diff --git a/autoemulate/emulators/neural_net_torch.py b/autoemulate/emulators/neural_net_torch.py
index 3fa8ec30..a0691505 100644
--- a/autoemulate/emulators/neural_net_torch.py
+++ b/autoemulate/emulators/neural_net_torch.py
@@ -56,7 +56,7 @@ def __init__(
         max_epochs: int = 1,
         module__input_size: int = 2,
         module__output_size: int = 1,
-        optimizer__weight_decay: float = 0.0001,
+        optimizer__weight_decay: float = 0.0,
         iterator_train__shuffle: bool = True,
         callbacks: List[Callback] = [InputShapeSetter()],
         train_split: bool = False,  # to run cross_validate without splitting the data
diff --git a/autoemulate/emulators/neural_networks/mlp.py b/autoemulate/emulators/neural_networks/mlp.py
index dd7ba242..f7d94e1f 100644
--- a/autoemulate/emulators/neural_networks/mlp.py
+++ b/autoemulate/emulators/neural_networks/mlp.py
@@ -18,7 +18,8 @@ def __init__(
         input_size: int = None,
         output_size: int = None,
         random_state: int = None,
-        hidden_sizes: Tuple[int] = (100,),
+        hidden_layers: int = 1,
+        hidden_size: int = 100,
         hidden_activation: Tuple[callable] = nn.ReLU,
     ):
         super(MLPModule, self).__init__(
@@ -28,7 +29,8 @@ def __init__(
             random_state=random_state,
         )
         modules = []
-        for hidden_size in hidden_sizes:
+        assert hidden_layers >= 1
+        for _ in range(hidden_layers):
             modules.append(nn.Linear(in_features=input_size, out_features=hidden_size))
             modules.append(hidden_activation())
             input_size = hidden_size
@@ -37,18 +39,23 @@ def __init__(
 
     def get_grid_params(self, search_type: str = "random"):
         param_space = {
-            "lr": loguniform(1e-06, 0.01),
             "max_epochs": np.arange(10, 110, 10).tolist(),
             "batch_size": np.arange(2, 128, 2).tolist(),
-            "module__hidden_sizes": [(50,), (100,), (100, 100), (100, 200), (200, 200)],
-            "module__hidden_activation": [nn.ReLU, nn.Tanh, nn.Sigmoid, nn.GELU],
-            "optimizer__weight_decay": (1 / 10 ** np.arange(1, 10)).tolist(),
+            "module__hidden_layers": np.arange(1, 4).tolist(),
+            "module__hidden_size": np.arange(50, 250, 50).tolist(),
+            "module__hidden_activation": [
+                nn.ReLU,
+                nn.Tanh,
+                nn.Sigmoid,
+                nn.GELU,
+            ],
+            "optimizer__weight_decay": (1 / 10 ** np.arange(1, 9)).tolist(),
         }
         match search_type:
             case "random":
-                pass
+                param_space |= {"lr": loguniform(1e-06, 1e-2)}
             case "bayes":
-                pass
+                param_space |= {"lr": Real(1e-06, 1e-2, prior="log-uniform")}
             case _:
                 raise ValueError(f"Invalid search type: {search_type}")