Multiscale Physics-Informed Neural Networks for Stiff Chemical Kinetics

Area of Science:

• Computational Chemistry
• Chemical Engineering
• Applied Mathematics

Background:

• Stiff ordinary differential equations (ODEs) pose significant challenges in modeling chemical kinetics.
• Traditional numerical methods and standard physics-informed neural networks (PINNs) struggle with the stiffness inherent in these problems.
• Existing methods may require stiffness-removal pre-processing or large datasets.

Purpose of the Study:

• To propose a multiscale physics-informed neural network (MPINN) approach for solving stiff chemical kinetic problems.
• To enhance the accuracy and efficiency of neural network-based solutions for stiff ODEs.
• To demonstrate the capability of MPINNs to handle stiffness without pre-processing and with limited data.

Main Methods:

• Developed a multiscale physics-informed neural network (MPINN) framework.
• Grouped chemical species by time scales and assigned dedicated neural networks.
• Implemented adaptive loss term weighting based on performance indicators.
• Incorporated a small amount of ground truth data (GTD) through data loss terms.

Main Results:

• MPINNs successfully solved stiff chemical kinetic problems without stiffness-removal artifacts.
• The approach demonstrated superior accuracy in representing stiff ODE solutions, even with minimal GTD.
• MPINNs effectively mitigated the impact of stiffness on neural network optimization.
• Achieved high-precision predictions for stiff chemical ODEs using significantly less data than traditional methods.

Conclusions:

• MPINNs offer a robust and accurate framework for tackling challenging stiff chemical kinetics.
• The method reduces reliance on extensive ground truth data for stiff ODE problems.
• MPINNs show significant promise for applications in chemical dynamics and related fields.