CompetitivePINN#

class CompetitivePINN(problem, model, discriminator=None, loss=MSELoss(), optimizer_model=<class 'torch.optim.adam.Adam'>, optimizer_model_kwargs={'lr': 0.001}, optimizer_discriminator=<class 'torch.optim.adam.Adam'>, optimizer_discriminator_kwargs={'lr': 0.001}, scheduler_model=<class 'torch.optim.lr_scheduler.ConstantLR'>, scheduler_model_kwargs={'factor': 1, 'total_iters': 0}, scheduler_discriminator=<class 'torch.optim.lr_scheduler.ConstantLR'>, scheduler_discriminator_kwargs={'factor': 1, 'total_iters': 0})[source]#

Bases: PINNInterface

Competitive Physics Informed Neural Network (PINN) solver class. This class implements Competitive Physics Informed Neural Network solvers, using a user specified model to solve a specific problem. It can be used for solving both forward and inverse problems.

The Competitive Physics Informed Network aims to find the solution \(\mathbf{u}:\Omega\rightarrow\mathbb{R}^m\) of the differential problem:

\[\begin{split}\begin{cases} \mathcal{A}[\mathbf{u}](\mathbf{x})=0\quad,\mathbf{x}\in\Omega\\ \mathcal{B}[\mathbf{u}](\mathbf{x})=0\quad, \mathbf{x}\in\partial\Omega \end{cases}\end{split}\]

with a minimization (on model parameters) maximation ( on discriminator parameters) of the loss function

\[\mathcal{L}_{\rm{problem}} = \frac{1}{N}\sum_{i=1}^N \mathcal{L}(D(\mathbf{x}_i)\mathcal{A}[\mathbf{u}](\mathbf{x}_i))+ \frac{1}{N}\sum_{i=1}^N \mathcal{L}(D(\mathbf{x}_i)\mathcal{B}[\mathbf{u}](\mathbf{x}_i))\]

where \(D\) is the discriminator network, which tries to find the points where the network performs worst, and \(\mathcal{L}\) is a specific loss function, default Mean Square Error:

\[\mathcal{L}(v) = \| v \|^2_2.\]