fastvpinns.physics.poisson2d_inverse module

This file poisson2d_inverse.py is implemntation of our efficient tensor-based loss calculation for poisson equation with inverse problem (constant).

Author: Thivin Anandh D

Date: 21/Sep/2023

History: Initial implementation

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

fastvpinns.physics.poisson2d_inverse.pde_loss_poisson_inverse(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, inverse_params_dict)[source]

Calculates and returns the loss for the Poisson problem Inverse (constant)

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_dict (dict) – The dictionary containing the bilinear parameters.

  • inverse_param_dict (dict) – The dictionary containing the parameters for the inverse problem.

Returns:

The calculated loss.

Return type:

tf.Tensor