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.

翻译：我们提出了一种综合数据驱动框架，旨在通过推理技术和机器学习增强方法来改进物理系统建模。作为示范应用，我们针对阴极电泳沉积（EPD，通常称为电泳涂装）进行建模。该方法通过实验数据推理识别物理模型的局限性，并引入可调模型增强以解决这些缺陷，系统性地阐述了改进物理模型的流程。首先，我们解决模型参数可辨识性问题，这揭示了模型中需要改进的方面。为提升泛化能力，我们引入了增强可辨识性的修改方案，但这些修改未能完全捕捉关键的实验行为。为克服这一局限，我们在基线模型中融入可解释且灵活的增强模块——这些模块通过简单的全连接神经网络（FNN）进行参数化，并利用机器学习工具（特别是神经常微分方程 Neural ODE）学习这些增强机制。仿真结果表明，机器学习增强模型能更准确地捕捉观测行为并提高预测精度。然而我们主张：尽管模型更新带来了更优性能并捕获了相关物理机制，但通过消除部分动力学过程（不影响下游预测目标量，尤其是膜厚预测的准确性与可解释性）可降低离线计算成本。本文所述完整流程提供了一种结构化数据驱动方法：首先帮助理解模型误差的根本原因，其次提供提升模型性能的原则性策略。