Despite the sudden rise of AI, it still leaves a question mark to many newcomers on its widespread adoption as it exhibits a lack of robustness and interpretability. For instance, the insufficient amount of training data usually hinders its performance due to the lack of generalization, and the black box nature of deep neural networks does not allow for a precise explanation behind its mechanism preventing a new scientific discovery. Such limitations have led to the development of several branches of deep learning one of which include physics-informed neural networks that will be covered in the rest of this paper. In this overview, we defined the general concept of informed deep learning followed by an extensive literature survey in the field of dynamical systems. We hope to make a contribution to our mechanical engineering community by conveying knowledge and insights on this emerging field of study through this survey paper.

尽管AI突然兴起，但由于它缺乏鲁棒性和可解释性，因此它在广泛采用方面仍然给许多新手留下了问号。例如，训练数据量不足通常会由于缺乏通用性而阻碍其性能，而深度神经网络的黑匣子性质无法对其防止新科学发现的机制进行精确解释。这种局限性导致了深度学习的几个分支的发展，其中一个分支将包括物理信息神经网络，本文的其余部分将对此进行介绍。在本概述中，我们定义了知情深度学习的一般概念，然后在动力学系统领域进行了广泛的文献调查。