Loss Function Evaluation#

Parameters for the loss function are set in LossParameters.

class drdmannturb.LossAggregator(params: LossParameters, k1space: Tensor, zref: float, tb_log_dir: str | None = None, tb_comment: str = '')[source]#

Combines all loss functions and evaluates each term for the optimizer. The loss function for spectra fitting is determined by the following minimization problem:

$$\underset{\mathit{\theta }}{min}\{\mathrm{MSE}[\mathit{\theta }]+\alpha \mathrm{Pen}[\mathit{\theta }]+\beta \mathrm{Reg}\left[{\mathit{\theta }}_{\mathrm{NN}}\right]\}$$

where the loss terms are defined in the class’s methods. In the following, $L$ is the number of data points $f_j\in \mathcal{D}$. The data $J_i(f_j)$ is evaluated using the Kaimal spectra. Note that the norm $||\cdot |{|}_{\mathcal{D}}$ is defined as

$$\Vert g{\Vert }_{\mathcal{D}}^2:={\int }_{\mathcal{D}}|g(f){|}^2\mathrm{d}(\log f).$$

Parameters:

• params (LossParameters) – Dataclass with parameters that determine the loss function

• k1space (torch.Tensor) – The spectra space for k1, this is assumed to be in logspace.

• zref (float) – Reference velocity, needed for computing penalty derivatives wrt k1 z.

• tb_log_dir (Optional[str]) – Logging directory for the TensorBoard logger. Conventions are those of TensorBoard, which by default result in the creation of a runs subdirectory where the script is being run if this parameter is left as None.

• fn_comment (str) – Filename comment used by tensorboard; useful for distinguishing between architectures and hyperparameters. Refer to tensorboard documentation for examples of use. By default, the empty string, which results in default tensorboard filenames.

• tb_comment (str) –

MSE_term(model: Tensor, target: Tensor, epoch: int) → Tensor[source]#

Evaluates the loss term

$$\mathrm{MSE}[\mathit{\theta }]:=\frac{1}{L}\sum _{i=1}^4\sum _{j=1}^L{(\log \left|J_i\left(f_j\right)\right|-\log \left|{\tilde{J}}_i(f_j,\mathit{\theta })\right|)}^2,$$

Parameters:

• model (torch.Tensor) – Model output of spectra on the k1space provided in the constructor.

• target (torch.Tensor) – True spectra data on the k1space provided in the constructor.

• epoch (int) – Epoch number, used for the TensorBoard loss writer.

Returns:

torch.Tensor – Evaluated MSE loss term.

Return type:

Tensor

Pen1stOrder(y: Tensor, epoch: int) → Tensor[source]#

Evaluates the first-order penalization term, defined as

$${\mathrm{Pen}}_1[\mathit{\theta }]:=\frac{1}{|\mathcal{D}|}\sum _{i=1}^4{\Vert \mathrm{ReLU}\left(\frac{\partial \log |{\tilde{J}}_i(\cdot ,\mathit{\theta })|}{\partial \log k_1}\right)\Vert }_{\mathcal{D}}^2.$$

Parameters:

• y (torch.Tensor) – Model spectra output.

• epoch (int) – Epoch number, used for the TensorBoard loss writer.

Returns:

torch.Tensor – 1st order penalty loss.

Return type:

Tensor

Pen2ndOrder(y: Tensor, epoch: int) → Tensor[source]#

Evaluates he second-order penalization term, defined as

$${\mathrm{Pen}}_2[\mathit{\theta }]:=\frac{1}{|\mathcal{D}|}\sum _{i=1}^4{\Vert \mathrm{ReLU}\left(\frac{{\partial }^2\log |{\tilde{J}}_i(\cdot ,\mathit{\theta })|}{{(\partial \log k_1)}^2}\right)\Vert }_{\mathcal{D}}^2,$$

Parameters:

• y (torch.Tensor) – Model spectra output.

• epoch (int) – Epoch number, used for the TensorBoard loss writer.

Returns:

torch.Tensor – 2nd order penalty loss term.

Return type:

Tensor

Regularization(theta_NN: Tensor, epoch: int) → Tensor[source]#

Evaluates the regularization term, defined as

$$\mathrm{Reg}\left[{\mathit{\theta }}_{\mathrm{NN}}\right]:=\frac{1}{N}\sum _{i=1}^N{\theta }_{\mathrm{NN},i}^2.$$

Parameters:

• theta_NN (torch.Tensor) – Neural network parameters.

• epoch (int) – Epoch number, used for the TensorBoard loss writer.

Returns:

torch.Tensor – Regularization loss of neural network model.

Return type:

Tensor

eval(y: Tensor, y_data: Tensor, theta_NN: Tensor | None, epoch: int) → Tensor[source]#

Evaluation method for computing the full loss term at a given epoch. This method sequentially evaluates each term in the loss and returns the sum total loss.

Parameters:

• y (torch.Tensor) – Model spectra output on k1space in constructor.

• y_data (torch.Tensor) – True spectra data on k1space in constructor.

• theta_NN (Optional[torch.Tensor]) – Neural network parameters, used in the regularization loss term if activated. Can be set to None if no neural network is used.

• epoch (int) – Epoch number, used for the TensorBoard loss writer.

Returns:

torch.Tensor – Evaluated total loss, as a weighted sum of all terms with non-zero hyperparameters.

Return type:

Tensor