The Role of Adaptive Activation Functions in Fractional Physics-Informed Neural Networks

In this work, we use adaptive activation functions for regression fractional physics-informed neural networks (fPINNs) to approximate nonsmooth solutions. The adaptive activation function has better learning capabilities than the traditional one because it improves the convergence rate and solution accuracy. Our simulation results show that the adaptive parameter contributes less to the improvement of the results as the singularity becomes more strong (a decreases), because the errors incurred from the discretization and optimization of the loss function become dominant.