diff --git a/pysindy/pysindy.py b/pysindy/pysindy.py
index e3b8de0b..e1d166a3 100644
--- a/pysindy/pysindy.py
+++ b/pysindy/pysindy.py
@@ -18,6 +18,7 @@
 from sklearn.utils.validation import check_is_fitted
 from typing_extensions import Self
 
+from .differentiation import BaseDifferentiation
 from .differentiation import FiniteDifference
 from .feature_library import BaseFeatureLibrary
 from .feature_library import PolynomialLibrary
@@ -54,6 +55,18 @@ class _BaseSINDy(BaseEstimator, ABC):
     def fit(self, x, t, *args, **kwargs) -> Self:
         ...
 
+    def _fit_shape(self):
+        """Assign shape attributes for the system that are used post-fit"""
+        self.n_features_in_ = self.feature_library.n_features_in_
+        self.n_output_features_ = self.feature_library.n_output_features_
+        if self.feature_names is None:
+            feature_names = []
+            for i in range(self.n_features_in_ - self.n_control_features_):
+                feature_names.append("x" + str(i))
+            for i in range(self.n_control_features_):
+                feature_names.append("u" + str(i))
+            self.feature_names = feature_names
+
     def equations(self, precision: int = 3) -> list[str]:
         """
         Get the right hand sides of the SINDy model equations.
@@ -242,12 +255,12 @@ class SINDy(_BaseSINDy):
 
     def __init__(
         self,
-        optimizer=None,
-        feature_library=None,
-        differentiation_method=None,
-        feature_names=None,
-        t_default=1,
-        discrete_time=False,
+        optimizer: Optional[BaseOptimizer] = None,
+        feature_library: Optional[BaseFeatureLibrary] = None,
+        differentiation_method: Optional[BaseDifferentiation] = None,
+        feature_names: Optional[list[str]] = None,
+        t_default: float = 1,
+        discrete_time: bool = False,
     ):
         if optimizer is None:
             optimizer = STLSQ()
@@ -350,17 +363,6 @@ def fit(
         self.model = Pipeline(steps)
         self.model.fit(x, x_dot)
 
-        self.n_features_in_ = self.feature_library.n_features_in_
-        self.n_output_features_ = self.feature_library.n_output_features_
-
-        if self.feature_names is None:
-            feature_names = []
-            for i in range(self.n_features_in_ - self.n_control_features_):
-                feature_names.append("x" + str(i))
-            for i in range(self.n_control_features_):
-                feature_names.append("u" + str(i))
-            self.feature_names = feature_names
-
         return self
 
     def predict(self, x, u=None):