diff --git a/sgptools/models/core/osgpr.py b/sgptools/models/core/osgpr.py
index 34f7f25..5078fc0 100644
--- a/sgptools/models/core/osgpr.py
+++ b/sgptools/models/core/osgpr.py
@@ -57,7 +57,16 @@ def __init__(self, data, kernel, mu_old, Su_old, Kaa_old, Z_old, Z, mean_functio
         self.Kaa_old = tf.Variable(Kaa_old, shape=tf.TensorShape(None), trainable=False)
         self.Z_old = tf.Variable(Z_old, shape=tf.TensorShape(None), trainable=False)
 
-    def update(self, data):
+    def init_Z(self):
+        M = self.inducing_variable.Z.shape[0]
+        M_old = int(0.7 * M)
+        M_new = M - M_old
+        old_Z = self.Z_old.numpy()[np.random.permutation(M)[0:M_old], :]
+        new_Z = self.X.numpy()[np.random.permutation(self.X.shape[0])[0:M_new], :]
+        Z = np.vstack((old_Z, new_Z))
+        return Z
+
+    def update(self, data, inducing_variable=None):
         """Configure the OSGPR to adapt to a new batch of data. 
         Note: The OSGPR needs to be trained using gradient-based approaches after update.
 
@@ -67,7 +76,11 @@ def update(self, data):
         self.X, self.Y = self.data = gpflow.models.util.data_input_to_tensor(data)
         self.num_data = self.X.shape[0]
 
+        # Update the inducing points        
         self.Z_old.assign(self.inducing_variable.Z.numpy())
+        if inducing_variable is None:
+            inducing_variable = self.init_Z()
+        self.inducing_variable.Z.assign(inducing_variable)
 
         # Get posterior mean and covariance for the old inducing points
         mu_old, Su_old = self.predict_f(self.Z_old, full_cov=True)