fastvpinns.physics.helmholtz2d module

The file helmholtz2d.py is implementation of our efficient tensor-based loss calculation for Helmholtz equation with inverse problem (Domain).

Author: Thivin Anandh D

Date: 21/Sep/2023

History: Initial implementation

Refer: https://arxiv.org/abs/2404.12063

fastvpinns.physics.helmholtz2d.pde_loss_helmholtz(test_shape_val_mat, test_grad_x_mat, test_grad_y_mat, pred_nn, pred_grad_x_nn, pred_grad_y_nn, forcing_function, bilinear_params)[source]

Calculates and returns the loss for the helmholtz problem

Parameters:

  • test_shape_val_mat (tf.Tensor) – The test shape value matrix.

  • test_grad_x_mat (tf.Tensor) – The x-gradient of the test matrix.

  • test_grad_y_mat (tf.Tensor) – The y-gradient of the test matrix.

  • pred_nn (tf.Tensor) – The predicted neural network output.

  • pred_grad_x_nn (tf.Tensor) – The x-gradient of the predicted neural network output.

  • pred_grad_y_nn (tf.Tensor) – The y-gradient of the predicted neural network output.

  • forcing_function (function) – The forcing function used in the PDE.

  • bilinear_params (list) – The parameters for the bilinear form.

Returns:

The calculated loss.

Return type:

tf.Tensor