Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics

Area of Science:

• Computational Chemistry
• Chemical Engineering
• Applied Mathematics

Background:

• Physics-informed neural networks (PINNs) integrate physical laws into neural network training.
• PINNs have shown success in various scientific and engineering fields by satisfying governing equations.

Purpose of the Study:

• To investigate the performance of PINNs in solving stiff chemical kinetic problems governed by stiff ordinary differential equations (ODEs).
• To address the challenges encountered by PINNs when applied to stiff ODE systems.

Main Methods:

• Investigated the direct application of PINNs to stiff chemical kinetic systems.
• Employed the quasi-steady-state assumption (QSSA) to simplify stiff ODE systems.
• Applied PINNs to the modified, non-/mild-stiff systems derived using QSSA.

Main Results:

• Standard PINNs face significant challenges when applied to stiff chemical kinetic ODE systems.
• The quasi-steady-state assumption (QSSA) effectively reduces the stiffness of these ODE systems.
• PINNs successfully solved the chemical kinetic problems after stiffness reduction via QSSA.

Conclusions:

• Stiffness in governing equations is a primary reason for PINN failure in stiff chemical kinetic systems.
• The developed stiff-PINN approach, incorporating QSSA, enables successful application of PINNs to stiff chemical kinetics.
• This method extends the applicability of PINNs to reaction-diffusion systems with stiff dynamics.