Enhancing Dynamical System Modeling through Interpretable Machine
  Learning Augmentations: A Case Study in Cathodic Electrophoretic Deposition
Christian Jacobsen Jiayuan Dong Mehdi Khalloufi Xun Huan Karthik Duraisamy Maryam Akram Wanjiao Liu
We introduce a comprehensive data-driven framework aimed at enhancing the
modeling of physical systems, employing inference techniques and machine
learning enhancements. As a demonstrative application, we pursue the modeling
of cathodic electrophoretic deposition (EPD), commonly known as e-coating. Our
approach illustrates a systematic procedure for enhancing physical models by
identifying their limitations through inference on experimental data and
introducing adaptable model enhancements to address these shortcomings. We
begin by tackling the issue of model parameter identifiability, which reveals
aspects of the model that require improvement. To address generalizability , we
introduce modifications which also enhance identifiability. However, these
modifications do not fully capture essential experimental behaviors. To
overcome this limitation, we incorporate interpretable yet flexible
augmentations into the baseline model. These augmentations are parameterized by
simple fully-connected neural networks (FNNs), and we leverage machine learning
tools, particularly Neural Ordinary Differential Equations (Neural ODEs), to
learn these augmentations. Our simulations demonstrate that the machine
learning-augmented model more accurately captures observed behaviors and
improves predictive accuracy. Nevertheless, we contend that while the model
updates offer superior performance and capture the relevant physics, we can
reduce off-line computational costs by eliminating certain dynamics without
compromising accuracy or interpretability in downstream predictions of
quantities of interest, particularly film thickness predictions. The entire
process outlined here provides a structured approach to leverage data-driven
methods. Firstly, it helps us comprehend the root causes of model inaccuracies,
and secondly, it offers a principled method for enhancing model performance.