(674b) Indirect Parameter Estimation of Dynamic Mechanistic Models via Hybrid and Neural Differential Equations.

Continued improvement to data-driven algorithms has led to a growing list of data-driven-driven solutions to real-world problems, including applications for material characterization, image recognition and discovery of novel chemical compounds. [1, 2] Many of these applications can be characterized by ‘static’ conditions. However, in process systems engineering the applications are more often ‘dynamic’, requiring models to accurately predict process performance under time-varying conditions. For such applications, data-driven approaches have been less robust due to their limited interpretability and failure to observe known physical laws, especially for conditions not considered in model training. Thus, modeling efforts in these domains rely primarily on building mechanistic models based on first principles, which can be a time and labor-intensive process. A union of mechanistic and data-driven modeling techniques (hybrid modeling, HM), has been proposed that can enhance model interpretability while greatly accelerating the model-development process. [3] Unlike purely data-driven methods, HM has yet to become a standard tool for many who could benefit from its accelerated workflow. This is partially due to the lack of automated, computationally efficient tools, enabling practitioners to use hybrid methods at a high level. Moreover, several competing frameworks make identifying which framework is optimal for a given system difficult.

In this presentation a framework is proposed for integrating data-driven models with mechanistic constraints for problems with the following characteristics: (1) nonlinear dynamic systems without steady state assumptions, (2) unknown mechanisms, and (3) incomplete and noisy data. We demonstrate how open-source software for automated parameter estimation, such as checkpointing, automated differentiation and adaptivity enable faster development of HMs. We weigh the merits of approaches that estimate parameters of the data-driven coupled with and without physical constraints. For methods coupling physical constraints, a formulation based on forward sensitivity equations is often used. [4] In contrast, in light of recent work [5], we investigate a backward adjoint-based formulation for enforcing physical constraints during model fitting. Through this comparison we demonstrate how the choice of numerical formulation plays an important role in the size and number of relationships that can be modeled via a hybrid framework. Advantages and limitations of hybrid frameworks will be identified with the aim of enabling practitioners to integrate hybrid workflows to answer domain-specific questions for applications common in (bio)chemical process engineering, such as reaction analysis, model-based optimization, and adaptive design of experiments.

References

1. Himanen, L., et al., Data-Driven Materials Science: Status, Challenges, and Perspectives. Advanced Science, 2019. 6(21): p. 1900808.
2. Venkatasubramanian, V., The promise of artificial intelligence in chemical engineering: Is it here, finally? AIChE Journal, 2019. 65(2): p. 466-478.
3. von Stosch, M., et al., Hybrid semi-parametric modeling in process systems engineering: Past, present and future. Computers & Chemical Engineering, 2014. 60: p. 86-101.
4. Oliveira, R., Combining first principles modelling and artificial neural networks: a general framework. Computers & Chemical Engineering, 2004. 28(5): p. 755-766.
5. Rackauckas, C., et al. Universal Differential Equations for Scientific Machine Learning. arXiv e-prints, 2020. arXiv:2001.04385.