# Enhancing Dynamical System Modeling through Interpretable Machine Learning Augmentations: A Case Study in Cathodic Electrophoretic Deposition

arXiv: https://arxiv.org/abs/2401.08414 · HTML: https://mlsanity.com/paper/2401.08414/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 16 Jan 2024.

## Builds on (most cited first, 9 of 9)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Stabilized Neural Ordinary Differential Equations for Long-Time Forecasting of Dynamical Systems](https://mlsanity.com/paper/2203.15706/) (2022)
- [Boosting Variational Inference](https://mlsanity.com/paper/1611.05559/) (2016)
- [A practical tutorial on Variational Bayes](https://mlsanity.com/paper/2103.01327/) (2021)
- [Near-optimal control of dynamical systems with neural ordinary differential equations](https://mlsanity.com/paper/2206.11120/) (2022)

## Built on by (most cited first, 1 of 1)

- [Variational Bayesian Optimal Experimental Design with Normalizing Flows](https://mlsanity.com/paper/2404.13056/) (2024)

## Abstract (arXiv)

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.