Backend PyTorch: Fix L2 regularizers for external_trainable_variables (…

…#1884)

deepxde/model.py

@@ -112,9 +112,10 @@ def compile(
                 weighted by the `loss_weights` coefficients.
             external_trainable_variables: A trainable ``dde.Variable`` object or a list
                 of trainable ``dde.Variable`` objects. The unknown parameters in the
-                physics systems that need to be recovered. If the backend is
-                tensorflow.compat.v1, `external_trainable_variables` is ignored, and all
-                trainable ``dde.Variable`` objects are automatically collected.
+                physics systems that need to be recovered. Regularization will not be
+                applied to these variables. If the backend is tensorflow.compat.v1,
+                `external_trainable_variables` is ignored, and all trainable ``dde.Variable``
+                objects are automatically collected.
             verbose (Integer): Controls the verbosity of the compile process.
         """
         if verbose > 0 and config.rank == 0:
@@ -330,30 +331,40 @@ def outputs_losses_test(inputs, targets, auxiliary_vars):
                 False, inputs, targets, auxiliary_vars, self.data.losses_test
             )
 
-        # Another way is using per-parameter options
-        # https://pytorch.org/docs/stable/optim.html#per-parameter-options,
-        # but not all optimizers (such as L-BFGS) support this.
-        trainable_variables = (
-            list(self.net.parameters()) + self.external_trainable_variables
-        )
-        if self.net.regularizer is None:
-            self.opt, self.lr_scheduler = optimizers.get(
-                trainable_variables, self.opt_name, learning_rate=lr, decay=decay
-            )
-        else:
-            if self.net.regularizer[0] == "l2":
-                self.opt, self.lr_scheduler = optimizers.get(
-                    trainable_variables,
-                    self.opt_name,
-                    learning_rate=lr,
-                    decay=decay,
-                    weight_decay=self.net.regularizer[1],
-                )
-            else:
+        weight_decay = 0
+        if self.net.regularizer is not None:
+            if self.net.regularizer[0] != "l2":
                 raise NotImplementedError(
                     f"{self.net.regularizer[0]} regularization to be implemented for "
-                    "backend pytorch."
+                    "backend pytorch"
                 )
+            weight_decay = self.net.regularizer[1]
+
+        optimizer_params = self.net.parameters()
+        if self.external_trainable_variables:
+            # L-BFGS doesn't support per-parameter options.
+            if self.opt_name in ["L-BFGS", "L-BFGS-B"]:
+                optimizer_params = (
+                    list(optimizer_params) + self.external_trainable_variables
+                )
+                if weight_decay > 0:
+                    print(
+                        "Warning: L2 regularization will also be applied to external_trainable_variables. "
+                        "Ensure this is intended behavior."
+                    )
+            else:
+                optimizer_params = [
+                    {"params": optimizer_params},
+                    {"params": self.external_trainable_variables, "weight_decay": 0},
+                ]
+
+        self.opt, self.lr_scheduler = optimizers.get(
+            optimizer_params,
+            self.opt_name,
+            learning_rate=lr,
+            decay=decay,
+            weight_decay=weight_decay,
+        )
 
         def train_step(inputs, targets, auxiliary_vars):
             def closure():