Base controller path: /home/judson/Neural-Networks-in-GNC/inverted_pendulum/training/controller_base.pth
Time Span: 0 to 10, Points: 1000
Learning Rate: 0.1
Weight Decay: 0.0001

Loss Function Name: two
Loss Function Exponent: 2

Current Loss Function (wrapper) Source Code:
    def current_loss_fn(state_traj):
        theta = state_traj[:, :, 0]         # [batch_size, t_points]
        desired_theta = state_traj[:, :, 3]   # [batch_size, t_points]
        return torch.mean(loss_fn(theta, desired_theta))

Specific Loss Function Source Code:
def square_loss(theta: torch.Tensor, desired_theta: torch.Tensor, min_val: float = 0.01) -> torch.Tensor:
    return normalized_loss(theta, desired_theta, exponent=2, min_val=min_val)

Normalized Loss Function Source Code:
def normalized_loss(theta: torch.Tensor, desired_theta: torch.Tensor, exponent: float, min_val: float = 0.01, delta: float = 1) -> torch.Tensor:
    """
    Computes a normalized loss that maps the error (|theta - desired_theta|) on [0, 2π]
    to the range [min_val, 1]. To avoid an infinite gradient at error=0 for exponents < 1,
    a shift 'delta' is added.

    The loss is given by:
    
      loss = min_val + (1 - min_val) * ( ((error + delta)^exponent - delta^exponent)
                                        / ((2π + delta)^exponent - delta^exponent) )
    
    so that:
      - When error = 0:   loss = min_val
      - When error = 2π:  loss = 1
    """
    error = torch.abs(theta - desired_theta)
    numerator = (error + delta) ** exponent - delta ** exponent
    denominator = (2 * math.pi + delta) ** exponent - delta ** exponent
    return min_val + (1 - min_val) * (numerator / denominator)

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]