diff --git a/deepmd/dpmodel/loss/ener.py b/deepmd/dpmodel/loss/ener.py
index a237138dee..55c427c678 100644
--- a/deepmd/dpmodel/loss/ener.py
+++ b/deepmd/dpmodel/loss/ener.py
@@ -260,7 +260,7 @@ def call(
             if self.loss_func == "mse":
                 l2_ener_loss = xp.mean(xp.square(energy - energy_hat))
                 if not self.use_huber:
-                    loss += atom_norm_ener * (pref_e * l2_ener_loss)
+                    loss += atom_norm_ener**2 * (pref_e * l2_ener_loss)
                 else:
                     l_huber_loss = custom_huber_loss(
                         atom_norm_ener * energy,
@@ -335,7 +335,7 @@ def call(
                     xp.square(virial_hat_reshape - virial_reshape),
                 )
                 if not self.use_huber:
-                    loss += atom_norm * (pref_v * l2_virial_loss)
+                    loss += atom_norm**2 * (pref_v * l2_virial_loss)
                 else:
                     l_huber_loss = custom_huber_loss(
                         atom_norm * virial_reshape,
diff --git a/deepmd/pd/loss/ener.py b/deepmd/pd/loss/ener.py
index 71ca164b7d..08b16fd4cf 100644
--- a/deepmd/pd/loss/ener.py
+++ b/deepmd/pd/loss/ener.py
@@ -243,7 +243,7 @@ def forward(
                         l2_ener_loss.detach(), find_energy
                     )
                 if not self.use_huber:
-                    loss += atom_norm * (pref_e * l2_ener_loss)
+                    loss += atom_norm**2 * (pref_e * l2_ener_loss)
                 else:
                     l_huber_loss = custom_huber_loss(
                         atom_norm * energy_pred,
@@ -414,7 +414,7 @@ def forward(
                     l2_virial_loss.detach(), find_virial
                 )
             if not self.use_huber:
-                loss += atom_norm * (pref_v * l2_virial_loss)
+                loss += atom_norm**2 * (pref_v * l2_virial_loss)
             else:
                 l_huber_loss = custom_huber_loss(
                     atom_norm * model_pred["virial"].reshape([-1]),
diff --git a/deepmd/pt/loss/ener.py b/deepmd/pt/loss/ener.py
index f793cefc96..1e614024cc 100644
--- a/deepmd/pt/loss/ener.py
+++ b/deepmd/pt/loss/ener.py
@@ -250,7 +250,7 @@ def forward(
                         l2_ener_loss.detach(), find_energy
                     )
                 if not self.use_huber:
-                    loss += atom_norm * (pref_e * l2_ener_loss)
+                    loss += atom_norm**2 * (pref_e * l2_ener_loss)
                 else:
                     l_huber_loss = custom_huber_loss(
                         atom_norm * energy_pred,
@@ -432,7 +432,7 @@ def forward(
                         l2_virial_loss.detach(), find_virial
                     )
                 if not self.use_huber:
-                    loss += atom_norm * (pref_v * l2_virial_loss)
+                    loss += atom_norm**2 * (pref_v * l2_virial_loss)
                 else:
                     l_huber_loss = custom_huber_loss(
                         atom_norm * model_pred["virial"].reshape(-1),
diff --git a/deepmd/tf/loss/ener.py b/deepmd/tf/loss/ener.py
index b477a1005f..d26d4ee075 100644
--- a/deepmd/tf/loss/ener.py
+++ b/deepmd/tf/loss/ener.py
@@ -356,7 +356,7 @@ def build(
         more_loss = {}
         if self.has_e:
             if not self.use_huber:
-                loss += atom_norm_ener * (pref_e * l2_ener_loss)
+                loss += atom_norm_ener**2 * (pref_e * l2_ener_loss)
             else:
                 l_huber_loss = custom_huber_loss(
                     atom_norm_ener * energy,
@@ -380,7 +380,9 @@ def build(
             )
         if self.has_v:
             if not self.use_huber:
-                loss += global_cvt_2_ener_float(atom_norm * (pref_v * l2_virial_loss))
+                loss += global_cvt_2_ener_float(
+                    atom_norm**2 * (pref_v * l2_virial_loss)
+                )
             else:
                 l_huber_loss = custom_huber_loss(
                     atom_norm * tf.reshape(virial, [-1]),