Can Machine Learning Identify Governing Laws For Dynamics in Complex Engineered Systems ? : A Study in Chemical Engineering

Machine learning recently has been used to identify the governing equations for dynamics in physical systems. The promising results from applications on systems such as fluid dynamics and chemical kinetics inspire further investigation of these methods on complex engineered systems. Dynamics of these systems play a crucial role in design and operations. Hence, it would be advantageous to learn about the mechanisms that may be driving the complex dynamics of systems. In this work, our research question was aimed at addressing this open question about applicability and usefulness of novel machine learning approach in identifying the governing dynamical equations for engineered systems. We focused on distillation column which is an ubiquitous unit operation in chemical engineering and demonstrates complex dynamics i.e. it's dynamics is a combination of heuristics and fundamental physical laws. We tested the method of Sparse Identification of Non-Linear Dynamics (SINDy) because of it's ability to produce white-box models with terms that can be used for physical interpretation of dynamics. Time series data for dynamics was generated from simulation of distillation column using ASPEN Dynamics. One promising result was reduction of number of equations for dynamic simulation from 1000s in ASPEN to only 13 - one for each state variable. Prediction accuracy was high on the test data from system within the perturbation range, however outside perturbation range equations did not perform well. In terms of physical law extraction, some terms were interpretable as related to Fick's law of diffusion (with concentration terms) and Henry's law (with ratio of concentration and pressure terms). While some terms were interpretable, we conclude that more research is needed on combining engineering systems with machine learning approach to improve understanding of governing laws for unknown dynamics.