An exact constraint strategy for solving stiff chemical kinetics based on physics-informed neural network

Abstract Stiff chemical kinetics plays a crucial role in various disciplines, including atmospheric chemistry, environmental engineering, and combustion science. In this work, we focus on the ROBER problem, a typical stiff system characterized by a set of strongly coupled ordinary differential equations (ODEs). The system’s stiffness arises from the coexistence of ultrafast reactions and slow dynamics, which poses computational challenges to numerical stability and accuracy. Recently, Physics-Informed Neural Networks (PINN), a deep learning based framework, has been widely applied to solve various partial differential equations. However, the standard PINN faces optimization difficulties in multi-scale, strongly nonlinear systems like the ROBER problem. To address this problem, we propose a new strategy called Exact-Constraint PINN (EC-PINN), which integrates conservation law as exact constraint directly into the loss function, enforcing rigorous conservation throughout the training procedure. Based on this framework, we introduce pure exact conservation approaches (with two formulations differing in the treatment of indirect variables) and a hybrid strategy applying soft constraint on the conservation law during the training procedure. Numerical experiments show that the hybrid approach achieves higher accuracy than pure methods and prior soft constraint approach, crucially preserving the conservation law. We also calculate the correlation coefficients among relative error, loss function and its gradient. Analysis reveals a strong correlation between relative error and loss function, validating loss minimization for solving PDEs. In summary, our EC-PINN presents a novel and effective approach for solving stiff chemical kinetics problems, offering improved computational reliability and physical consistency.