Complex Physics-Informed Neural Network
This work addresses the problem of improving accuracy in physics-informed neural networks for researchers and practitioners working with complex physical systems, offering an incremental yet significant advancement.
The authors tackled the challenge of solving high-dimensional physics-informed neural network problems and achieved an order of magnitude improvement in accuracy. Their compleX-PINN model consistently showed substantially greater precision than existing methods.
We propose compleX-PINN, a novel physics-informed neural network (PINN) architecture incorporating a learnable activation function inspired by the Cauchy integral theorem. By optimizing the activation parameters, compleX-PINN achieves high accuracy with just a single hidden layer. Empirically, we demonstrate that compleX-PINN solves high-dimensional problems that pose significant challenges for PINNs. Our results show that compleX-PINN consistently achieves substantially greater precision, often improving accuracy by an order of magnitude, on these complex tasks.