Deeper-PINNs: Unlocking the power of deep physics-informed neural networks

Jiang, F. and Hou, X. and Ye, J. and Xia, M. (2025) Deeper-PINNs: Unlocking the power of deep physics-informed neural networks. Applied Soft Computing, 185 (B): 114048. ISSN 1568-4946

Abstract

Physics-Informed Neural Networks (PINNs) have emerged as a promising framework for solving partial differential equations (PDEs) and have garnered significant attention across industrial and scientific domains. However, their effectiveness is often constrained by limited approximation capacity and performance degradation in deep network structures. In this work, we propose the Deeper Physics-Informed Neural Network (Deeper-PINN), a novel architecture designed to address these challenges. The Deeper-PINN incorporates element-wise multiplication operations into the PINN structure, which effectively mitigates the initialization pathologies of PINNs and enables the utilization of deeper network structures. Additionally, this operation projects features into high-dimensional, nonlinear spaces, thereby enhancing the approximation capacity of PINNs. The proposed architecture is evaluated on multiple benchmark problems, demonstrating that Deeper-PINNs can effectively leverage deep neural network structures while maintaining high parameter efficiency. The complete codes of the experiments can be found on https://github.com/flongjiang/Deeper-PINNs