diff --git a/deepxde/model.py b/deepxde/model.py
index feefe7a9f..34a58c027 100644
--- a/deepxde/model.py
+++ b/deepxde/model.py
@@ -353,13 +353,23 @@ def outputs_losses_test(inputs, targets, auxiliary_vars):
                     "backend pytorch."
                 )
 
-        def train_step(inputs, targets, auxiliary_vars, perform_backward=True):
+        def train_step(inputs, targets, auxiliary_vars):
+            def closure():
+                losses = outputs_losses_train(inputs, targets, auxiliary_vars)[1]
+                total_loss = torch.sum(losses)
+                self.opt.zero_grad()
+                total_loss.backward()
+                return total_loss
+
+            self.opt.step(closure)
+            if self.lr_scheduler is not None:
+                self.lr_scheduler.step()
+
+        def train_step_nncg(inputs, targets, auxiliary_vars):
             def closure():
                 losses = outputs_losses_train(inputs, targets, auxiliary_vars)[1]
                 total_loss = torch.sum(losses)
                 self.opt.zero_grad()
-                if perform_backward:
-                    total_loss.backward()
                 return total_loss
 
             self.opt.step(closure)
@@ -370,7 +380,7 @@ def closure():
         self.outputs = outputs
         self.outputs_losses_train = outputs_losses_train
         self.outputs_losses_test = outputs_losses_test
-        self.train_step = train_step
+        self.train_step = train_step if self.opt_name != "NNCG" else train_step_nncg
 
     def _compile_jax(self, lr, loss_fn, decay):
         """jax"""
@@ -652,7 +662,7 @@ def train(
                 if self.opt_name == "L-BFGS":
                     self._train_pytorch_lbfgs()
                 elif self.opt_name == "NNCG":
-                    self._train_pytorch_nncg(iterations, display_every)
+                    self._train_sgd(iterations, display_every)
             elif backend_name == "paddle":
                 self._train_paddle_lbfgs()
         else:
@@ -796,32 +806,6 @@ def _train_pytorch_lbfgs(self):
             if self.stop_training:
                 break
 
-    def _train_pytorch_nncg(self, iterations, display_every):
-        for i in range(iterations):
-            self.callbacks.on_epoch_begin()
-            self.callbacks.on_batch_begin()
-
-            self.train_state.set_data_train(
-                *self.data.train_next_batch(self.batch_size)
-            )
-            self.train_step(
-                self.train_state.X_train,
-                self.train_state.y_train,
-                self.train_state.train_aux_vars,
-                perform_backward=False,
-            )
-
-            self.train_state.epoch += 1
-            self.train_state.step += 1
-            if self.train_state.step % display_every == 0 or i + 1 == iterations:
-                self._test()
-
-            self.callbacks.on_batch_end()
-            self.callbacks.on_epoch_end()
-
-            if self.stop_training:
-                break
-
     def _train_paddle_lbfgs(self):
         prev_n_iter = 0