  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.
