Complex Physics-Informed Neural Network

We propose compleX-PINN, a novel physics-informed neural network (PINN) architecture that incorporates a learnable activation function inspired by Cauchy integral theorem. By learning the parameters of the activation function, compleX-PINN achieves high accuracy with just a single hidden layer. Empirical results show that compleX-PINN effectively solves problems where traditional PINNs struggle and consistently delivers significantly higher precision, often by an order of magnitude.