Multiscale Physics-Informed Neural Networks for Stiff Chemical Kinetics

Abstract

In this paper, a multiscale physics-informed neural network (MPINN) approach is proposed based on the regular physics-informed neural network (PINN) for solving stiff chemical kinetic problems with governing equations of stiff ordinary differential equations (ODEs). In MPINNs, chemical species with different time scales are grouped and trained by multiple corresponding neural networks with the same structure. The adaptive weight based on a key performance indicator is assigned to each loss term when calculating the summation of loss residues. With this structure, MPINNs provide a framework to solve challenging stiff chemical kinetic problems without any stiffness-removal artifacts before training. In addition, by introducing a small number of ground truth data (GTD) points (less than 10% of the number required for residual loss calculation) and adding data loss terms into loss functions, MPINNs show superior ability to represent stiff ODE solutions at any desired time. The accuracy of MPINNs is tested with classical chemical kinetic problems, by comparing with the regular PINN and other state-of-the-art methods with special consideration for solving stiff chemical kinetic problems with PINNs. The validation results show that MPINNs can effectively avoid the influence of stiffness on neural network optimization. Compared with the traditional deep neural network only trained by GTD, MPINNs can use no data or a relatively small amount of data to achieve high-precision prediction of stiff chemical ODEs. The proposed approach is very promising for solving stiff chemical kinetics, opening up possibilities of MPINN application in different fields involving stiff chemical dynamics.

Scientific Deep Machine Learning Concepts for the Prediction of Concentration Profiles and Chemical Reaction Kinetics: Consideration of Reaction Conditions

“…It is therefore often not necessary to evaluate the concentrations for small time steps, which could lead to corresponding problems. In addition, the concepts of scaling as well as those presented in other studies 58 can help to overcome these problems, if necessary. Furthermore, it should be noted that stiffness problems in ODEs mainly arise in complex chemical reactions.…”

“…49,52 Noteworthily, PINNs were already used for the prediction of chemical reaction dynamics in terms of simple 57 and more advanced chemical reaction networks (CRNs). 58 A modification of standard PINNs for chemical reaction kinetics was also presented in ref 56. The detailed evaluation of rather complex chemical reactions showed certain limitations of PINNs that are related to the numerical and physical stiffness of the underlying CRN.…”

“…Noteworthily, PINNs were already used for the prediction of chemical reaction dynamics in terms of simple and more advanced chemical reaction networks (CRNs) . A modification of standard PINNs for chemical reaction kinetics was also presented in ref .…”

“…In more detail, stiffness usually results from the nonlinearity and complexity of the reaction network, where the characteristic timescales for species span a wide range. Accordingly, the authors have shown that the consideration of quasi-steady-state assumptions in the context of so-called stiff PINNs significantly improves the prediction accuracy. , Moreover, recent Bayesian approaches were also introduced to estimate the kinetic properties of reactions. In terms of such probabilistic approaches, the resulting calculations also provide reasonable estimates for the uncertainty of the kinetic outcomes .…”

LearnCK: mass conserving neural network reduction of chemistry and species of microkinetic models

“…ChemNODE, 44 a new type of NN named neural ordinary differential equations (NODEs), 45 is computationally efficient but has not been demonstrated for stiff systems. Physics-informed NN-based models (PINN) do not perform well for stiff ODEs; 46,47 alternatives such as stiff-PINN 48 and MPINN 46 were developed to alleviate stiffness. Stiff-PINN 48 reduces the system complexity by ignoring short-lived species with the quasi-steady-state approximation.…”