(363g) Data Driven Discovery of Chemical Reaction Kinetics

Traditional physics-based kinetic modeling of a chemical reaction system requires a functional form to
represent the rate of change of the chemical species involved and the unknown kinetic model parameters
are estimated using the experimental data. Using the neural ODEs approach precludes the need for expert
knowledge in identifying prior knowledge for physics-based kinetic models (1). Furthermore, modeling
the time-series data using neural ODEs enables handling of both irregularly and incomplete sampled data
which is not possible with traditional neural network modeling, such as recurrent neural networks (3).
Additionally, the implementation of neural ODEs models can be made efficient by taking advantage of
modern ODE solvers and adjoint methods available in the recently developed differential programming
package of DifferentialEquations.jl written in Julia language (4).

The first representative system investigated in this work is a reaction system consisting of three irre-
versible, elementary liquid phase reactions in an isothermal batch reactor. This reaction network com-
prises five chemical species labeled as [A, B, C, D, E] that react through the consecutive and parallel
reactions shown in Eq. 1.
A + B → C
C → 2 E
2 A → D (1)
The training dataset for the neural ODEs is synthetically generated by simulating the system of ODEs and
comprises of data points sampled at t = [0, 0.5, 1, 2, 10] minutes. The loss function for training is optimized
using the stochastic gradient descent ADAM optimizer. The predicted component concentrations compare
well with the simulated data (see Figure 1).

The use of neural ODEs to describe a dynamical system is also useful in the development of mathematical
models for biomass pyrolysis. We further apply the neural ODEs to establish a model for pyrolysis of wood
and compare results with the model proposed by Thurner and Mann (5). In this model, the biomass
is decomposed during primary reactions to produce non-condensable, bio-oil, and bio-char products.
Subsequently, the condensable phase is converted to char and light gas by secondary reactions as depicted
in Figure 2. Thurner et al. proposed all these reactions are treated as pseudo-first order reactions.
The kinetic parameters and predicted product compositions from neural ODEs modeling are compared
with the reported experimental measurements. The results show that neural ODEs are a robust tool
to integrate partial prior knowledge with experimental data which allows development of accurate and
predictive hybrid models for real-world complex processes.

References
[1] C. Rackauckas, Y. Ma, J. Martensen, C. Warner, K. Zubov, R. Supekar, D. Skinner, A. Ramadhan, and
A. Edelman, “Universal Differential Equations for Scientific Machine Learning,” pp. 1–55, 2020.
[2] C. Rackauckas, M. Innes, Y. Ma, J. Bettencourt, L. White, and V. Dixit, “DiffEqFlux.jl - A Julia Library for
Neural Differential Equations,” pp. 1–17, 2019.
[3] R. T. Q. Chen, Y. Rubanova, J. Bettencourt, and D. K. Duvenaud, “Neural Ordinary Differential Equations,”
in Advances in Neural Information Processing Systems (S. Bengio, H. Wallach, H. Larochelle, K. Grauman,
N. Cesa-Bianchi, and R. Garnett, eds.), vol. 31, Curran Associates, Inc., 2018.
[4] C. Rackauckas and Q. Nie, “DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving
Differential Equations in Julia,” Journal of Open Research Software, vol. 5, 2017.
[5] F. Thurner and U. Mann, “Kinetic Investigation of Wood Pyrolysis,” Industrial and Engineering Chemistry
Process Design and Development, vol. 20, no. 3, pp. 482–488, 1981.