diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 1269e18978..1fe4f18ada 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -32,12 +32,17 @@ repos:
     hooks:
       - id: pyupgrade
         args: [--py37-plus]
-        name: Upgrade code
+        name: Upgrade code excluding monai networks
         exclude: |
-          (?x)^(
-              versioneer.py|
-              monai/_version.py
-          )$
+          (?x)(
+              ^versioneer.py|
+              ^monai/_version.py|
+              ^monai/networks/  # no PEP 604 for torchscript tensorrt
+          )
+      - id: pyupgrade
+        args: [--py37-plus, --keep-runtime-typing]
+        name: Upgrade monai networks
+        files: (?x)(^monai/networks/)
 
   - repo: https://github.com/asottile/yesqa
     rev: v1.4.0
diff --git a/monai/networks/nets/basic_unet.py b/monai/networks/nets/basic_unet.py
index a29d620ced..7fc57edc42 100644
--- a/monai/networks/nets/basic_unet.py
+++ b/monai/networks/nets/basic_unet.py
@@ -12,7 +12,7 @@
 from __future__ import annotations
 
 from collections.abc import Sequence
-from typing import Any
+from typing import Optional
 
 import torch
 import torch.nn as nn
@@ -150,7 +150,7 @@ def __init__(
         self.convs = TwoConv(spatial_dims, cat_chns + up_chns, out_chns, act, norm, bias, dropout)
         self.is_pad = is_pad
 
-    def forward(self, x: torch.Tensor, x_e: Any):
+    def forward(self, x: torch.Tensor, x_e: Optional[torch.Tensor]):
         """
 
         Args:
@@ -159,7 +159,7 @@ def forward(self, x: torch.Tensor, x_e: Any):
         """
         x_0 = self.upsample(x)
 
-        if torch.jit.isinstance(x_e, torch.Tensor):
+        if x_e is not None and torch.jit.isinstance(x_e, torch.Tensor):
             if self.is_pad:
                 # handling spatial shapes due to the 2x maxpooling with odd edge lengths.
                 dimensions = len(x.shape) - 2
diff --git a/monai/networks/nets/dints.py b/monai/networks/nets/dints.py
index 437789ef0c..6e3420d136 100644
--- a/monai/networks/nets/dints.py
+++ b/monai/networks/nets/dints.py
@@ -13,6 +13,7 @@
 
 import datetime
 import warnings
+from typing import Optional
 
 import numpy as np
 import torch
@@ -40,7 +41,7 @@
 class CellInterface(torch.nn.Module):
     """interface for torchscriptable Cell"""
 
-    def forward(self, x: torch.Tensor, weight) -> torch.Tensor:  # type: ignore
+    def forward(self, x: torch.Tensor, weight: Optional[torch.Tensor]) -> torch.Tensor:  # type: ignore
         pass
 
 
@@ -170,7 +171,7 @@ def __init__(self, c: int, ops: dict, arch_code_c=None):
             if arch_c > 0:
                 self.ops.append(ops[op_name](c))
 
-    def forward(self, x: torch.Tensor, weight: torch.Tensor | None = None):
+    def forward(self, x: torch.Tensor, weight: Optional[torch.Tensor] = None):
         """
         Args:
             x: input tensor.
@@ -298,7 +299,7 @@ def __init__(
 
         self.op = MixedOp(c, self.OPS, arch_code_c)
 
-    def forward(self, x: torch.Tensor, weight: torch.Tensor | None) -> torch.Tensor:
+    def forward(self, x: torch.Tensor, weight: Optional[torch.Tensor]) -> torch.Tensor:
         """
         Args:
             x: input tensor
diff --git a/monai/networks/nets/dynunet.py b/monai/networks/nets/dynunet.py
index a761f5993a..59e1e4a758 100644
--- a/monai/networks/nets/dynunet.py
+++ b/monai/networks/nets/dynunet.py
@@ -9,9 +9,9 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-from __future__ import annotations
+# isort: dont-add-import: from __future__ import annotations
 
-from collections.abc import Sequence
+from typing import List, Optional, Sequence, Tuple, Union
 
 import torch
 import torch.nn as nn
@@ -32,7 +32,7 @@ class DynUNetSkipLayer(nn.Module):
     forward passes of the network.
     """
 
-    heads: list[torch.Tensor] | None
+    heads: Optional[List[torch.Tensor]]
 
     def __init__(self, index, downsample, upsample, next_layer, heads=None, super_head=None):
         super().__init__()
@@ -132,13 +132,13 @@ def __init__(
         spatial_dims: int,
         in_channels: int,
         out_channels: int,
-        kernel_size: Sequence[Sequence[int] | int],
-        strides: Sequence[Sequence[int] | int],
-        upsample_kernel_size: Sequence[Sequence[int] | int],
-        filters: Sequence[int] | None = None,
-        dropout: tuple | str | float | None = None,
-        norm_name: tuple | str = ("INSTANCE", {"affine": True}),
-        act_name: tuple | str = ("leakyrelu", {"inplace": True, "negative_slope": 0.01}),
+        kernel_size: Sequence[Union[Sequence[int], int]],
+        strides: Sequence[Union[Sequence[int], int]],
+        upsample_kernel_size: Sequence[Union[Sequence[int], int]],
+        filters: Optional[Sequence[int]] = None,
+        dropout: Optional[Union[Tuple, str, float]] = None,
+        norm_name: Union[Tuple, str] = ("INSTANCE", {"affine": True}),
+        act_name: Union[Tuple, str] = ("leakyrelu", {"inplace": True, "negative_slope": 0.01}),
         deep_supervision: bool = False,
         deep_supr_num: int = 1,
         res_block: bool = False,
@@ -169,7 +169,7 @@ def __init__(
         self.deep_supervision = deep_supervision
         self.deep_supr_num = deep_supr_num
         # initialize the typed list of supervision head outputs so that Torchscript can recognize what's going on
-        self.heads: list[torch.Tensor] = [torch.rand(1)] * self.deep_supr_num
+        self.heads: List[torch.Tensor] = [torch.rand(1)] * self.deep_supr_num
         if self.deep_supervision:
             self.deep_supervision_heads = self.get_deep_supervision_heads()
             self.check_deep_supr_num()
@@ -305,24 +305,30 @@ def get_output_block(self, idx: int):
     def get_downsamples(self):
         inp, out = self.filters[:-2], self.filters[1:-1]
         strides, kernel_size = self.strides[1:-1], self.kernel_size[1:-1]
-        return self.get_module_list(inp, out, kernel_size, strides, self.conv_block)
+        return self.get_module_list(inp, out, kernel_size, strides, self.conv_block)  # type: ignore
 
     def get_upsamples(self):
         inp, out = self.filters[1:][::-1], self.filters[:-1][::-1]
         strides, kernel_size = self.strides[1:][::-1], self.kernel_size[1:][::-1]
         upsample_kernel_size = self.upsample_kernel_size[::-1]
         return self.get_module_list(
-            inp, out, kernel_size, strides, UnetUpBlock, upsample_kernel_size, trans_bias=self.trans_bias
+            inp,  # type: ignore
+            out,  # type: ignore
+            kernel_size,
+            strides,
+            UnetUpBlock,  # type: ignore
+            upsample_kernel_size,
+            trans_bias=self.trans_bias,
         )
 
     def get_module_list(
         self,
-        in_channels: Sequence[int],
-        out_channels: Sequence[int],
-        kernel_size: Sequence[Sequence[int] | int],
-        strides: Sequence[Sequence[int] | int],
-        conv_block: type[nn.Module],
-        upsample_kernel_size: Sequence[Sequence[int] | int] | None = None,
+        in_channels: List[int],
+        out_channels: List[int],
+        kernel_size: Sequence[Union[Sequence[int], int]],
+        strides: Sequence[Union[Sequence[int], int]],
+        conv_block: nn.Module,
+        upsample_kernel_size: Optional[Sequence[Union[Sequence[int], int]]] = None,
         trans_bias: bool = False,
     ):
         layers = []