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Fully-Connected Neural Network

Solver ID: FC

Usage

from invert import Solver

# fwd = ...    (mne.Forward object)
# evoked = ... (mne.Evoked object)

solver = Solver("FC")
solver.make_inverse_operator(fwd)
stc = solver.apply_inverse_operator(evoked)
stc.plot()

Overview

Supervised fully-connected network trained on simulated data to map sensor time series to source activity.

References

  1. Lukas Hecker 2025, unpublished

API Reference

Bases: BaseSolver

Class for the Fully-Connected Neural Network (FC) for EEG inverse solutions.

Source code in invert/solvers/neural_networks/fc.py 
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class SolverFC(BaseSolver):
    """Class for the Fully-Connected Neural Network (FC) for
    EEG inverse solutions.

    """

    meta = SolverMeta(
        acronym="FC",
        full_name="Fully-Connected Neural Network",
        category="Neural Networks",
        description=(
            "Supervised fully-connected network trained on simulated data to map "
            "sensor time series to source activity."
        ),
        references=["Lukas Hecker 2025, unpublished"],
    )

    def __init__(self, name="Fully-Connected", **kwargs):
        self.name = name
        self.model = None
        self.optimizer = None
        self.device = None
        return super().__init__(**kwargs)

    def make_inverse_operator(
        self,
        forward,
        simulation_config,
        *args,
        n_dense_units=300,
        activation_function="tanh",
        epochs=300,
        learning_rate=1e-3,
        loss="cosine_similarity",
        size_validation_set=256,
        patience=100,
        alpha="auto",
        **kwargs,
    ):
        """Calculate inverse operator.

        Parameters
        ----------
        forward : mne.Forward
            The mne-python Forward model instance.
        activation_function : str
            The activation function of the hidden layers.
        batch_size : ["auto", int]
            The batch_size used during training. If "auto", the batch_size
            defaults to the number of dipoles in the source/ forward model.
            Choose a smaller batch_size (e.g., 1000) if you run into memory
            problems (RAM or GPU memory).
        n_timepoints : int
            The number of time points to simulate and ultimately train the
            neural network on.
        batch_repetitions : int
            The number of learning repetitions on the same batch of training
            data until a new batch is simulated.
        epochs : int
            The number of epochs to train.
        learning_rate : float
            The learning rate of the optimizer that trains the neural network.
        loss : str
            The loss function of the neural network.
        n_sources : int
            The maximum number of sources to simulate for the training data.
        n_orders : int
            Controls the maximum smoothness of the sources.
        size_validation_set : int
            The size of validation data set.
        snr_range : tuple
            The range of signal to noise ratios (SNRs) in the training data (in dB).
        patience : int
            Stopping criterion for the training.
        alpha : float
            The regularization parameter.
        correlation_mode : None/str
            None implies no correlation between the noise in different channels.
            'bounded' : Colored bounded noise, where channels closer to each other will be more correlated.
            'diagonal' : Some channels have varying degrees of noise.
        noise_color_coeff : float
            The magnitude of spatial coloring of the noise.

        Return
        ------
        self : object returns itself for convenience
        """
        super().make_inverse_operator(
            forward, *args, alpha=alpha, verbose=self.verbose, **kwargs
        )
        n_channels, n_dipoles = self.leadfield.shape

        # Store simulation config
        self.simulation_config = simulation_config

        # Store Parameters
        # Architecture
        self.n_dense_units = n_dense_units
        self.activation_function = activation_function
        # Training
        self.batch_size = self.simulation_config.batch_size
        self.epochs = epochs
        self.learning_rate = learning_rate
        self.loss = loss
        self.size_validation_set = size_validation_set
        self.patience = patience
        # Training Data (from simulation_config)
        self.n_timepoints = self.simulation_config.n_timepoints
        self.n_sources = self.simulation_config.n_sources
        self.n_orders = self.simulation_config.n_orders
        self.batch_repetitions = self.simulation_config.batch_repetitions
        self.snr_range = self.simulation_config.snr_range
        self.add_forward_error = self.simulation_config.add_forward_error
        self.forward_error = self.simulation_config.forward_error
        self.correlation_mode = self.simulation_config.correlation_mode
        self.noise_color_coeff = self.simulation_config.noise_color_coeff
        # Inference
        logger.info("Create Generator:..")
        self.create_generator()
        logger.info("Build Model:..")
        self.build_model()
        logger.info("Train Model:..")
        self.train_model()

        self.inverse_operators = []
        return self

    def apply_inverse_operator(self, mne_obj) -> mne.SourceEstimate:
        """Apply the inverse operator.

        Parameters
        ----------
        mne_obj : [mne.Evoked, mne.Epochs, mne.io.Raw]
            The MNE data object.

        Return
        ------
        stc : mne.SourceEstimate
            The mne Source Estimate object.
        """
        data = self.unpack_data_obj(mne_obj)

        source_mat = self.apply_model(data)
        stc = self.source_to_object(source_mat)

        return stc

    def apply_model(self, data) -> np.ndarray:
        """Compute the inverse solution of the M/EEG data.

        Parameters
        ----------
        data : numpy.ndarray
            The M/EEG data matrix.

        Return
        ------
        x_hat : numpy.ndarray
            The source esimate.

        """

        y = deepcopy(data)
        y /= np.linalg.norm(y, axis=0)
        y /= abs(y).max()

        n_channels, n_times = y.shape

        # Add empty batch and (color-) channel dimension
        y = y.T[np.newaxis]
        # Predict source(s)
        assert self.model is not None
        self.model.eval()
        device = self.device or get_torch_device()
        with torch.no_grad():
            source_pred = (
                self.model(torch.as_tensor(y, dtype=torch.float32, device=device))
                .detach()
                .cpu()
                .numpy()
            )
        source_pred = np.swapaxes(source_pred, 1, 2)  # (batch, dipoles, time)
        logger.debug(source_pred.shape)

        # Rescale sources
        y_original = deepcopy(data)
        y_original = y_original[np.newaxis]
        source_pred_scaled = rescale_sources(self.leadfield, source_pred[0], y_original)

        return source_pred_scaled

    def train_model(
        self,
    ):
        """Train the neural network model."""
        if self.model is None:
            raise RuntimeError("Model not initialized. Call build_model() first.")
        if self.optimizer is None:
            raise RuntimeError("Optimizer not initialized. Call build_model() first.")

        loss_fn = loss_from_name(self.loss)
        device = self.device or get_torch_device()

        # Get Validation data from generator
        x_val, y_val = next(self.generator)
        x_val = x_val[: self.size_validation_set]
        y_val = y_val[: self.size_validation_set]
        x_val_t = torch.as_tensor(x_val, dtype=torch.float32, device=device)
        y_val_t = torch.as_tensor(y_val, dtype=torch.float32, device=device)

        history: dict[str, list[float]] = {"loss": [], "val_loss": []}
        best_val = float("inf")
        best_state = None
        patience_left = int(self.patience)

        for _epoch in range(int(self.epochs)):
            self.model.train()
            running = 0.0
            for _step in range(int(self.batch_repetitions)):
                x_batch, y_batch = next(self.generator)
                x_t = torch.as_tensor(x_batch, dtype=torch.float32, device=device)
                y_t = torch.as_tensor(y_batch, dtype=torch.float32, device=device)

                self.optimizer.zero_grad(set_to_none=True)
                y_pred = self.model(x_t)
                loss = loss_fn(y_pred, y_t)
                loss.backward()
                self.optimizer.step()
                running += float(loss.detach().cpu().item())

            train_loss = running / float(self.batch_repetitions)

            self.model.eval()
            with torch.no_grad():
                val_loss = float(loss_fn(self.model(x_val_t), y_val_t).cpu().item())

            history["loss"].append(train_loss)
            history["val_loss"].append(val_loss)

            if val_loss < best_val:
                best_val = val_loss
                best_state = deepcopy(self.model.state_dict())
                patience_left = int(self.patience)
            else:
                patience_left -= 1
                if patience_left <= 0:
                    break

        if best_state is not None:
            self.model.load_state_dict(best_state)
        self.model.eval()
        self.history = history

    def build_model(
        self,
    ):
        """Build the neural network model."""
        n_channels, n_dipoles = self.leadfield.shape
        self.device = get_torch_device()
        self.model = _FCNet(
            n_channels,
            n_dipoles,
            n_dense_units=int(self.n_dense_units),
            activation_function=str(self.activation_function),
        ).to(self.device)
        self.optimizer = torch.optim.Adam(
            self.model.parameters(), lr=float(self.learning_rate)
        )
        logger.info(
            "Total number of trainable parameters: %d",
            count_trainable_parameters(self.model),
        )

    def create_generator(
        self,
    ):
        """Creat the data generator used for the simulations."""
        gen_args = dict(
            use_cov=False,
            return_mask=False,
            batch_size=self.batch_size,
            batch_repetitions=self.batch_repetitions,
            n_sources=self.n_sources,
            n_orders=self.n_orders,
            n_timepoints=self.n_timepoints,
            snr_range=self.snr_range,
            add_forward_error=self.add_forward_error,
            forward_error=self.forward_error,
            correlation_mode=self.correlation_mode,
            noise_color_coeff=self.noise_color_coeff,
            scale_data=True,
        )
        self.generator = generator(self.forward, **gen_args)
        self.generator.__next__()

__init__ 

__init__(name='Fully-Connected', **kwargs)
Source code in invert/solvers/neural_networks/fc.py 
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def __init__(self, name="Fully-Connected", **kwargs):
    self.name = name
    self.model = None
    self.optimizer = None
    self.device = None
    return super().__init__(**kwargs)

make_inverse_operator 

make_inverse_operator(
    forward,
    simulation_config,
    *args,
    n_dense_units=300,
    activation_function="tanh",
    epochs=300,
    learning_rate=0.001,
    loss="cosine_similarity",
    size_validation_set=256,
    patience=100,
    alpha="auto",
    **kwargs,
)

Calculate inverse operator.

Parameters:

Name Type Description Default
forward Forward

The mne-python Forward model instance.

 required
activation_function str

The activation function of the hidden layers.

 'tanh'
batch_size ['auto', int]

The batch_size used during training. If "auto", the batch_size defaults to the number of dipoles in the source/ forward model. Choose a smaller batch_size (e.g., 1000) if you run into memory problems (RAM or GPU memory).

 required
n_timepoints int

The number of time points to simulate and ultimately train the neural network on.

 required
batch_repetitions int

The number of learning repetitions on the same batch of training data until a new batch is simulated.

 required
epochs int

The number of epochs to train.

 300
learning_rate float

The learning rate of the optimizer that trains the neural network.

 0.001
loss str

The loss function of the neural network.

 'cosine_similarity'
n_sources int

The maximum number of sources to simulate for the training data.

 required
n_orders int

Controls the maximum smoothness of the sources.

 required
size_validation_set int

The size of validation data set.

 256
snr_range tuple

The range of signal to noise ratios (SNRs) in the training data (in dB).

 required
patience int

Stopping criterion for the training.

 100
alpha float

The regularization parameter.

 'auto'
correlation_mode None / str

None implies no correlation between the noise in different channels. 'bounded' : Colored bounded noise, where channels closer to each other will be more correlated. 'diagonal' : Some channels have varying degrees of noise.

 required
noise_color_coeff float

The magnitude of spatial coloring of the noise.

 required
Return

self : object returns itself for convenience

Source code in invert/solvers/neural_networks/fc.py 
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def make_inverse_operator(
    self,
    forward,
    simulation_config,
    *args,
    n_dense_units=300,
    activation_function="tanh",
    epochs=300,
    learning_rate=1e-3,
    loss="cosine_similarity",
    size_validation_set=256,
    patience=100,
    alpha="auto",
    **kwargs,
):
    """Calculate inverse operator.

    Parameters
    ----------
    forward : mne.Forward
        The mne-python Forward model instance.
    activation_function : str
        The activation function of the hidden layers.
    batch_size : ["auto", int]
        The batch_size used during training. If "auto", the batch_size
        defaults to the number of dipoles in the source/ forward model.
        Choose a smaller batch_size (e.g., 1000) if you run into memory
        problems (RAM or GPU memory).
    n_timepoints : int
        The number of time points to simulate and ultimately train the
        neural network on.
    batch_repetitions : int
        The number of learning repetitions on the same batch of training
        data until a new batch is simulated.
    epochs : int
        The number of epochs to train.
    learning_rate : float
        The learning rate of the optimizer that trains the neural network.
    loss : str
        The loss function of the neural network.
    n_sources : int
        The maximum number of sources to simulate for the training data.
    n_orders : int
        Controls the maximum smoothness of the sources.
    size_validation_set : int
        The size of validation data set.
    snr_range : tuple
        The range of signal to noise ratios (SNRs) in the training data (in dB).
    patience : int
        Stopping criterion for the training.
    alpha : float
        The regularization parameter.
    correlation_mode : None/str
        None implies no correlation between the noise in different channels.
        'bounded' : Colored bounded noise, where channels closer to each other will be more correlated.
        'diagonal' : Some channels have varying degrees of noise.
    noise_color_coeff : float
        The magnitude of spatial coloring of the noise.

    Return
    ------
    self : object returns itself for convenience
    """
    super().make_inverse_operator(
        forward, *args, alpha=alpha, verbose=self.verbose, **kwargs
    )
    n_channels, n_dipoles = self.leadfield.shape

    # Store simulation config
    self.simulation_config = simulation_config

    # Store Parameters
    # Architecture
    self.n_dense_units = n_dense_units
    self.activation_function = activation_function
    # Training
    self.batch_size = self.simulation_config.batch_size
    self.epochs = epochs
    self.learning_rate = learning_rate
    self.loss = loss
    self.size_validation_set = size_validation_set
    self.patience = patience
    # Training Data (from simulation_config)
    self.n_timepoints = self.simulation_config.n_timepoints
    self.n_sources = self.simulation_config.n_sources
    self.n_orders = self.simulation_config.n_orders
    self.batch_repetitions = self.simulation_config.batch_repetitions
    self.snr_range = self.simulation_config.snr_range
    self.add_forward_error = self.simulation_config.add_forward_error
    self.forward_error = self.simulation_config.forward_error
    self.correlation_mode = self.simulation_config.correlation_mode
    self.noise_color_coeff = self.simulation_config.noise_color_coeff
    # Inference
    logger.info("Create Generator:..")
    self.create_generator()
    logger.info("Build Model:..")
    self.build_model()
    logger.info("Train Model:..")
    self.train_model()

    self.inverse_operators = []
    return self

apply_inverse_operator 

apply_inverse_operator(mne_obj) -> mne.SourceEstimate

Apply the inverse operator.

Parameters:

Name Type Description Default
mne_obj [Evoked, Epochs, Raw]

The MNE data object.

 required
Return

stc : mne.SourceEstimate The mne Source Estimate object.

Source code in invert/solvers/neural_networks/fc.py 
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def apply_inverse_operator(self, mne_obj) -> mne.SourceEstimate:
    """Apply the inverse operator.

    Parameters
    ----------
    mne_obj : [mne.Evoked, mne.Epochs, mne.io.Raw]
        The MNE data object.

    Return
    ------
    stc : mne.SourceEstimate
        The mne Source Estimate object.
    """
    data = self.unpack_data_obj(mne_obj)

    source_mat = self.apply_model(data)
    stc = self.source_to_object(source_mat)

    return stc