Koopman参与预测的matlab代码

以下是使用现代Koopman理论进行预测的Matlab代码示例：

% Load data
load('data.mat')

% Define number of snapshots
N = size(data, 2);

% Define the delay embedding dimension
m = 3;

% Define the number of Koopman modes to retain
n = 5;

% Compute delay embedding
X = zeros(m*N, N-m+1);
for i = 1:N-m+1
    X(:,i) = reshape(data(:,i:i+m-1), [], 1);
end

% Compute Koopman operator
K = zeros(m*N, m*N);
for i = 1:N-m
    K(:,i) = X(:,i+1);
end
[U, S, V] = svd(K, 'econ');
U = U(:,1:n);
S = S(1:n,1:n);
V = V(:,1:n);
A = S*V'*U';

% Compute initial condition
x0 = reshape(data(:,1:m), [], 1);

% Predict future states
T = 100; % Number of time steps to predict
x = x0;
x_pred = zeros(size(x,1), T);
for i = 1:T
    x_pred(:,i) = reshape(x, [], m);
    x = A*x;
end

% Plot results
t = 1:T;
figure;
plot(t, x_pred(1,:), 'b', 'LineWidth', 2);
hold on
plot(t, data(1,m+1:m+T), 'r--', 'LineWidth', 2);
xlabel('Time step');
ylabel('State variable');
legend('Predicted', 'Actual');

此代码对一维时间序列数据进行预测，使用了延迟嵌入来构造状态向量，并使用SVD来计算Koopman算子的近似。预测结果与实际数据进行比较，以评估预测的准确性。