ESN Example

import numpy as np

class EchoStateNetwork:
    def __init__(self, input_size, reservoir_size, output_size, spectral_radius=0.9):
        self.input_size = input_size
        self.reservoir_size = reservoir_size
        self.output_size = output_size
        self.spectral_radius = spectral_radius
        self.input_weights = np.random.rand(reservoir_size, input_size) - 0.5
        self.reservoir_weights = np.random.rand(reservoir_size, reservoir_size) - 0.5
        self.output_weights = np.random.rand(output_size, reservoir_size) - 0.5

        # Scale the reservoir weights so that the largest eigenvalue is equal to the spectral radius
        max_eigenvalue = np.max(np.abs(np.linalg.eigvals(self.reservoir_weights)))
        self.reservoir_weights = self.reservoir_weights * (spectral_radius / max_eigenvalue)

    def train(self, inputs, targets, washout=100):
        # Generate the reservoir state matrix
        state = np.zeros((self.reservoir_size, 1))
        for i in range(inputs.shape[0]):
            input_vector = inputs[i, :].reshape(self.input_size, 1)
            state = np.tanh(np.dot(self.input_weights, input_vector) + np.dot(self.reservoir_weights, state))

            if i >= washout:
                # Update the output weights using linear regression
                output_vector = targets[i, :].reshape(self.output_size, 1)
                input_matrix = np.vstack((input_vector, state))
                self.output_weights += np.dot(output_vector, input_matrix.T)

    def predict(self, inputs):
        state = np.zeros((self.reservoir_size, 1))
        outputs = np.zeros((inputs.shape[0], self.output_size))
        for i in range(inputs.shape[0]):
            input_vector = inputs[i, :].reshape(self.input_size, 1)
            state = np.tanh(np.dot(self.input_weights, input_vector) + np.dot(self.reservoir_weights, state))
            output_vector = np.dot(self.output_weights, np.vstack((input_vector, state)))
            outputs[i, :] = output_vector.flatten()
        return outputs

  

# Create an ESN with input size 1, reservoir size 100, and output size 1
esn = EchoStateNetwork(input_size=1, reservoir_size=100, output_size=1)

# Generate some training data (e.g. the Mackey-Glass time series)
train_length = 2000
train_data = np.zeros((train_length, 1))
train_data[0] = 0.96  # Initial condition