  In recent years, the gap between Deep Learning (DL) methods and analytical or
numerical approaches in scientific computing is tried to be filled by the
evolution of Physics-Informed Neural Networks (PINNs). However, still, there
are many complications in the training of PINNs and optimal interleaving of
physical models. Here, we introduced the concept of Physical Activation
Functions (PAFs). This concept offers that instead of using general activation
functions (AFs) such as ReLU, tanh, and sigmoid for all the neurons, one can
use generic AFs that their mathematical expression is inherited from the
physical laws of the investigating phenomena. The formula of PAFs may be
inspired by the terms in the analytical solution of the problem. We showed that
the PAFs can be inspired by any mathematical formula related to the
investigating phenomena such as the initial or boundary conditions of the PDE
system. We validated the advantages of PAFs for several PDEs including the
harmonic oscillations, Burgers, Advection-Convection equation, and the
heterogeneous diffusion equations. The main advantage of PAFs was in the more
efficient constraining and interleaving of PINNs with the investigating
physical phenomena and their underlying mathematical models. This added
constraint significantly improved the predictions of PINNs for the testing data
that was out-of-training distribution. Furthermore, the application of PAFs
reduced the size of the PINNs up to 75% in different cases. Also, the value of
loss terms was reduced by 1 to 2 orders of magnitude in some cases which is
noteworthy for upgrading the training of the PINNs. The iterations required for
finding the optimum values were also significantly reduced. It is concluded
that using the PAFs helps in generating PINNs with less complexity and much
more validity for longer ranges of prediction.
