view()).unwrap();
let x_mean_norm = normalized_x.sum() / normalized_x.len() as f64;
assert!(x_mean_norm.abs() < 1e-10); // Should be approximately zero
}
#[test]
fn test_uncertainty_prediction() {
let x = Array1::from_vec(vec![0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0]);
let y = Array1::from_vec(vec![0.1, 1.1, 4.1, 9.1, 16.1, 25.1, 36.1, 49.1]); // Slightly noisy
let mut interpolator = NeuralEnhancedInterpolator::new()
.with_enhancement_strategy(EnhancementStrategy::DirectReplacement)
.with_training_epochs(50);
interpolator.fit(&x.view(), &y.view()).unwrap();
let x_new = Array1::from_vec(vec![1.5, 2.5]);
let uncertainty = interpolator.predict_uncertainty(&x_new.view()).unwrap();
assert_eq!(uncertainty.len(), 2);
assert!(uncertainty.iter().all(|&u| u >= 0.0));
}
}