diff --git a/check_for_cuda.py b/check_for_cuda.py
new file mode 100644
index 0000000..dbbc901
--- /dev/null
+++ b/check_for_cuda.py
@@ -0,0 +1,8 @@
+import torch
+
+if torch.cuda.is_available():
+    print("CUDA is available")
+    print("Number of CUDA devices:", torch.cuda.device_count())
+    print("Device name:", torch.cuda.get_device_name(0))
+else:
+    print("CUDA is not available")
\ No newline at end of file
diff --git a/clamped_no_time_penalty/1_validation.png b/clamped_no_time_penalty/1_validation.png
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diff --git a/clamped_no_time_penalty/3_validation.png b/clamped_no_time_penalty/3_validation.png
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diff --git a/clamped_no_time_penalty/4_validation.png b/clamped_no_time_penalty/4_validation.png
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diff --git a/clamped_no_time_penalty/5_validation.png b/clamped_no_time_penalty/5_validation.png
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diff --git a/clamped_no_time_penalty/6_validation.png b/clamped_no_time_penalty/6_validation.png
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diff --git a/clamped_no_time_penalty/trainer.py b/clamped_no_time_penalty/trainer.py
new file mode 100644
index 0000000..18247a9
--- /dev/null
+++ b/clamped_no_time_penalty/trainer.py
@@ -0,0 +1,161 @@
+import torch
+import torch.nn as nn
+import torch.optim as optim
+from torchdiffeq import odeint
+import numpy as np
+import matplotlib.pyplot as plt
+
+# ----------------------------------------------------------------
+# 1) 3D Controller: [theta, omega, alpha] -> torque
+# ----------------------------------------------------------------
+class PendulumController3D(nn.Module):
+    def __init__(self):
+        super().__init__()
+        self.net = nn.Sequential(
+            nn.Linear(3, 64),
+            nn.ReLU(),
+            nn.Linear(64, 64),
+            nn.ReLU(),
+            nn.Linear(64, 1)
+        )
+
+    def forward(self, x_3d):
+        """
+        x_4d: shape (batch_size, 4) => [theta, cos(theta), omega, alpha].
+        Returns shape: (batch_size, 1) => torque.
+        """
+        raw_torque = self.net(x_3d)
+        clamped_torque = torch.clamp(raw_torque, -250, 250)  # Clamp torque within [-250, 250]
+        return clamped_torque
+
+
+# ----------------------------------------------------------------
+# 2) Define ODE System Using `odeint`
+# ----------------------------------------------------------------
+m = 10.0
+g = 9.81
+R = 1.0
+
+class PendulumDynamics3D(nn.Module):
+    """
+    Defines the ODE system for [theta, omega, alpha] with torque tracking.
+    """
+
+    def __init__(self, controller):
+        super().__init__()
+        self.controller = controller
+
+    def forward(self, t, state):
+        """
+        state: (batch_size, 4) => [theta, omega, alpha, tau_prev]
+        Returns: (batch_size, 4) => [dtheta/dt, domega/dt, dalpha/dt, dtau/dt]
+        """
+
+        theta = state[:, 0]
+        omega = state[:, 1]
+        alpha = state[:, 2]
+        tau_prev = state[:, 3]
+        
+        # Create tensor input for controller: [theta, omega, alpha]
+        input_3d = torch.stack([theta, omega, alpha], dim=1)  # shape (batch_size, 3)
+
+        # Compute torque using the controller
+        tau = self.controller(input_3d).squeeze(-1)  # shape (batch_size,)
+
+        # Compute desired alpha
+        alpha_desired = (g / R) * torch.sin(theta) + tau / (m * R**2)
+
+        # Define ODE system
+        dtheta = omega
+        domega = alpha
+        dalpha = alpha_desired - alpha  # Relaxation term
+        dtau = tau - tau_prev  # Keep track of torque evolution
+
+        return torch.stack([dtheta, domega, dalpha, dtau], dim=1)  # (batch_size, 4)
+
+# ----------------------------------------------------------------
+# 3) Loss Function
+# ----------------------------------------------------------------
+def loss_fn(state_traj, t_span):
+    """
+    Computes loss based on the trajectory with inverse time weighting (1/t) for theta and omega.
+
+    Args:
+        state_traj: Tensor of shape (time_steps, batch_size, 4).
+        t_span: Tensor of time steps (time_steps,).
+
+    Returns:
+        total_loss, (loss_theta, loss_omega)
+    """
+    theta = state_traj[:, :, 0]  # (time_steps, batch_size)
+
+    loss_theta = 1e3 * torch.mean(theta**2)
+
+    # Combine the losses
+    total_loss = loss_theta
+
+    return total_loss, (loss_theta)
+
+# ----------------------------------------------------------------
+# 4) Training Setup
+# ----------------------------------------------------------------
+device = torch.device("cpu")
+
+# Create the controller and pendulum dynamics model
+controller = PendulumController3D().to(device)
+pendulum_dynamics = PendulumDynamics3D(controller).to(device)
+
+# Define optimizer
+optimizer = optim.Adam(controller.parameters(), lr=1e-1)
+
+# Initial conditions: [theta, omega, alpha, tau_prev]
+initial_conditions = [
+    [0.1,  0.0, 0.0, 0.0],   # Small perturbation
+    [-0.5,  0.0, 0.0, 0.0],  
+    [6.28,  6.28, 0.0, 0.0],  
+    [1.57, 0.5, 0.0, 0.0],  
+    [0.0, -6.28, 0.0, 0.0],  
+    [1.57, -6.28, 0.0, 0.0],
+]
+
+# Convert to torch tensor (batch_size, 4)
+state_0 = torch.tensor(initial_conditions, dtype=torch.float32, device=device)
+
+# Time grid
+t_span = torch.linspace(0, 10, 200, device=device)
+
+num_epochs = 100_000
+print_every = 25
+
+# ----------------------------------------------------------------
+# 5) Training Loop
+# ----------------------------------------------------------------
+for epoch in range(num_epochs):
+    optimizer.zero_grad()
+
+    # Integrate the ODE
+    state_traj = odeint(pendulum_dynamics, state_0, t_span, method='rk4')  
+    # state_traj shape: (time_steps, batch_size, 4)
+
+    # Compute loss
+    total_loss, (l_theta) = loss_fn(state_traj, t_span)
+
+    # Check for NaN values
+    if torch.isnan(total_loss):
+        print(f"NaN detected at epoch {epoch}. Skipping step.")
+        optimizer.zero_grad()
+        continue  # Skip this iteration
+
+    # Backprop
+    total_loss.backward()
+    optimizer.step()
+
+
+    # Print progress
+    if epoch % print_every == 0:
+        print(f"Epoch {epoch:4d}/{num_epochs} | "
+              f"Total: {total_loss.item():.6f} | "
+              f"Theta: {l_theta.item():.6f}")
+
+        torch.save(controller.state_dict(), "controller_cpu_clamped_no_time_penalty.pth")
+        print("Model saved as 'controller_cpu_clamped_no_time_penalty.pth'.")
diff --git a/clamped_no_time_penalty/validator.py b/clamped_no_time_penalty/validator.py
new file mode 100644
index 0000000..9b618d6
--- /dev/null
+++ b/clamped_no_time_penalty/validator.py
@@ -0,0 +1,118 @@
+import torch
+import torch.nn as nn
+import numpy as np
+from scipy.integrate import solve_ivp
+import matplotlib.pyplot as plt
+
+
+controller_file_name = "controller_cpu_clamped_no_time_penalty.pth"
+
+# ----------------------------------------------------------------
+# 1) 3D Controller: [theta, omega, alpha] -> torque
+# ----------------------------------------------------------------
+class PendulumController3D(nn.Module):
+    def __init__(self):
+        super(PendulumController3D, self).__init__()
+        self.net = nn.Sequential(
+            nn.Linear(3, 64),
+            nn.ReLU(),
+            nn.Linear(64, 64),
+            nn.ReLU(),
+            nn.Linear(64, 1)
+        )
+
+    def forward(self, x_3d):
+        return self.net(x_3d)
+
+# Load the trained 3D model
+controller = PendulumController3D()
+controller.load_state_dict(torch.load(controller_file_name))
+controller.eval()
+print(f"{controller_file_name} loaded.")
+
+# ----------------------------------------------------------------
+# 2) ODE: State = [theta, omega, alpha].
+# ----------------------------------------------------------------
+m = 10.0
+g = 9.81
+R = 1.0
+
+def pendulum_ode_3d(t, state):
+    theta, omega, alpha = state
+
+    # Evaluate NN -> torque
+    inp = torch.tensor([[theta, omega, alpha]], dtype=torch.float32)
+    with torch.no_grad():
+        torque = controller(inp).item()
+        # Clamp torque to ±250 for consistency with training
+        torque = np.clip(torque, -250, 250)
+
+    alpha_des = (g/R)*np.sin(theta) + torque/(m*(R**2))
+
+    dtheta = omega
+    domega = alpha
+    dalpha = alpha_des - alpha
+    return [dtheta, domega, dalpha]
+
+# ----------------------------------------------------------------
+# 3) Validate for multiple initial conditions
+# ----------------------------------------------------------------
+initial_conditions_3d = [
+    (0.1,  0.0, 0.0),
+    (0.5,  0.0, 0.0),
+    (1.0,  0.0, 0.0),
+    (1.57, 0.5, 0.0),
+    (0.0, -6.28, 0.0),
+    (6.28, 6.28, 0.0),
+]
+
+t_span = (0, 20)
+t_eval = np.linspace(0, 20, 2000)
+
+for idx, (theta0, omega0, alpha0) in enumerate(initial_conditions_3d):
+    sol = solve_ivp(
+        pendulum_ode_3d,
+        t_span,
+        [theta0, omega0, alpha0],
+        t_eval=t_eval,
+        method='RK45'
+    )
+
+    t         = sol.t
+    theta     = sol.y[0]
+    omega     = sol.y[1]
+    alpha_arr = sol.y[2]
+
+    # Recompute torque over time
+    torques = []
+    alpha_des_vals = []
+    for (th, om, al) in zip(theta, omega, alpha_arr):
+        with torch.no_grad():
+            torque_val = controller(torch.tensor([[th, om, al]], dtype=torch.float32)).item()
+            torque_val = np.clip(torque_val, -250, 250)
+        torques.append(torque_val)
+        alpha_des_vals.append( (g/R)*np.sin(th) + torque_val/(m*(R**2)) )
+    torques = np.array(torques)
+
+    # Plot
+    fig, ax1 = plt.subplots(figsize=(10,6))
+    ax1.plot(t, theta,     label="theta",      color="blue")
+    ax1.plot(t, omega,     label="omega",      color="green")
+    ax1.plot(t, alpha_arr, label="alpha",      color="red")
+    # optional: ax1.plot(t, alpha_des_vals, label="alpha_des", color="red", linestyle="--")
+
+    ax1.set_xlabel("time [s]")
+    ax1.set_ylabel("theta, omega, alpha")
+    ax1.grid(True)
+    ax1.legend(loc="upper left")
+
+    ax2 = ax1.twinx()
+    ax2.plot(t, torques, label="torque", color="purple", linestyle="--")
+    ax2.set_ylabel("Torque [Nm]")
+    ax2.legend(loc="upper right")
+
+    plt.title(f"IC (theta={theta0}, omega={omega0}, alpha={alpha0})")
+    plt.tight_layout()
+    plt.savefig(f"{idx+1}_validation.png")
+    plt.close()
+    print(f"Saved {idx+1}_validation.png")
diff --git a/trainer.py b/trainer.py
index dc40681..e1089b7 100644
--- a/trainer.py
+++ b/trainer.py
@@ -3,173 +3,134 @@ import torch.nn as nn
 import torch.optim as optim
 from torchdiffeq import odeint
 import numpy as np
-import matplotlib.pyplot as plt
+import random
 
-# ----------------------------------------------------------------
-# 1) 3D Controller: [theta, omega, alpha] -> torque
-# ----------------------------------------------------------------
-class PendulumController3D(nn.Module):
+# Generate a random seed
+random_seed = random.randint(0, 10000)
+
+# Set the seeds for reproducibility
+torch.manual_seed(random_seed)
+np.random.seed(random_seed)
+
+# Print the chosen random seed
+print(f"Random seed for torch and numpy: {random_seed}")
+
+class PendulumController(nn.Module):
     def __init__(self):
         super().__init__()
         self.net = nn.Sequential(
-            nn.Linear(3, 64),
+            nn.Linear(4, 64),
             nn.ReLU(),
             nn.Linear(64, 64),
             nn.ReLU(),
             nn.Linear(64, 1)
         )
 
-    def forward(self, x_3d):
-        """
-        x_4d: shape (batch_size, 4) => [theta, cos(theta), omega, alpha].
-        Returns shape: (batch_size, 1) => torque.
-        """
-        raw_torque = self.net(x_3d)
-        clamped_torque = torch.clamp(raw_torque, -250, 250)  # Clamp torque within [-250, 250]
-        return clamped_torque
+    def forward(self, x):
+        raw_torque = self.net(x)
+        return torch.clamp(raw_torque, -250, 250)  # Clamp torque
 
-
-# ----------------------------------------------------------------
-# 2) Define ODE System Using `odeint`
-# ----------------------------------------------------------------
+# Constants
 m = 10.0
 g = 9.81
 R = 1.0
 
-class PendulumDynamics3D(nn.Module):
-    """
-    Defines the ODE system for [theta, omega, alpha] with torque tracking.
-    """
-
+class PendulumDynamics(nn.Module):
     def __init__(self, controller):
         super().__init__()
         self.controller = controller
 
     def forward(self, t, state):
-        """
-        state: (batch_size, 4) => [theta, omega, alpha, tau_prev]
-        Returns: (batch_size, 4) => [dtheta/dt, domega/dt, dalpha/dt, dtau/dt]
-        """
-
         theta = state[:, 0]
         omega = state[:, 1]
         alpha = state[:, 2]
-        tau_prev = state[:, 3]
+        desired_theta = state[:, 3]  # Extract desired theta
 
+        # Pass desired_theta as input to the controller
+        input = torch.stack([theta, omega, alpha, desired_theta], dim=1)
+        tau = self.controller(input).squeeze(-1)
 
-        # Create tensor input for controller: [theta, omega, alpha]
-        input_3d = torch.stack([theta, omega, alpha], dim=1)  # shape (batch_size, 3)
-
-        # Compute torque using the controller
-        tau = self.controller(input_3d).squeeze(-1)  # shape (batch_size,)
-
-        # Compute desired alpha
         alpha_desired = (g / R) * torch.sin(theta) + tau / (m * R**2)
 
-        # Define ODE system
         dtheta = omega
         domega = alpha
-        dalpha = alpha_desired - alpha  # Relaxation term
-        dtau = tau - tau_prev  # Keep track of torque evolution
+        dalpha = alpha_desired - alpha
 
-        return torch.stack([dtheta, domega, dalpha, dtau], dim=1)  # (batch_size, 4)
+        return torch.stack([dtheta, domega, dalpha, torch.zeros_like(desired_theta)], dim=1)
 
-# ----------------------------------------------------------------
-# 3) Loss Function
-# ----------------------------------------------------------------
-def loss_fn(state_traj, t_span):
-    """
-    Computes loss based on the trajectory with inverse time weighting (1/t) for theta and omega.
+def loss_fn(state_traj):
+    theta = state_traj[:, :, 0]  # Extract theta
+    desired_theta = state_traj[:, :, 3]  # Extract desired theta
 
-    Args:
-        state_traj: Tensor of shape (time_steps, batch_size, 4).
-        t_span: Tensor of time steps (time_steps,).
+    loss_theta = 1e3 * torch.mean((theta - desired_theta)**2)
+    return loss_theta
 
-    Returns:
-        total_loss, (loss_theta, loss_omega)
-    """
-    theta = state_traj[:, :, 0]  # (time_steps, batch_size)
-    omega = state_traj[:, :, 1]  # (time_steps, batch_size)
-    torque = state_traj[:, :, 3]
+# Device setup
+device = torch.device("cpu")
 
-    # Inverse time weights w(t) = 1 / t
-    # Add a small epsilon to avoid division by zero
-    epsilon = 1e-6
-    inverse_time_weights = 1.0 / (t_span + epsilon).unsqueeze(1)  # Shape: (time_steps, 1)
-    linear_time_weights = t_span.unsqueeze(1)
+# Initial conditions (theta0, omega0, alpha0, desired_theta)
+state_0 = torch.tensor([
+    # Theta perturbations
+    [1/6 * torch.pi,    0.0, 0.0, 0.0],
+    [-1/6 * torch.pi,   0.0, 0.0, 0.0],
+    [2/3 * torch.pi,    0.0, 0.0, 0.0],
+    [-2/3 * torch.pi,   0.0, 0.0, 0.0],
 
-    # Apply inverse time weighting for theta and omega
-    loss_theta = 1e-1 * torch.mean(inverse_time_weights * theta**2)  # Weighted theta loss
-    loss_omega = 1e-2 * torch.mean(inverse_time_weights * omega**2)  # Weighted omega loss
-    loss_torque = 1e-2 * torch.mean(linear_time_weights * torque**2)
+    # Omega perturbations
+    [0.0, 1/3 * torch.pi,     0.0, 0.0],
+    [0.0, -1/3 * torch.pi,    0.0, 0.0],
+    [0.0, 2 * torch.pi,     0.0, 0.0],
+    [0.0, -2 * torch.pi,    0.0, 0.0],
 
-    # Combine the losses
-    total_loss = loss_theta #+ loss_torque
+    # Return to non-zero theta
+    [0.0, 0.0, 0.0,     2*torch.pi],
+    [0.0, 0.0, 0.0,     -2*torch.pi],
+    [0.0, 0.0, 0.0,     1/2 * torch.pi],
+    [0.0, 0.0, 0.0,     -1/2 *torch.pi],
+    [0.0, 0.0, 0.0,     1/3 * torch.pi],
+    [0.0, 0.0, 0.0,     -1/3 *torch.pi],
 
-    return total_loss, (loss_theta, loss_omega, loss_torque)
+    # Mix cases
+    [1/4 * torch.pi,    1 * torch.pi,   0.0,    0.0],
+    [-1/4 * torch.pi,   -1 * torch.pi,  0.0,    0.0],
+    [1/2 * torch.pi,    -1 * torch.pi,  0.0,    1/3 * torch.pi],
+    [-1/2 * torch.pi,   1 * torch.pi,   0.0,    -1/3 *torch.pi],
+    [1/4 * torch.pi,    1 * torch.pi,   0.0,    2 * torch.pi],
+    [-1/4 * torch.pi,   -1 * torch.pi,  0.0,    2 * torch.pi],
+    [1/2 * torch.pi,    -1 * torch.pi,  0.0,    4 * torch.pi],
+    [-1/2 * torch.pi,   1 * torch.pi,   0.0,    -4 *torch.pi],
 
-# ----------------------------------------------------------------
-# 4) Training Setup
-# ----------------------------------------------------------------
-device = torch.device("cpu" if torch.cuda.is_available() else "cpu")
-
-# Create the controller and pendulum dynamics model
-controller = PendulumController3D().to(device)
-pendulum_dynamics = PendulumDynamics3D(controller).to(device)
-
-# Define optimizer
-optimizer = optim.Adam(controller.parameters(), lr=1e-1)
-
-# Initial conditions: [theta, omega, alpha, tau_prev]
-initial_conditions = [
-    [0.1,  0.0, 0.0, 0.0],   # Small perturbation
-    [-0.5,  0.0, 0.0, 0.0],  
-    [6.28,  6.28, 0.0, 0.0],  
-    [1.57, 0.5, 0.0, 0.0],  
-    [0.0, -6.28, 0.0, 0.0],  
-    [1.57, -6.28, 0.0, 0.0],
-]
-
-# Convert to torch tensor (batch_size, 4)
-state_0 = torch.tensor(initial_conditions, dtype=torch.float32, device=device)
+], dtype=torch.float32, device=device)
 
 # Time grid
 t_span = torch.linspace(0, 10, 1000, device=device)
 
-num_epochs = 100_000
+# Initialize controller and dynamics
+controller = PendulumController().to(device)
+pendulum_dynamics = PendulumDynamics(controller).to(device)
+
+# Optimizer
+optimizer = optim.Adam(controller.parameters(), lr=1e-1, weight_decay=0)
+
+# Training parameters
+num_epochs = 10_000
 print_every = 25
 
-# ----------------------------------------------------------------
-# 5) Training Loop
-# ----------------------------------------------------------------
 for epoch in range(num_epochs):
     optimizer.zero_grad()
+    
+    state_traj = odeint(pendulum_dynamics, state_0, t_span, method='rk4')
+    loss = loss_fn(state_traj)
 
-    # Integrate the ODE
-    state_traj = odeint(pendulum_dynamics, state_0, t_span, method='rk4')  
-    # state_traj shape: (time_steps, batch_size, 4)
-
-    # Compute loss
-    total_loss, (l_theta, l_omega, l_torque) = loss_fn(state_traj, t_span)
-
-    # Check for NaN values
-    if torch.isnan(total_loss):
+    if torch.isnan(loss):
         print(f"NaN detected at epoch {epoch}. Skipping step.")
         optimizer.zero_grad()
-        continue  # Skip this iteration
+        continue
 
-    # Backprop
-    total_loss.backward()
+    loss.backward()
     optimizer.step()
 
-
-    # Print progress
     if epoch % print_every == 0:
-        print(f"Epoch {epoch:4d}/{num_epochs} | "
-              f"Total: {total_loss.item():.6f} | "
-              f"Theta: {l_theta.item():.6f} | "
-              f"Omega: {l_omega.item():.6f} | "
-              f"Torque: {l_torque.item():.6f}")
-
-        torch.save(controller.state_dict(), "controller_cpu_clamped_inverse_time_punish.pth")
-        print("Model saved as 'controller_cpu_clamped_inverse_time_punish.pth'.")
+        print(f"Epoch {epoch}/{num_epochs} | Loss: {loss.item():.6f}")
+        torch.save(controller.state_dict(), "controller_with_desired_theta.pth")
+        print("Model saved as 'controller_with_desired_theta.pth'.")
diff --git a/validator.py b/validator.py
index 6958f31..d67dc7b 100644
--- a/validator.py
+++ b/validator.py
@@ -1,103 +1,174 @@
 import torch
 import torch.nn as nn
 import numpy as np
-from scipy.integrate import solve_ivp
 import matplotlib.pyplot as plt
+import pandas as pd
 
-# ----------------------------------------------------------------
-# 1) 3D Controller: [theta, omega, alpha] -> torque
-# ----------------------------------------------------------------
-class PendulumController3D(nn.Module):
+# Load Controller
+controller_file_name = "controller_with_desired_theta.pth"
+
+class PendulumController(nn.Module):
     def __init__(self):
-        super(PendulumController3D, self).__init__()
+        super().__init__()
         self.net = nn.Sequential(
-            nn.Linear(3, 64),
+            nn.Linear(4, 64),
             nn.ReLU(),
             nn.Linear(64, 64),
             nn.ReLU(),
             nn.Linear(64, 1)
         )
 
-    def forward(self, x_3d):
-        return self.net(x_3d)
+    def forward(self, x):
+        return self.net(x)  
 
-# Load the trained 3D model
-controller = PendulumController3D()
-controller.load_state_dict(torch.load("controller_cpu_clamped_inverse_time_punish.pth"))
-# controller.load_state_dict(torch.load("controller_cpu_clamped.pth"))
+controller = PendulumController()
+controller.load_state_dict(torch.load(controller_file_name))
 controller.eval()
-print("3D Controller loaded.")
+print(f"{controller_file_name} loaded.")
 
-# ----------------------------------------------------------------
-# 2) ODE: State = [theta, omega, alpha].
-# ----------------------------------------------------------------
+# Constants
 m = 10.0
 g = 9.81
 R = 1.0
 
-def pendulum_ode_3d(t, state):
+# Time step settings
+dt = 0.01  # Fixed time step
+T = 20.0   # Total simulation time
+num_steps = int(T / dt)
+t_eval = np.linspace(0, T, num_steps)
+
+# Define ODE System (RK4) - Also Returns Torque
+def pendulum_ode_step(state, dt, desired_theta):
     theta, omega, alpha = state
 
-    # Evaluate NN -> torque
-    inp = torch.tensor([[theta, omega, alpha]], dtype=torch.float32)
-    with torch.no_grad():
-        torque = controller(inp).item()
-        # Clamp torque to ±250 for consistency with training
-        torque = np.clip(torque, -250, 250)
+    def compute_torque(th, om, al):
+        # Evaluate NN -> torque
+        inp = torch.tensor([[th, om, al, desired_theta]], dtype=torch.float32)
+        with torch.no_grad():
+            torque = controller(inp)
+            torque = torch.clamp(torque, -250, 250)
+        return float(torque)
 
-    alpha_des = (g/R)*np.sin(theta) + torque/(m*(R**2))
+    def derivatives(state, torque):
+        th, om, al = state
+        a = (g / R) * np.sin(th) + torque / (m * R**2)
+        return np.array([om, a, 0])  # dtheta, domega, dalpha
 
-    dtheta = omega
-    domega = alpha
-    dalpha = alpha_des - alpha
-    return [dtheta, domega, dalpha]
+    # Compute k1
+    torque1 = compute_torque(theta, omega, alpha)
+    k1 = dt * derivatives(state, torque1)
 
-# ----------------------------------------------------------------
-# 3) Validate for multiple initial conditions
-# ----------------------------------------------------------------
-initial_conditions_3d = [
-    (0.1,  0.0, 0.0),
-    (0.5,  0.0, 0.0),
-    (1.0,  0.0, 0.0),
-    (1.57, 0.5, 0.0),
-    (0.0, -6.28, 0.0),
-    (6.28, 6.28, 0.0),
+    # Compute k2
+    state_k2 = state + 0.5 * k1
+    torque2 = compute_torque(state_k2[0], state_k2[1], state_k2[2])
+    k2 = dt * derivatives(state_k2, torque2)
+
+    # Compute k3
+    state_k3 = state + 0.5 * k2
+    torque3 = compute_torque(state_k3[0], state_k3[1], state_k3[2])
+    k3 = dt * derivatives(state_k3, torque3)
+
+    # Compute k4
+    state_k4 = state + k3
+    torque4 = compute_torque(state_k4[0], state_k4[1], state_k4[2])
+    k4 = dt * derivatives(state_k4, torque4)
+
+    # Update state using RK4 formula
+    new_state = state +  (k1 + 2*k2 + 2*k3 + k4) / 6.0
+
+    # Compute weighted final torque
+    final_torque = (torque1 + 2*torque2 + 2*torque3 + torque4) / 6.0
+
+    return new_state, final_torque
+
+
+
+
+# Run Simulations for Different Initial Conditions
+# [theta0, omega0, alpha0, desired_theta]
+in_sample_cases = [
+    # Theta perturbations
+    (1/6 * np.pi,    0.0, 0.0, 0.0),
+    (-1/6 * np.pi,   0.0, 0.0, 0.0),
+    (2/3 * np.pi,    0.0, 0.0, 0.0),
+    (-2/3 * np.pi,   0.0, 0.0, 0.0),
+
+    # Omega perturbations
+    (0.0, 1/3 * np.pi,      0.0, 0.0),
+    (0.0, -1/3 * np.pi,     0.0, 0.0),
+    (0.0, 2 * np.pi,        0.0, 0.0),
+    (0.0, -2 * np.pi,       0.0, 0.0),
+
+    # Return to non-zero theta
+    (0.0, 0.0, 0.0,     2*np.pi),
+    (0.0, 0.0, 0.0,     -2*np.pi),
+    (0.0, 0.0, 0.0,     1/2 * np.pi),
+    (0.0, 0.0, 0.0,     -1/2 *np.pi),
+    (0.0, 0.0, 0.0,     1/3 * np.pi),
+    (0.0, 0.0, 0.0,     -1/3 *np.pi),
+
+    # Mix cases
+    (1/4 * np.pi,    1 * np.pi,     0.0,      0.0),
+    (-1/4 * np.pi,   -1 * np.pi,    0.0,     0.0),
+    (1/2 * np.pi,    -1 * np.pi,    0.0,     1/3 * np.pi),
+    (-1/2 * np.pi,   1 * np.pi,     0.0,      -1/3 *np.pi),
+    (1/4 * np.pi,    1 * np.pi,     0.0,      2 * np.pi),
+    (-1/4 * np.pi,   -1 * np.pi,    0.0,     2 * np.pi),
+    (1/2 * np.pi,    -1 * np.pi,    0.0,     4 * np.pi),
+    (-1/2 * np.pi,   1 * np.pi,     0.0,      -4 *np.pi),
 ]
 
-t_span = (0, 20)
-t_eval = np.linspace(0, 20, 2000)
+# Validation in-sample cases
+print("Performing in-sample validation")
 
-for idx, (theta0, omega0, alpha0) in enumerate(initial_conditions_3d):
-    sol = solve_ivp(
-        pendulum_ode_3d,
-        t_span,
-        [theta0, omega0, alpha0],
-        t_eval=t_eval,
-        method='RK45'
-    )
+losses = []
+final_thetas = []
 
-    t         = sol.t
-    theta     = sol.y[0]
-    omega     = sol.y[1]
-    alpha_arr = sol.y[2]
+for idx, (theta0, omega0, alpha0, desired_theta) in enumerate(in_sample_cases):
+    state = np.array([theta0, omega0, alpha0])
 
-    # Recompute torque over time
-    torques = []
-    alpha_des_vals = []
-    for (th, om, al) in zip(theta, omega, alpha_arr):
-        with torch.no_grad():
-            torque_val = controller(torch.tensor([[th, om, al]], dtype=torch.float32)).item()
-            torque_val = np.clip(torque_val, -250, 250)
-        torques.append(torque_val)
-        alpha_des_vals.append( (g/R)*np.sin(th) + torque_val/(m*(R**2)) )
-    torques = np.array(torques)
+    theta_vals, omega_vals, alpha_vals, torque_vals = [], [], [], []
 
-    # Plot
-    fig, ax1 = plt.subplots(figsize=(10,6))
-    ax1.plot(t, theta,     label="theta",      color="blue")
-    ax1.plot(t, omega,     label="omega",      color="green")
-    ax1.plot(t, alpha_arr, label="alpha",      color="red")
-    # optional: ax1.plot(t, alpha_des_vals, label="alpha_des", color="red", linestyle="--")
+    for _ in range(num_steps):
+        # Save values
+        theta_vals.append(state[0])
+        omega_vals.append(state[1])
+        alpha_vals.append(state[2])
+
+        # Compute ODE step with real state
+        state, torque = pendulum_ode_step(state, dt, desired_theta)
+
+        # Store torque
+        torque_vals.append(torque)
+
+    # Convert lists to arrays
+    theta_vals = np.array(theta_vals)
+    omega_vals = np.array(omega_vals)
+    alpha_vals = np.array(alpha_vals)
+    torque_vals = np.array(torque_vals)
+
+    # Get the final theta of the system at t=t_final
+    final_theta = theta_vals[-1]
+    final_thetas.append(final_theta)
+
+    # Calculate this specific condition's loss
+    loss = 1e3 * np.mean((theta_vals - desired_theta)**2)
+    losses.append(loss)
+
+    # Plot Results
+    fig, ax1 = plt.subplots(figsize=(10, 6))
+    ax1.plot(t_eval, theta_vals, label="theta", color="blue")
+    ax1.plot(t_eval, omega_vals, label="omega", color="green")
+    ax1.plot(t_eval, alpha_vals, label="alpha", color="red")
+    ax1.axhline(desired_theta, label="Desired Theta", color="black")
+
+    # Draw horizontal lines at theta = 2n*pi (as many as fit within range)
+    y_min = min(np.min(theta_vals), np.min(omega_vals), np.min(alpha_vals))
+    y_max = max(np.max(theta_vals), np.max(omega_vals), np.max(alpha_vals))
+
+    n_min = int(np.ceil(y_min / (2 * np.pi)))
+    n_max = int(np.floor(y_max / (2 * np.pi)))
+    theta_lines = [2 * n * np.pi for n in range(n_min, n_max + 1)]
 
     ax1.set_xlabel("time [s]")
     ax1.set_ylabel("theta, omega, alpha")
@@ -105,12 +176,133 @@ for idx, (theta0, omega0, alpha0) in enumerate(initial_conditions_3d):
     ax1.legend(loc="upper left")
 
     ax2 = ax1.twinx()
-    ax2.plot(t, torques, label="torque", color="purple", linestyle="--")
+    ax2.plot(t_eval, torque_vals, label="torque", color="purple", linestyle="--")
     ax2.set_ylabel("Torque [Nm]")
     ax2.legend(loc="upper right")
 
     plt.title(f"IC (theta={theta0}, omega={omega0}, alpha={alpha0})")
     plt.tight_layout()
-    plt.savefig(f"{idx+1}_validation.png")
+
+    filename = f"{idx+1}_theta0_{theta0:.3f}_omega0_{omega0:.3f}_alpha0_{alpha0:.3f}_desiredtheta_{desired_theta:.3f}_finaltheta_{final_theta:.3f}.png"
+    plt.savefig(f"validation/in-sample/{filename}")
     plt.close()
-    print(f"Saved {idx+1}_validation.png")
+
+    print(f"Saved in-sample validation case {idx+1}")
+
+# Create a DataFrame for tabular representation
+df_losses = pd.DataFrame(in_sample_cases, columns=["theta0", "omega0", "alpha0", "desired_theta"])
+df_losses["final_theta"] = final_theta
+df_losses["loss"] = losses
+
+# Add run # column
+df_losses.insert(0, "Run #", range(1, len(in_sample_cases) + 1))
+
+# Print the table
+print(df_losses.to_string(index=False))
+
+
+# Out-of-sample validation
+print("\nPerforming out-of-sample validation")
+
+# Out of sample cases previously generated by numpy
+out_sample_cases = [
+    (-2.198958, -4.428501, 0.450833, 0.000000),
+    (1.714196, -0.769896, 0.202738, 0.000000),
+    (0.241195, -5.493715, 0.438996, 0.000000),
+    (0.030605, 4.901513, -0.479243, 0.000000),
+    (1.930445, -1.301926, -0.454050, 0.000000),
+    (-0.676063, 4.246865, 0.036303, 0.000000),
+    (0.734920, -5.925202, 0.047097, 0.000000),
+    (-3.074471, -3.535424, 0.315438, 0.000000),
+    (-0.094486, 6.111091, 0.150525, 0.000000),
+    (-1.647671, 5.720526, 0.334181, 0.000000),
+    (-2.611260, 5.087704, 0.045460, -3.610785),
+    (1.654137, 0.982081, -0.192725, 1.003872),
+    (-2.394899, 3.550547, -0.430938, 3.261897),
+    (0.474917, 0.555166, -0.285173, 1.866752),
+    (-0.640369, -4.678490, -0.340663, 3.150098),
+    (1.747517, -3.248204, -0.001520, 1.221787),
+    (2.505283, -2.875006, -0.065617, -3.690269),
+    (1.337244, 2.221707, 0.044979, -2.459730),
+    (1.531012, 2.230981, -0.291206, -1.924535),
+    (-1.065792, 4.320740, 0.075405, -1.550644),
+]
+
+
+
+for idx, (theta0, omega0, alpha0, desired_theta) in enumerate(out_sample_cases):
+    state = np.array([theta0, omega0, alpha0])
+
+    theta_vals, omega_vals, alpha_vals, torque_vals = [], [], [], []
+
+    for _ in range(num_steps):
+        # Save values
+        theta_vals.append(state[0])
+        omega_vals.append(state[1])
+        alpha_vals.append(state[2])
+
+        # Compute ODE step with real state
+        state, torque = pendulum_ode_step(state, dt, desired_theta)
+
+        # Store torque
+        torque_vals.append(torque)
+
+    # Convert lists to arrays
+    theta_vals = np.array(theta_vals)
+    omega_vals = np.array(omega_vals)
+    alpha_vals = np.array(alpha_vals)
+    torque_vals = np.array(torque_vals)
+
+    # Get the final theta of the system at t=t_final
+    final_theta = theta_vals[-1]
+    final_thetas.append(final_theta)
+
+    # Calculate this specific condition's loss
+    loss = 1e3 * np.mean((theta_vals - desired_theta)**2)
+    losses.append(loss)
+
+    # Plot Results
+    fig, ax1 = plt.subplots(figsize=(10, 6))
+    ax1.plot(t_eval, theta_vals, label="theta", color="blue")
+    ax1.plot(t_eval, omega_vals, label="omega", color="green")
+    ax1.plot(t_eval, alpha_vals, label="alpha", color="red")
+    ax1.axhline(desired_theta, label="Desired Theta", color="black")
+
+    # Draw horizontal lines at theta = 2n*pi (as many as fit within range)
+    y_min = min(np.min(theta_vals), np.min(omega_vals), np.min(alpha_vals))
+    y_max = max(np.max(theta_vals), np.max(omega_vals), np.max(alpha_vals))
+
+    n_min = int(np.ceil(y_min / (2 * np.pi)))
+    n_max = int(np.floor(y_max / (2 * np.pi)))
+    theta_lines = [2 * n * np.pi for n in range(n_min, n_max + 1)]
+
+    ax1.set_xlabel("time [s]")
+    ax1.set_ylabel("theta, omega, alpha")
+    ax1.grid(True)
+    ax1.legend(loc="upper left")
+
+    ax2 = ax1.twinx()
+    ax2.plot(t_eval, torque_vals, label="torque", color="purple", linestyle="--")
+    ax2.set_ylabel("Torque [Nm]")
+    ax2.legend(loc="upper right")
+
+    plt.title(f"IC (theta={theta0}, omega={omega0}, alpha={alpha0})")
+    plt.tight_layout()
+
+    filename = f"{idx+1}_theta0_{theta0:.3f}_omega0_{omega0:.3f}_alpha0_{alpha0:.3f}_desiredtheta_{desired_theta:.3f}_finaltheta_{final_theta:.3f}.png"
+    plt.savefig(f"validation/out-of-sample/{filename}")
+    plt.close()
+
+    print(f"Saved out-of-sample validation case {idx+1}")
+
+
+# Create a DataFrame for tabular representation
+df_losses = pd.DataFrame(out_sample_cases, columns=["theta0", "omega0", "alpha0", "desired_theta"])
+df_losses["final_theta"] = final_theta
+df_losses["loss"] = losses
+
+# Add run # column
+df_losses.insert(0, "Run #", range(1, len(out_sample_cases) + 1))
+
+# Print the table
+print(df_losses.to_string(index=False))
\ No newline at end of file