scirs2-optimize 0.4.2

//! Neural ODE Optimization
//!
//! Implementation of neural ordinary differential equation-based optimization.

use crate::error::OptimizeResult;
use scirs2_core::ndarray::{Array1, ArrayView1};

/// Neural ODE system for optimization
#[derive(Debug, Clone)]
pub struct NeuralODE {
    /// Network parameters (weights)
    pub weights: Array1<f64>,
    /// System state
    pub state: Array1<f64>,
    /// Time step
    pub dt: f64,
}

impl NeuralODE {
    /// Create new Neural ODE system
    pub fn new(state_size: usize, dt: f64) -> Self {
        Self {
            weights: Array1::from(vec![0.1; state_size * state_size]),
            state: Array1::zeros(state_size),
            dt,
        }
    }

    /// Compute state derivative
    pub fn compute_derivative(
        &self,
        state: &ArrayView1<f64>,
        objective_gradient: &ArrayView1<f64>,
    ) -> Array1<f64> {
        let n = state.len();
        let mut derivative = Array1::zeros(n);

        // Neural dynamics: dx/dt = -Wx + u
        // where W is weight matrix, x is state, u is input (objective gradient)
        for i in 0..n {
            for j in 0..n {
                let weight_idx = i * n + j;
                if weight_idx < self.weights.len() {
                    derivative[i] -= self.weights[weight_idx] * state[j];
                }
            }

            // Add objective gradient as driving input
            if i < objective_gradient.len() {
                derivative[i] += objective_gradient[i];
            }
        }

        derivative
    }

    /// Integrate one step using Euler method
    pub fn integrate_step(&mut self, objective_gradient: &ArrayView1<f64>) {
        let derivative = self.compute_derivative(&self.state.view(), objective_gradient);

        for i in 0..self.state.len() {
            self.state[i] += self.dt * derivative[i];
        }
    }

    /// Get current state as parameter estimate
    pub fn get_parameters(&self) -> &Array1<f64> {
        &self.state
    }

    /// Set initial state
    pub fn set_initial_state(&mut self, initial_state: &ArrayView1<f64>) {
        self.state = initial_state.to_owned();
    }
}

/// Neural ODE-based optimization
#[allow(dead_code)]
pub fn neural_ode_optimize<F>(
    objective: F,
    initial_params: &ArrayView1<f64>,
    num_steps: usize,
    dt: f64,
) -> OptimizeResult<Array1<f64>>
where
    F: Fn(&ArrayView1<f64>) -> f64,
{
    let mut neural_ode = NeuralODE::new(initial_params.len(), dt);
    neural_ode.set_initial_state(initial_params);

    for _step in 0..num_steps {
        // Compute objective gradient
        let current_params = neural_ode.get_parameters();
        let gradient = compute_finite_difference_gradient(&objective, &current_params.view());

        // Integrate Neural ODE
        neural_ode.integrate_step(&(-1.0 * &gradient).view()); // Negative for minimization
    }

    Ok(neural_ode.get_parameters().clone())
}

/// Compute finite difference gradient
#[allow(dead_code)]
fn compute_finite_difference_gradient<F>(objective: &F, params: &ArrayView1<f64>) -> Array1<f64>
where
    F: Fn(&ArrayView1<f64>) -> f64,
{
    let n = params.len();
    let mut gradient = Array1::zeros(n);
    let h = 1e-6;
    let f0 = objective(params);

    for i in 0..n {
        let mut params_plus = params.to_owned();
        params_plus[i] += h;
        let f_plus = objective(&params_plus.view());
        gradient[i] = (f_plus - f0) / h;
    }

    gradient
}

#[allow(dead_code)]
pub fn placeholder() {
    // Placeholder function to prevent unused module warnings
}