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

TL;DR

This study investigates the use of machine learning, specifically SINDy, to identify governing equations in complex chemical engineering systems like distillation columns, aiming to create interpretable models that capture system dynamics.

Contribution

It demonstrates the application of SINDy to distillation column data, reducing complex models to a few interpretable equations, and assesses the method's effectiveness in physical law extraction.

Findings

Reduced model equations from thousands to 13 for distillation dynamics

High prediction accuracy within perturbation range

Some identified terms align with known physical laws like Fick's and Henry's laws

Abstract

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.