MTN-PINN: integrating multi-dimensional Taylor network with physics-informed neural networks for solving nonlinear partial differential equations

Automatic differentiation might bring about numerical instability in the solution of partial differential equations (PDEs). Therefore, to address this challenge, an MTN-PINN framework is proposed, which brings about the integration of the Multi-dimensional Taylor Network (MTN) and the Physics-Informed Neural Network (PINN). The proposed architecture, with higher-order polynomial expansion incorporated into the network, allows the network to effectively represent local information related to higher-order derivatives. Additionally, the analytical differentiation and automatic differentiation combination of the framework helps solve the gradient vanishing and gradient explosion issues, which are common with higher-order differential equations. The results reveal that the MTN-PINN model presents better precision in comparison to the conventional PINN method. In addition, the model presents better capability in the precise solution of coupled PDEs, which involve velocity-pressure fields. This reveals the capability of the MTN-PINN framework in the precise solution of nonlinear PDEs, which are usually associated with strong coupling effects and high-order derivative terms.

International Conference on AI and Engineering (AI+E 2026)