Hybrid acceleration techniques for the physics-informed neural networks: a comparative analysis

Physics-informed neural networks (PINN) has emerged as a promising approach for solving partial differential equations (PDEs). However, the training process for PINN can be computationally expensive, limiting its practical applications. To address this issue, we investigate several acceleration techniques for PINN that combine Fourier neural operators, separable PINN, and first-order PINN. We also propose novel acceleration techniques based on second-order PINN and Koopman neural operators. We evaluate the efficiency of these techniques on various PDEs, and our results show that the hybrid models can provide much more accurate results than classical PINN under time constraints for the training, making PINN a more viable option for practical applications. The proposed methodology in the manuscript is generic and can be extended on a larger set of problems including inverse problems.