diff --git a/ppsci/constraint/boundary_constraint.py b/ppsci/constraint/boundary_constraint.py
index 6420a96850..afbad13c16 100644
--- a/ppsci/constraint/boundary_constraint.py
+++ b/ppsci/constraint/boundary_constraint.py
@@ -85,10 +85,9 @@ def __init__(
         weight_dict: Optional[Dict[str, Union[float, Callable]]] = None,
         name: str = "BC",
     ):
-        self.output_expr = output_expr
         self.label_dict = label_dict
         self.input_keys = geom.dim_keys
-        self.output_keys = list(label_dict.keys())
+        self.output_keys = tuple(label_dict.keys())
         self.output_expr = {
             k: v for k, v in output_expr.items() if k in self.output_keys
         }
diff --git a/ppsci/constraint/initial_constraint.py b/ppsci/constraint/initial_constraint.py
index d32d8c00c4..351af60c74 100644
--- a/ppsci/constraint/initial_constraint.py
+++ b/ppsci/constraint/initial_constraint.py
@@ -88,10 +88,9 @@ def __init__(
         weight_dict: Optional[Dict[str, Callable]] = None,
         name: str = "IC",
     ):
-        self.output_expr = output_expr
         self.label_dict = label_dict
         self.input_keys = geom.dim_keys
-        self.output_keys = list(label_dict.keys())
+        self.output_keys = tuple(label_dict.keys())
         self.output_expr = {
             k: v for k, v in output_expr.items() if k in self.output_keys
         }
diff --git a/ppsci/constraint/integral_constraint.py b/ppsci/constraint/integral_constraint.py
index 511f823738..63d8314fa3 100644
--- a/ppsci/constraint/integral_constraint.py
+++ b/ppsci/constraint/integral_constraint.py
@@ -85,10 +85,9 @@ def __init__(
         weight_dict: Optional[Dict[str, Callable]] = None,
         name: str = "IgC",
     ):
-        self.output_expr = output_expr
         self.label_dict = label_dict
         self.input_keys = geom.dim_keys
-        self.output_keys = list(label_dict.keys())
+        self.output_keys = tuple(label_dict.keys())
         self.output_expr = {
             k: v for k, v in output_expr.items() if k in self.output_keys
         }
diff --git a/ppsci/constraint/interior_constraint.py b/ppsci/constraint/interior_constraint.py
index d0c77df10a..a333c82db3 100644
--- a/ppsci/constraint/interior_constraint.py
+++ b/ppsci/constraint/interior_constraint.py
@@ -85,10 +85,9 @@ def __init__(
         weight_dict: Optional[Dict[str, Union[Callable, float]]] = None,
         name: str = "EQ",
     ):
-        self.output_expr = output_expr
         self.label_dict = label_dict
         self.input_keys = geom.dim_keys
-        self.output_keys = list(label_dict.keys())
+        self.output_keys = tuple(label_dict.keys())
         self.output_expr = {
             k: v for k, v in output_expr.items() if k in self.output_keys
         }
diff --git a/ppsci/constraint/periodic_constraint.py b/ppsci/constraint/periodic_constraint.py
index 7ad3e2fc1d..6aace571ec 100644
--- a/ppsci/constraint/periodic_constraint.py
+++ b/ppsci/constraint/periodic_constraint.py
@@ -72,9 +72,8 @@ def __init__(
         weight_dict: Optional[Dict[str, Callable]] = None,
         name: str = "PeriodicBC",
     ):
-        self.output_expr = output_expr
         self.input_keys = geom.dim_keys
-        self.output_keys = list(output_expr.keys())
+        self.output_keys = tuple(output_expr.keys())
         self.output_expr = {
             k: v for k, v in output_expr.items() if k in self.output_keys
         }
diff --git a/ppsci/constraint/supervised_constraint.py b/ppsci/constraint/supervised_constraint.py
index a0c34d8bec..84b8816222 100644
--- a/ppsci/constraint/supervised_constraint.py
+++ b/ppsci/constraint/supervised_constraint.py
@@ -60,19 +60,20 @@ def __init__(
         output_expr: Optional[Dict[str, Callable]] = None,
         name: str = "Sup",
     ):
-        self.output_expr = output_expr
-
         # build dataset
         _dataset = dataset.build_dataset(dataloader_cfg["dataset"])
 
         self.input_keys = _dataset.input_keys
         self.output_keys = (
-            list(output_expr.keys()) if output_expr is not None else _dataset.label_keys
+            tuple(output_expr.keys())
+            if output_expr is not None
+            else _dataset.label_keys
         )
 
+        self.output_expr = output_expr
         if self.output_expr is None:
             self.output_expr = {
-                key: lambda out, k=key: out[k] for key in self.output_keys
+                key: (lambda out, k=key: out[k]) for key in self.output_keys
             }
 
         # construct dataloader with dataset and dataloader_cfg
diff --git a/ppsci/validate/geo_validator.py b/ppsci/validate/geo_validator.py
index b9b781f87a..6741baddc7 100644
--- a/ppsci/validate/geo_validator.py
+++ b/ppsci/validate/geo_validator.py
@@ -86,7 +86,7 @@ def __init__(
         self.output_expr = output_expr
         self.label_dict = label_dict
         self.input_keys = geom.dim_keys
-        self.output_keys = list(label_dict.keys())
+        self.output_keys = tuple(label_dict.keys())
 
         nx = dataloader_cfg["total_size"]
         self.num_timestamps = 1
diff --git a/ppsci/validate/sup_validator.py b/ppsci/validate/sup_validator.py
index a45a28f983..56f2b9a50a 100644
--- a/ppsci/validate/sup_validator.py
+++ b/ppsci/validate/sup_validator.py
@@ -75,7 +75,9 @@ def __init__(
 
         self.input_keys = _dataset.input_keys
         self.output_keys = (
-            list(output_expr.keys()) if output_expr is not None else _dataset.label_keys
+            tuple(output_expr.keys())
+            if output_expr is not None
+            else _dataset.label_keys
         )
 
         if self.output_expr is None: