Physics-Enhanced Neural Ordinary Differential Equations: Application to Industrial Chemical Reaction Systems

Abstract

Ordinary differential equations (ODEs) are extremely important in modeling dynamic systems, such as chemical reaction networks. However, many challenges exist for building ODEs to describe such systems accurately, which often requires careful experimentation and domain expertise. Recent advances for solving so-called inverse kinetic modeling problems have focused on the use of new data-driven methods that account for the physical structure of the governing equations, including physics-informed neural networks (PINNs), sparse identification of nonlinear dynamical systems (SINDy), and neural ODEs (NODEs). This work focuses on the NODE framework due to its ability to straightforwardly account for parameter dependencies, partial state observations, and sparse and nonuniform measurements over time. Specifically, we introduce a framework referred to as “physics-enhanced NODEs” that enables a combination of partially known mechanistic models with universal surrogate approximators, which enables scientific-based learning from limited datasets. We further specialize this framework for kinetic models, introducing r-NODE and k-NODE structures that utilize stoichiometric and reaction rate information, respectively, to improve the learning and extrapolation capabilities of the model in chemical reaction systems. The physics-enhanced NODE framework is tested on multiple case studies including real-world experimental datasets collected on complex multiphase reaction systems. Our results indicate that the type of accuracy of the supplied prior information has a significant impact on the performance of the NODE; however, the flexibility of the framework (combined with computationally efficient training protocols) enables the discovery of ODEs capable of outperforming expert-trained models at a fraction of the cost.