用正交投影正则化，让物理先验与神经网络协同学习更高效。
Orthogonal projection-based regularization for efficient model augmentation
- 通过正交投影约束模型参数，实现物理先验与数据驱动部分的解耦优化
- 在非线性系统辨识中提升模型精度，同时保持物理可解释性
- 适合需要融合物理规律的工业建模场景，尤其关注可解释性的研究者
基于深度学习的非线性系统辨识已在实践中展现出高可靠性和高精度。然而，这些黑箱模型缺乏物理可解释性，且大量学习资源被用于捕捉已知的系统行为——这类行为可通过物理第一性原理准确描述。一种潜在解决方案是将此类先验物理知识直接嵌入模型结构，融合物理建模与数据驱动识别的优势。最常见的方法是采用加法式模型增强结构，即物理模型与机器学习（ML）组件并联相加。但此类模型存在参数冗余问题，训练困难，可能导致物理部分失去可解释性。为此，本文提出一种基于正交投影的正则化技术，以提升学习型增强模型中的参数学习效率，甚至提高整体模型精度。
原文摘要 · Abstract (English)
Deep-learning-based nonlinear system identification has shown the ability to produce reliable and highly accurate models in practice. However, these black-box models lack physical interpretability, and a considerable part of the learning effort is often spent on capturing already expected/known behavior of the system, that can be accurately described by first-principles laws of physics. A potential solution is to directly integrate such prior physical knowledge into the model structure, combining the strengths of physics-based modeling and deep-learning-based identification. The most common approach is to use an additive model augmentation structure, where the physics-based and the machine-learning (ML) components are connected in parallel, i.e., additively. However, such models are overparametrized, training them is challenging, potentially causing the physics-based part to lose interpretability. To overcome this challenge, this paper proposes an orthogonal projection-based regularization technique to enhance parameter learning and even model accuracy in learning-based augmentation of nonlinear baseline models.
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