Complex Physics-Informed Neural Network

TL;DR

This paper introduces compleX-PINN, a novel physics-informed neural network architecture with learnable activation functions, achieving high accuracy and solving high-dimensional problems more effectively than traditional PINNs.

Contribution

The paper presents a new PINN architecture with learnable activation functions inspired by complex analysis, enabling high accuracy with a single hidden layer.

Findings

Achieves significantly higher accuracy on complex, high-dimensional problems.

Improves precision by an order of magnitude over existing PINN methods.

Successfully solves challenging high-dimensional PDE problems.

Abstract

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.