diff --git a/pina/solvers/__init__.py b/pina/solvers/__init__.py
index 2751e481..6b755661 100644
--- a/pina/solvers/__init__.py
+++ b/pina/solvers/__init__.py
@@ -9,11 +9,10 @@
     "SupervisedSolver",
     "ReducedOrderModelSolver",
     "GAROM",
-    ]
+]
 
 from .solver import SolverInterface
 from .pinns import *
 from .supervised import SupervisedSolver
 from .rom import ReducedOrderModelSolver
 from .garom import GAROM
-
diff --git a/pina/solvers/pinns/basepinn.py b/pina/solvers/pinns/basepinn.py
index 726cdf92..53d4d3a9 100644
--- a/pina/solvers/pinns/basepinn.py
+++ b/pina/solvers/pinns/basepinn.py
@@ -12,11 +12,12 @@
 
 torch.pi = torch.acos(torch.zeros(1)).item() * 2  # which is 3.1415927410125732
 
+
 class PINNInterface(SolverInterface, metaclass=ABCMeta):
     """
     Base PINN solver class. This class implements the Solver Interface
     for Physics Informed Neural Network solvers.
-    
+
     This class can be used to
     define PINNs with multiple ``optimizers``, and/or ``models``.
     By default it takes
@@ -72,7 +73,7 @@ def __init__(
             self._clamp_params = self._clamp_inverse_problem_params
         else:
             self._params = None
-            self._clamp_params = lambda : None
+            self._clamp_params = lambda: None
 
         # variable used internally to store residual losses at each epoch
         # this variable save the residual at each iteration (not weighted)
@@ -107,7 +108,7 @@ def training_step(self, batch, _):
             condition = self.problem.conditions[condition_name]
             pts = batch["pts"]
             # condition name is logged (if logs enabled)
-            self.__logged_metric = condition_name 
+            self.__logged_metric = condition_name
 
             if len(batch) == 2:
                 samples = pts[condition_idx == condition_id]
@@ -160,7 +161,7 @@ def loss_phys(self, samples, equation):
         :rtype: LabelTensor
         """
         pass
-        
+
     def compute_residual(self, samples, equation):
         """
         Compute the residual for Physics Informed learning. This function
@@ -182,7 +183,7 @@ def compute_residual(self, samples, equation):
                 samples, self.forward(samples), self._params
             )
         return residual
-    
+
     def store_log(self, loss_value):
         """
         Stores the loss value in the logger. This function should be
@@ -195,13 +196,13 @@ def store_log(self, loss_value):
         :param torch.Tensor loss_value: The value of the loss.
         """
         self.log(
-                self.__logged_metric+'_loss',
-                loss_value,
-                prog_bar=True,
-                logger=True,
-                on_epoch=True,
-                on_step=False,
-            )
+            self.__logged_metric + "_loss",
+            loss_value,
+            prog_bar=True,
+            logger=True,
+            on_epoch=True,
+            on_step=False,
+        )
         self.__logged_res_losses.append(loss_value)
 
     def on_train_epoch_end(self):
@@ -211,10 +212,10 @@ def on_train_epoch_end(self):
         """
         if self.__logged_res_losses:
             # storing mean loss
-            self.__logged_metric = 'mean'
+            self.__logged_metric = "mean"
             self.store_log(
-                sum(self.__logged_res_losses)/len(self.__logged_res_losses)
-                )
+                sum(self.__logged_res_losses) / len(self.__logged_res_losses)
+            )
             # free the logged losses
             self.__logged_res_losses = []
         return super().on_train_epoch_end()
@@ -244,4 +245,4 @@ def current_condition_name(self):
         :meth:`loss_phys` to extract the condition at which the loss is
         computed.
         """
-        return self.__logged_metric
\ No newline at end of file
+        return self.__logged_metric
diff --git a/pina/solvers/pinns/causalpinn.py b/pina/solvers/pinns/causalpinn.py
index fea0fe47..476e4c55 100644
--- a/pina/solvers/pinns/causalpinn.py
+++ b/pina/solvers/pinns/causalpinn.py
@@ -97,25 +97,27 @@ def __init__(
         :param dict scheduler_kwargs: LR scheduler constructor keyword args.
         :param int | float eps: The exponential decay parameter. Note that this
             value is kept fixed during the training, but can be changed by means
-            of a callback, e.g. for annealing. 
+            of a callback, e.g. for annealing.
         """
         super().__init__(
-                        problem=problem,
-                        model=model,
-                        extra_features=extra_features,
-                        loss=loss,
-                        optimizer=optimizer,
-                        optimizer_kwargs=optimizer_kwargs,
-                        scheduler=scheduler,
-                        scheduler_kwargs=scheduler_kwargs,
+            problem=problem,
+            model=model,
+            extra_features=extra_features,
+            loss=loss,
+            optimizer=optimizer,
+            optimizer_kwargs=optimizer_kwargs,
+            scheduler=scheduler,
+            scheduler_kwargs=scheduler_kwargs,
         )
 
         # checking consistency
-        check_consistency(eps, (int,float))
+        check_consistency(eps, (int, float))
         self._eps = eps
         if not isinstance(self.problem, TimeDependentProblem):
-            raise ValueError('Casual PINN works only for problems'
-                             'inheritig from TimeDependentProblem.')
+            raise ValueError(
+                "Casual PINN works only for problems"
+                "inheritig from TimeDependentProblem."
+            )
 
     def loss_phys(self, samples, equation):
         """
@@ -144,14 +146,14 @@ def loss_phys(self, samples, equation):
             )
             time_loss.append(loss_val)
         # store results
-        self.store_log(loss_value=float(sum(time_loss)/len(time_loss)))
+        self.store_log(loss_value=float(sum(time_loss) / len(time_loss)))
         # concatenate residuals
         time_loss = torch.stack(time_loss)
         # compute weights (without the gradient storing)
         with torch.no_grad():
             weights = self._compute_weights(time_loss)
         return (weights * time_loss).mean()
-    
+
     @property
     def eps(self):
         """
@@ -205,8 +207,8 @@ def _split_tensor_into_chunks(self, tensor):
         _, idx_split = time_tensor.unique(return_counts=True)
         # splitting
         chunks = torch.split(tensor, tuple(idx_split))
-        return chunks, labels # return chunks
-    
+        return chunks, labels  # return chunks
+
     def _compute_weights(self, loss):
         """
         Computes the weights for the physics loss based on the cumulative loss.
diff --git a/pina/solvers/pinns/competitive_pinn.py b/pina/solvers/pinns/competitive_pinn.py
index 6404c0bb..5e011a47 100644
--- a/pina/solvers/pinns/competitive_pinn.py
+++ b/pina/solvers/pinns/competitive_pinn.py
@@ -117,7 +117,7 @@ def __init__(
                 optimizer_discriminator_kwargs,
             ],
             extra_features=None,  # CompetitivePINN doesn't take extra features
-            loss=loss
+            loss=loss,
         )
 
         # set automatic optimization for GANs
@@ -131,9 +131,7 @@ def __init__(
 
         # assign schedulers
         self._schedulers = [
-            scheduler_model(
-                self.optimizers[0], **scheduler_model_kwargs
-            ),
+            scheduler_model(self.optimizers[0], **scheduler_model_kwargs),
             scheduler_discriminator(
                 self.optimizers[1], **scheduler_discriminator_kwargs
             ),
@@ -141,7 +139,7 @@ def __init__(
 
         self._model = self.models[0]
         self._discriminator = self.models[1]
-    
+
     def forward(self, x):
         r"""
         Forward pass implementation for the PINN solver. It returns the function
@@ -195,8 +193,11 @@ def loss_data(self, input_tensor, output_tensor):
         :rtype: torch.Tensor
         """
         self.optimizer_model.zero_grad()
-        loss_val = super().loss_data(
-            input_tensor, output_tensor).as_subclass(torch.Tensor)
+        loss_val = (
+            super()
+            .loss_data(input_tensor, output_tensor)
+            .as_subclass(torch.Tensor)
+        )
         loss_val.backward()
         self.optimizer_model.step()
         return loss_val
@@ -221,7 +222,7 @@ def configure_optimizers(self):
             )
         return self.optimizers, self._schedulers
 
-    def on_train_batch_end(self,outputs, batch, batch_idx):
+    def on_train_batch_end(self, outputs, batch, batch_idx):
         """
         This method is called at the end of each training batch, and ovverides
         the PytorchLightining implementation for logging the checkpoints.
@@ -235,7 +236,9 @@ def on_train_batch_end(self,outputs, batch, batch_idx):
         :rtype: Any
         """
         # increase by one the counter of optimization to save loggers
-        self.trainer.fit_loop.epoch_loop.manual_optimization.optim_step_progress.total.completed += 1
+        self.trainer.fit_loop.epoch_loop.manual_optimization.optim_step_progress.total.completed += (
+            1
+        )
         return super().on_train_batch_end(outputs, batch, batch_idx)
 
     def _train_discriminator(self, samples, equation, discriminator_bets):
@@ -252,13 +255,14 @@ def _train_discriminator(self, samples, equation, discriminator_bets):
         self.optimizer_discriminator.zero_grad()
         # compute residual, we detach because the weights of the generator
         # model are fixed
-        residual = self.compute_residual(samples=samples,
-                                         equation=equation).detach()
+        residual = self.compute_residual(
+            samples=samples, equation=equation
+        ).detach()
         # compute competitive residual, the minus is because we maximise
         competitive_residual = residual * discriminator_bets
-        loss_val = - self.loss(
+        loss_val = -self.loss(
             torch.zeros_like(competitive_residual, requires_grad=True),
-            competitive_residual
+            competitive_residual,
         ).as_subclass(torch.Tensor)
         # backprop
         self.manual_backward(loss_val)
@@ -283,16 +287,13 @@ def _train_model(self, samples, equation, discriminator_bets):
         residual = self.compute_residual(samples=samples, equation=equation)
         # store logging
         with torch.no_grad():
-            loss_residual = self.loss(
-                                torch.zeros_like(residual),
-                                residual
-                                )
+            loss_residual = self.loss(torch.zeros_like(residual), residual)
         # compute competitive residual, discriminator_bets are detached becase
         # we optimize only the generator model
         competitive_residual = residual * discriminator_bets.detach()
         loss_val = self.loss(
             torch.zeros_like(competitive_residual, requires_grad=True),
-            competitive_residual
+            competitive_residual,
         ).as_subclass(torch.Tensor)
         # backprop
         self.manual_backward(loss_val)
@@ -357,4 +358,4 @@ def scheduler_discriminator(self):
         :return: The scheduler for the discriminator.
         :rtype: torch.optim.lr_scheduler._LRScheduler
         """
-        return self._schedulers[1]
\ No newline at end of file
+        return self._schedulers[1]
diff --git a/pina/solvers/pinns/gpinn.py b/pina/solvers/pinns/gpinn.py
index 6eca1eac..5f259ca2 100644
--- a/pina/solvers/pinns/gpinn.py
+++ b/pina/solvers/pinns/gpinn.py
@@ -90,22 +90,23 @@ def __init__(
         :param dict scheduler_kwargs: LR scheduler constructor keyword args.
         """
         super().__init__(
-                        problem=problem,
-                        model=model,
-                        extra_features=extra_features,
-                        loss=loss,
-                        optimizer=optimizer,
-                        optimizer_kwargs=optimizer_kwargs,
-                        scheduler=scheduler,
-                        scheduler_kwargs=scheduler_kwargs,
+            problem=problem,
+            model=model,
+            extra_features=extra_features,
+            loss=loss,
+            optimizer=optimizer,
+            optimizer_kwargs=optimizer_kwargs,
+            scheduler=scheduler,
+            scheduler_kwargs=scheduler_kwargs,
         )
         if not isinstance(self.problem, SpatialProblem):
-            raise ValueError('Gradient PINN computes the gradient of the '
-                             'PINN loss with respect to the spatial '
-                             'coordinates, thus the PINA problem must be '
-                             'a SpatialProblem.')
+            raise ValueError(
+                "Gradient PINN computes the gradient of the "
+                "PINN loss with respect to the spatial "
+                "coordinates, thus the PINA problem must be "
+                "a SpatialProblem."
+            )
 
-    
     def loss_phys(self, samples, equation):
         """
         Computes the physics loss for the GPINN solver based on given
@@ -126,9 +127,9 @@ def loss_phys(self, samples, equation):
         self.store_log(loss_value=float(loss_value))
         # gradient PINN loss
         loss_value = loss_value.reshape(-1, 1)
-        loss_value.labels = ['__LOSS']
+        loss_value.labels = ["__LOSS"]
         loss_grad = grad(loss_value, samples, d=self.problem.spatial_variables)
         g_loss_phys = self.loss(
             torch.zeros_like(loss_grad, requires_grad=True), loss_grad
         )
-        return loss_value + g_loss_phys
\ No newline at end of file
+        return loss_value + g_loss_phys
diff --git a/pina/solvers/pinns/pinn.py b/pina/solvers/pinns/pinn.py
index 318283a3..15f90818 100644
--- a/pina/solvers/pinns/pinn.py
+++ b/pina/solvers/pinns/pinn.py
@@ -87,7 +87,7 @@ def __init__(
             optimizers=[optimizer],
             optimizers_kwargs=[optimizer_kwargs],
             extra_features=extra_features,
-            loss=loss
+            loss=loss,
         )
 
         # check consistency
@@ -131,7 +131,6 @@ def loss_phys(self, samples, equation):
         self.store_log(loss_value=float(loss_value))
         return loss_value
 
-
     def configure_optimizers(self):
         """
         Optimizer configuration for the PINN
@@ -153,7 +152,6 @@ def configure_optimizers(self):
             )
         return self.optimizers, [self.scheduler]
 
-
     @property
     def scheduler(self):
         """
@@ -161,10 +159,9 @@ def scheduler(self):
         """
         return self._scheduler
 
-
     @property
     def neural_net(self):
         """
         Neural network for the PINN training.
         """
-        return self._neural_net
\ No newline at end of file
+        return self._neural_net
diff --git a/pina/solvers/pinns/sapinn.py b/pina/solvers/pinns/sapinn.py
index 8de2d14c..751e21ef 100644
--- a/pina/solvers/pinns/sapinn.py
+++ b/pina/solvers/pinns/sapinn.py
@@ -14,6 +14,7 @@
 
 from torch.optim.lr_scheduler import ConstantLR
 
+
 class Weights(torch.nn.Module):
     """
     This class aims to implements the mask model for
@@ -27,11 +28,9 @@ def __init__(self, func):
         """
         super().__init__()
         check_consistency(func, torch.nn.Module)
-        self.sa_weights = torch.nn.Parameter(
-            torch.Tensor()
-        )
+        self.sa_weights = torch.nn.Parameter(torch.Tensor())
         self.func = func
-    
+
     def forward(self):
         """
         Forward pass implementation for the mask module.
@@ -43,6 +42,7 @@ def forward(self):
         """
         return self.func(self.sa_weights)
 
+
 class SAPINN(PINNInterface):
     r"""
     Self Adaptive Physics Informed Neural Network (SAPINN) solver class.
@@ -106,22 +106,22 @@ class SAPINN(PINNInterface):
         DOI: `10.1016/
         j.jcp.2022.111722 <https://doi.org/10.1016/j.jcp.2022.111722>`_.
     """
-    
+
     def __init__(
-            self,
-            problem,
-            model,
-            weights_function=torch.nn.Sigmoid(),
-            extra_features=None,
-            loss=torch.nn.MSELoss(),
-            optimizer_model=torch.optim.Adam,
-            optimizer_model_kwargs={"lr" : 0.001},
-            optimizer_weights=torch.optim.Adam,
-            optimizer_weights_kwargs={"lr" : 0.001},
-            scheduler_model=ConstantLR,
-            scheduler_model_kwargs={"factor" : 1, "total_iters" : 0},
-            scheduler_weights=ConstantLR,
-            scheduler_weights_kwargs={"factor" : 1, "total_iters" : 0}
+        self,
+        problem,
+        model,
+        weights_function=torch.nn.Sigmoid(),
+        extra_features=None,
+        loss=torch.nn.MSELoss(),
+        optimizer_model=torch.optim.Adam,
+        optimizer_model_kwargs={"lr": 0.001},
+        optimizer_weights=torch.optim.Adam,
+        optimizer_weights_kwargs={"lr": 0.001},
+        scheduler_model=ConstantLR,
+        scheduler_model_kwargs={"factor": 1, "total_iters": 0},
+        scheduler_weights=ConstantLR,
+        scheduler_weights_kwargs={"factor": 1, "total_iters": 0},
     ):
         """
         :param AbstractProblem problem: The formualation of the problem.
@@ -167,19 +167,18 @@ def __init__(
             weights_dict[condition_name] = Weights(weights_function)
         weights_dict = torch.nn.ModuleDict(weights_dict)
 
-
         super().__init__(
             models=[model, weights_dict],
             problem=problem,
             optimizers=[optimizer_model, optimizer_weights],
             optimizers_kwargs=[
                 optimizer_model_kwargs,
-                optimizer_weights_kwargs
+                optimizer_weights_kwargs,
             ],
             extra_features=extra_features,
-            loss=loss
+            loss=loss,
         )
-        
+
         # set automatic optimization
         self.automatic_optimization = False
 
@@ -191,12 +190,8 @@ def __init__(
 
         # assign schedulers
         self._schedulers = [
-            scheduler_model(
-                self.optimizers[0], **scheduler_model_kwargs
-            ),
-            scheduler_weights(
-                self.optimizers[1], **scheduler_weights_kwargs
-            ),
+            scheduler_model(self.optimizers[0], **scheduler_model_kwargs),
+            scheduler_weights(self.optimizers[1], **scheduler_weights_kwargs),
         ]
 
         self._model = self.models[0]
@@ -204,7 +199,7 @@ def __init__(
 
         self._vectorial_loss = deepcopy(loss)
         self._vectorial_loss.reduction = "none"
-    
+
     def forward(self, x):
         """
         Forward pass implementation for the PINN
@@ -219,7 +214,7 @@ def forward(self, x):
         :rtype: LabelTensor
         """
         return self.neural_net(x)
-    
+
     def loss_phys(self, samples, equation):
         """
         Computes the physics loss for the SAPINN solver based on given
@@ -235,7 +230,7 @@ def loss_phys(self, samples, equation):
         # train weights
         self.optimizer_weights.zero_grad()
         weighted_loss, _ = self._loss_phys(samples, equation)
-        loss_value = - weighted_loss.as_subclass(torch.Tensor)
+        loss_value = -weighted_loss.as_subclass(torch.Tensor)
         self.manual_backward(loss_value)
         self.optimizer_weights.step()
 
@@ -271,7 +266,7 @@ def loss_data(self, input_tensor, output_tensor):
         # train weights
         self.optimizer_weights.zero_grad()
         weighted_loss, _ = self._loss_data(input_tensor, output_tensor)
-        loss_value = - weighted_loss.as_subclass(torch.Tensor)
+        loss_value = -weighted_loss.as_subclass(torch.Tensor)
         self.manual_backward(loss_value)
         self.optimizer_weights.step()
 
@@ -291,7 +286,7 @@ def loss_data(self, input_tensor, output_tensor):
         # store loss without weights
         self.store_log(loss_value=float(loss))
         return loss_value
-    
+
     def configure_optimizers(self):
         """
         Optimizer configuration for the SAPINN
@@ -312,8 +307,8 @@ def configure_optimizers(self):
                 }
             )
         return self.optimizers, self._schedulers
-    
-    def on_train_batch_end(self,outputs, batch, batch_idx):
+
+    def on_train_batch_end(self, outputs, batch, batch_idx):
         """
         This method is called at the end of each training batch, and ovverides
         the PytorchLightining implementation for logging the checkpoints.
@@ -327,9 +322,11 @@ def on_train_batch_end(self,outputs, batch, batch_idx):
         :rtype: Any
         """
         # increase by one the counter of optimization to save loggers
-        self.trainer.fit_loop.epoch_loop.manual_optimization.optim_step_progress.total.completed += 1
+        self.trainer.fit_loop.epoch_loop.manual_optimization.optim_step_progress.total.completed += (
+            1
+        )
         return super().on_train_batch_end(outputs, batch, batch_idx)
-    
+
     def on_train_start(self):
         """
         This method is called at the start of the training for setting
@@ -343,12 +340,11 @@ def on_train_start(self):
             self.trainer._accelerator_connector._accelerator_flag
         )
         for condition_name, tensor in self.problem.input_pts.items():
-            self.weights_dict.torchmodel[condition_name].sa_weights.data = torch.rand(
-                (tensor.shape[0], 1),
-                device = device
+            self.weights_dict.torchmodel[condition_name].sa_weights.data = (
+                torch.rand((tensor.shape[0], 1), device=device)
             )
         return super().on_train_start()
-    
+
     def on_load_checkpoint(self, checkpoint):
         """
         Overriding the Pytorch Lightning ``on_load_checkpoint`` to handle
@@ -358,8 +354,8 @@ def on_load_checkpoint(self, checkpoint):
         :param dict checkpoint: Pytorch Lightning checkpoint dict.
         """
         for condition_name, tensor in self.problem.input_pts.items():
-            self.weights_dict.torchmodel[condition_name].sa_weights.data = torch.rand(
-                (tensor.shape[0], 1)
+            self.weights_dict.torchmodel[condition_name].sa_weights.data = (
+                torch.rand((tensor.shape[0], 1))
             )
         return super().on_load_checkpoint(checkpoint)
 
@@ -370,13 +366,13 @@ def _loss_phys(self, samples, equation):
         :param LabelTensor samples: Input samples to evaluate the physics loss.
         :param EquationInterface equation: the governing equation representing
             the physics.
-        
+
         :return: tuple with weighted and not weighted scalar loss
         :rtype: List[LabelTensor, LabelTensor]
         """
         residual = self.compute_residual(samples, equation)
         return self._compute_loss(residual)
-    
+
     def _loss_data(self, input_tensor, output_tensor):
         """
         Elaboration of the loss related to data for the SAPINN solver.
@@ -384,7 +380,7 @@ def _loss_data(self, input_tensor, output_tensor):
         :param LabelTensor input_tensor: The input to the neural networks.
         :param LabelTensor output_tensor: The true solution to compare the
             network solution.
-        
+
         :return: tuple with weighted and not weighted scalar loss
         :rtype: List[LabelTensor, LabelTensor]
         """
@@ -396,19 +392,21 @@ def _compute_loss(self, residual):
         Elaboration of the pointwise loss through the mask model and the
         self adaptive weights
 
-        :param LabelTensor residual: the matrix of residuals that have to 
+        :param LabelTensor residual: the matrix of residuals that have to
             be weighted
 
         :return: tuple with weighted and not weighted loss
         :rtype List[LabelTensor, LabelTensor]
         """
         weights = self.weights_dict.torchmodel[
-            self.current_condition_name].forward()
-        loss_value = self._vectorial_loss(torch.zeros_like(
-            residual, requires_grad=True), residual)
+            self.current_condition_name
+        ].forward()
+        loss_value = self._vectorial_loss(
+            torch.zeros_like(residual, requires_grad=True), residual
+        )
         return (
             self._vect_to_scalar(weights * loss_value),
-            self._vect_to_scalar(loss_value)
+            self._vect_to_scalar(loss_value),
         )
 
     def _vect_to_scalar(self, loss_value):
@@ -426,10 +424,11 @@ def _vect_to_scalar(self, loss_value):
         elif self.loss.reduction == "sum":
             ret = torch.sum(loss_value)
         else:
-            raise RuntimeError(f"Invalid reduction, got {self.loss.reduction} "
-                               "but expected mean or sum.")
+            raise RuntimeError(
+                f"Invalid reduction, got {self.loss.reduction} "
+                "but expected mean or sum."
+            )
         return ret
-        
 
     @property
     def neural_net(self):
@@ -440,7 +439,7 @@ def neural_net(self):
         :rtype: torch.nn.Module
         """
         return self.models[0]
-    
+
     @property
     def weights_dict(self):
         """
@@ -462,7 +461,7 @@ def scheduler_model(self):
         :rtype: torch.optim.lr_scheduler._LRScheduler
         """
         return self._scheduler[0]
-    
+
     @property
     def scheduler_weights(self):
         """
@@ -482,7 +481,7 @@ def optimizer_model(self):
         :rtype: torch.optim.Optimizer
         """
         return self.optimizers[0]
-    
+
     @property
     def optimizer_weights(self):
         """
@@ -491,4 +490,4 @@ def optimizer_weights(self):
         :return: The optimizer for the mask model.
         :rtype: torch.optim.Optimizer
         """
-        return self.optimizers[1]
\ No newline at end of file
+        return self.optimizers[1]
diff --git a/pina/solvers/rom.py b/pina/solvers/rom.py
index 733d76f4..ee4bcff4 100644
--- a/pina/solvers/rom.py
+++ b/pina/solvers/rom.py
@@ -4,6 +4,7 @@
 
 from pina.solvers import SupervisedSolver
 
+
 class ReducedOrderModelSolver(SupervisedSolver):
     r"""
     ReducedOrderModelSolver solver class. This class implements a
@@ -114,10 +115,13 @@ def __init__(
             rate scheduler.
         :param dict scheduler_kwargs: LR scheduler constructor keyword args.
         """
-        model = torch.nn.ModuleDict({
-            'reduction_network' : reduction_network,
-            'interpolation_network' : interpolation_network})
-        
+        model = torch.nn.ModuleDict(
+            {
+                "reduction_network": reduction_network,
+                "interpolation_network": interpolation_network,
+            }
+        )
+
         super().__init__(
             model=model,
             problem=problem,
@@ -125,18 +129,22 @@ def __init__(
             optimizer=optimizer,
             optimizer_kwargs=optimizer_kwargs,
             scheduler=scheduler,
-            scheduler_kwargs=scheduler_kwargs
+            scheduler_kwargs=scheduler_kwargs,
         )
 
         # assert reduction object contains encode/ decode
-        if not hasattr(self.neural_net['reduction_network'], 'encode'):
-            raise SyntaxError('reduction_network must have encode method. '
-                               'The encode method should return a lower '
-                               'dimensional representation of the input.')
-        if not hasattr(self.neural_net['reduction_network'], 'decode'):
-            raise SyntaxError('reduction_network must have decode method. '
-                               'The decode method should return a high '
-                               'dimensional representation of the encoding.')
+        if not hasattr(self.neural_net["reduction_network"], "encode"):
+            raise SyntaxError(
+                "reduction_network must have encode method. "
+                "The encode method should return a lower "
+                "dimensional representation of the input."
+            )
+        if not hasattr(self.neural_net["reduction_network"], "decode"):
+            raise SyntaxError(
+                "reduction_network must have decode method. "
+                "The decode method should return a high "
+                "dimensional representation of the encoding."
+            )
 
     def forward(self, x):
         """
@@ -149,8 +157,8 @@ def forward(self, x):
         :return: Solver solution.
         :rtype: torch.Tensor
         """
-        reduction_network = self.neural_net['reduction_network']
-        interpolation_network = self.neural_net['interpolation_network']
+        reduction_network = self.neural_net["reduction_network"]
+        interpolation_network = self.neural_net["interpolation_network"]
         return reduction_network.decode(interpolation_network(x))
 
     def loss_data(self, input_pts, output_pts):
@@ -167,17 +175,18 @@ def loss_data(self, input_pts, output_pts):
         :rtype: torch.Tensor
         """
         # extract networks
-        reduction_network = self.neural_net['reduction_network']
-        interpolation_network = self.neural_net['interpolation_network']
+        reduction_network = self.neural_net["reduction_network"]
+        interpolation_network = self.neural_net["interpolation_network"]
         # encoded representations loss
         encode_repr_inter_net = interpolation_network(input_pts)
         encode_repr_reduction_network = reduction_network.encode(output_pts)
-        loss_encode = self.loss(encode_repr_inter_net,
-                                encode_repr_reduction_network)
+        loss_encode = self.loss(
+            encode_repr_inter_net, encode_repr_reduction_network
+        )
         # reconstruction loss
         loss_reconstruction = self.loss(
-            reduction_network.decode(encode_repr_reduction_network),
-            output_pts)
+            reduction_network.decode(encode_repr_reduction_network), output_pts
+        )
 
         return loss_encode + loss_reconstruction
 
diff --git a/pina/solvers/solver.py b/pina/solvers/solver.py
index 729a9d48..ec2f40c8 100644
--- a/pina/solvers/solver.py
+++ b/pina/solvers/solver.py
@@ -142,13 +142,13 @@ def problem(self):
         """
         The problem formulation."""
         return self._pina_problem
-    
+
     def on_train_start(self):
         """
         On training epoch start this function is call to do global checks for
         the different solvers.
         """
-        
+
         # 1. Check the verison for dataloader
         dataloader = self.trainer.train_dataloader
         if sys.version_info < (3, 8):
diff --git a/pina/solvers/supervised.py b/pina/solvers/supervised.py
index 28a634b0..42536461 100644
--- a/pina/solvers/supervised.py
+++ b/pina/solvers/supervised.py
@@ -118,7 +118,7 @@ def training_step(self, batch, batch_idx):
         :return: The sum of the loss functions.
         :rtype: LabelTensor
         """
-        
+
         condition_idx = batch["condition"]
 
         for condition_id in range(condition_idx.min(), condition_idx.max() + 1):
@@ -162,7 +162,7 @@ def loss_data(self, input_pts, output_pts):
         :rtype: torch.Tensor
         """
         return self.loss(self.forward(input_pts), output_pts)
-    
+
     @property
     def scheduler(self):
         """
diff --git a/pina/trainer.py b/pina/trainer.py
index 90779a6e..40f4eb69 100644
--- a/pina/trainer.py
+++ b/pina/trainer.py
@@ -67,9 +67,9 @@ def _create_or_update_loader(self):
         pb = self._model.problem
         if hasattr(pb, "unknown_parameters"):
             for key in pb.unknown_parameters:
-                pb.unknown_parameters[key] = torch.nn.Parameter(pb.unknown_parameters[key].data.to(device))
-
-
+                pb.unknown_parameters[key] = torch.nn.Parameter(
+                    pb.unknown_parameters[key].data.to(device)
+                )
 
     def train(self, **kwargs):
         """