Random Seed: 4529
Time Span: 0 to 10, Points: 1000
Learning Rate: 0.1
Weight Decay: 0.0001

Loss Function:
    def loss_fn(state_traj, t_span):
        theta = state_traj[:, :, 0]            # Size: [batch_size, t_points]
        desired_theta = state_traj[:, :, 3]    # Size: [batch_size, t_points]
        weights = weight_fn(t_span)            # Initially Size: [t_points]

        # Reshape or expand weights to match theta dimensions
        weights = weights.view(-1, 1)  # Now Size: [batch_size, t_points]

        # Calculate the weighted loss
        return torch.mean(weights * (theta - desired_theta) ** 2)

Training Cases:
[theta0, omega0, alpha0, desired_theta]
[0.5235987901687622, 0.0, 0.0, 0.0]
[-0.5235987901687622, 0.0, 0.0, 0.0]
[2.094395160675049, 0.0, 0.0, 0.0]
[-2.094395160675049, 0.0, 0.0, 0.0]
[0.0, 1.0471975803375244, 0.0, 0.0]
[0.0, -1.0471975803375244, 0.0, 0.0]
[0.0, 6.2831854820251465, 0.0, 0.0]
[0.0, -6.2831854820251465, 0.0, 0.0]
[0.0, 0.0, 0.0, 6.2831854820251465]
[0.0, 0.0, 0.0, -6.2831854820251465]
[0.0, 0.0, 0.0, 1.5707963705062866]
[0.0, 0.0, 0.0, -1.5707963705062866]
[0.0, 0.0, 0.0, 1.0471975803375244]
[0.0, 0.0, 0.0, -1.0471975803375244]
[0.7853981852531433, 3.1415927410125732, 0.0, 0.0]
[-0.7853981852531433, -3.1415927410125732, 0.0, 0.0]
[1.5707963705062866, -3.1415927410125732, 0.0, 1.0471975803375244]
[-1.5707963705062866, 3.1415927410125732, 0.0, -1.0471975803375244]
[0.7853981852531433, 3.1415927410125732, 0.0, 6.2831854820251465]
[-0.7853981852531433, -3.1415927410125732, 0.0, 6.2831854820251465]
[1.5707963705062866, -3.1415927410125732, 0.0, 12.566370964050293]
[-1.5707963705062866, 3.1415927410125732, 0.0, -12.566370964050293]