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 = '')

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

\[\min _{\boldsymbol{\theta}}\left\{\operatorname{MSE}[\boldsymbol{\theta}]+\alpha \operatorname{Pen}[\boldsymbol{\theta}]+\beta \operatorname{Reg}\left[\boldsymbol{\theta}_{\mathrm{NN}}\right]\right\}\]

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

\[\|g\|_{\mathcal{D}}^2:=\int_{\mathcal{D}}|g(f)|^2 \mathrm{~d}(\log f).\]

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

Evaluates the loss term

\[\operatorname{MSE}[\boldsymbol{\theta}]:=\frac{1}{L} \sum_{i=1}^4 \sum_{j=1}^L\left(\log \left|J_i\left(f_j\right)\right|-\log \left|\widetilde{J}_i\left(f_j, \boldsymbol{\theta}\right)\right|\right)^2,\]

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

Evaluates the first-order penalization term, defined as

\[\operatorname{Pen}_1[\boldsymbol{\theta}]:=\frac{1}{|\mathcal{D}|} \sum_{i=1}^4\left\|\operatorname{ReLU}\left(\frac{\partial \log \left|\widetilde{J}_i(\cdot, \boldsymbol{\theta})\right|}{\partial \log k_1}\right)\right\|_{\mathcal{D}}^2.\]

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

Evaluates he second-order penalization term, defined as

\[\operatorname{Pen}_2[\boldsymbol{\theta}]:=\frac{1}{|\mathcal{D}|} \sum_{i=1}^4\left\|\operatorname{ReLU}\left(\frac{\partial^2 \log \left|\widetilde{J}_i(\cdot, \boldsymbol{\theta})\right|}{\left(\partial \log k_1\right)^2}\right)\right\|_{\mathcal{D}}^2,\]

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

Evaluates the regularization term, defined as

\[\operatorname{Reg}\left[\boldsymbol{\theta}_{\mathrm{NN}}\right]:=\frac{1}{N} \sum_{i=1}^N \theta_{\mathrm{NN}, i}^2.\]

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

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