标题： 基于正交投影的正则化方法用于高效模型增强 显示英文标题

标题： Orthogonal projection-based regularization for efficient model augmentation

摘要： 基于深度学习的非线性系统辨识在实践中已显示出生成可靠且高度准确模型的能力。 然而，这些黑箱模型缺乏物理可解释性，而且学习过程中的相当一部分努力通常用于捕捉系统已经预期/已知的行为，这些行为可以通过物理学的第一性原理定律准确描述。 一个可能的解决方案是直接将这种先验物理知识整合到模型结构中，结合基于物理的建模和基于深度学习的辨识的优势。 最常用的方法是使用加法模型增强结构，其中基于物理的和机器学习（ML）组件并行连接，即相加方式。 然而，这样的模型参数过多，训练具有挑战性，可能导致基于物理的部分失去可解释性。 为克服这一挑战，本文提出了一种基于正交投影的正则化技术，以提高基于学习的非线性基线模型增强中的参数学习甚至模型精度。 显示英文摘要

摘要： 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.