Long-time Simulation of Stiff Chemical Kinetics Using Conservation-constrained Physics-informed Neural Network

Long-term simulation of Partial Differential Equations (PDEs) holds significant applications across various fields, including space physics and atmospheric science. Conventional numerical techniques, such as the finite difference, finite element, and finite volume methods have been extensively employed to solve PDEs across various disciplines. However, these methods often struggle with dimensional curse and complex geometry. In recent years, Physics-Informed Neural Network (PINN), which integrates physical laws within deep learning frameworks, has emerged as a powerful alternative for solving PDEs. Since PINN and its variants are mesh-free, they can avoid dimensional curse to a certain degree. Nonetheless, deep learning related approaches frequently encounter optimization challenges, particularly when applied to multi-time scale issues such as stiff chemical kinetics equations, which involve multiple reactions with different rates, leading to both fast and slow dynamics coexisting. To address these issues, this study introduces a novel Conservation-Constrained Physics-Informed Neural Network (CC-PINN) approach. This method combines shared-branch networks with a segmented sampling strategy. First, the shared-branch networks can effectively deal with coupling equations and reduce the difficulties during the optimization of neural networks. On the other hand, the conservation constraint is embedded into the loss function, ensuring the conservation of physical laws and the accuracy of the simulation results, which significantly improves the performance of PINN. At the same time, according to the dynamics of chemical kinetics in different time intervals, the segmented sampling strategy is adopted, which further improves the accuracy and stability of long-term simulation. In addition, the influence of different expressions of conservation constraints has also been discussed. Experimental results clearly show that, by combining the shared-branch networks and segmented sampling strategy, the new proposed CC-PINN can accurately integrate the stiff chemical kinetics equations in a long-time scale. In summary, this research contributes a new tool for solving problems, such as collisionless plasma fluctuations and interstellar matter chemical reaction, in space science.