diff --git a/firedrake/ml/jax/fem_operator.py b/firedrake/ml/jax/fem_operator.py
index 94f2875202..cee0d23a86 100644
--- a/firedrake/ml/jax/fem_operator.py
+++ b/firedrake/ml/jax/fem_operator.py
@@ -173,7 +173,8 @@ def to_jax(x: Union[Function, Constant], gather: Optional[bool] = False, batched
             x_P = jnp.array(np.ravel(x.dat.global_data), **kwargs)
         else:
             # Use local data
-            x_P = jnp.array(np.ravel(x.dat.data_ro), **kwargs)
+            with x.dat.vec_ro as vec:
+                x_P = jnp.array(np.ravel(vec.buffer_r), **kwargs)
         if batched:
             # Default behaviour: add batch dimension after converting to JAX
             return x_P[None, :]
@@ -222,5 +223,7 @@ def from_jax(x: "jax.Array", V: Optional[WithGeometry] = None) -> Union[Function
             val = val[0]
         return Constant(val)
     else:
-        x_F = Function(V, val=np.asarray(x))
+        x_F = Function(V)
+        with x_F.dat.vec_wo as vec:
+            vec.array_w = np.asarray(x)
         return x_F
diff --git a/firedrake/ml/pytorch/fem_operator.py b/firedrake/ml/pytorch/fem_operator.py
index 868c4cbb34..22b57501c5 100644
--- a/firedrake/ml/pytorch/fem_operator.py
+++ b/firedrake/ml/pytorch/fem_operator.py
@@ -178,7 +178,8 @@ def to_torch(x, gather=False, batched=True, **kwargs):
             x_P = torch.tensor(np.ravel(x.dat.global_data), **kwargs)
         else:
             # Use local data
-            x_P = torch.tensor(np.ravel(x.dat.data_ro), **kwargs)
+            with x.dat.vec_ro as vec:
+                x_P = torch.tensor(np.ravel(vec.buffer_r), **kwargs)
         if batched:
             # Default behaviour: add batch dimension after converting to PyTorch
             return x_P[None, :]
@@ -218,5 +219,7 @@ def from_torch(x, V=None):
             val = val[0]
         return Constant(val)
     else:
-        x_F = Function(V, val=x.detach().numpy())
+        x_F = Function(V)
+        with x_F.dat.vec_wo as vec:
+            vec.array_w = x.detach().numpy()
         return x_F
diff --git a/tests/firedrake/external_operators/test_jax_operator.py b/tests/firedrake/external_operators/test_jax_operator.py
index 55d2e752d4..4ee66ebb42 100644
--- a/tests/firedrake/external_operators/test_jax_operator.py
+++ b/tests/firedrake/external_operators/test_jax_operator.py
@@ -117,6 +117,40 @@ def test_forward(u, nn):
     assert np.allclose(y_F.dat.data_ro, assembled_N.dat.data_ro)
 
 
+@pytest.mark.skipcomplex  # Taping for complex-valued 0-forms not yet done
+@pytest.mark.skipjax  # Skip if JAX is not installed
+def test_forward_mixed(V, nn):
+
+    W = V * V
+    u = Function(W)
+    u1, u2 = u.subfunctions
+    x, y = SpatialCoordinate(V.mesh())
+    u1.interpolate(sin(pi * x) * sin(pi * y))
+    u2.interpolate(sin(2 * pi * x) * sin(2 * pi * y))
+
+    # Set JaxOperator
+    n = W.dim()
+    model = Linear(n, n)
+
+    N = ml_operator(model, function_space=W)(u)
+    # Get model
+    model = N.model
+
+    # Assemble NeuralNet
+    assembled_N = assemble(N)
+    assert isinstance(assembled_N, Function)
+
+    # Convert from Firedrake to JAX
+    x_P = to_jax(u)
+    # Forward pass
+    y_P = model(x_P)
+    # Convert from JAX to Firedrake
+    y_F = from_jax(y_P, u.function_space())
+
+    # Check
+    assert np.allclose(y_F.dat.data_ro, assembled_N.dat.data_ro)
+
+
 @pytest.mark.skipcomplex  # Taping for complex-valued 0-forms not yet done
 @pytest.mark.skipjax  # Skip if JAX is not installed
 def test_jvp(u, nn, rg):
diff --git a/tests/firedrake/external_operators/test_pytorch_operator.py b/tests/firedrake/external_operators/test_pytorch_operator.py
index d9782d1644..7e0ffef7ba 100644
--- a/tests/firedrake/external_operators/test_pytorch_operator.py
+++ b/tests/firedrake/external_operators/test_pytorch_operator.py
@@ -109,6 +109,41 @@ def test_forward(u, nn):
     assert np.allclose(y_F.dat.data_ro, assembled_N.dat.data_ro)
 
 
+@pytest.mark.skipcomplex  # Taping for complex-valued 0-forms not yet done
+@pytest.mark.skiptorch  # Skip if PyTorch is not installed
+def test_forward_mixed(V, nn):
+
+    W = V * V
+    u = Function(W)
+    u1, u2 = u.subfunctions
+    x, y = SpatialCoordinate(V.mesh())
+    u1.interpolate(sin(pi * x) * sin(pi * y))
+    u2.interpolate(sin(2 * pi * x) * sin(2 * pi * y))
+
+    # Set PytorchOperator
+    n = W.dim()
+    model = Linear(n, n)
+
+    N = ml_operator(model, function_space=W)(u)
+    # Get model
+    model = N.model
+
+    # Assemble NeuralNet
+    assembled_N = assemble(N)
+
+    assert isinstance(assembled_N, Function)
+
+    # Convert from Firedrake to PyTorch
+    x_P = to_torch(u)
+    # Forward pass
+    y_P = model(x_P)
+    # Convert from PyTorch to Firedrake
+    y_F = from_torch(y_P, u.function_space())
+
+    # Check
+    assert np.allclose(y_F.dat.data_ro, assembled_N.dat.data_ro)
+
+
 @pytest.mark.skipcomplex  # Taping for complex-valued 0-forms not yet done
 @pytest.mark.skiptorch  # Skip if PyTorch is not installed
 def test_jvp(u, nn, rg):