In this paper, we propose a probabilistic physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM). The framework is especially targeted to the inference of the characteristics and latent structure of nonlinear dynamical systems from measurement data, where it is typically intractable to perform exact inference of latent variables. A recently surfaced option pertains to leveraging variational inference to perform approximate inference. In such a scheme, transition and emission functions of the system are parameterized via feed-forward neural networks (deep generative models). However, due to the generalized and highly versatile formulation of neural network functions, the learned latent space is often prone to lack physical interpretation and structured representation. To address this, we bridge physics-based state space models with Deep Markov Models, thus delivering a hybrid modelling framework for unsupervised learning and identification for nonlinear dynamical systems. The proposed framework takes advantage of the expressive power of deep learning, while retaining the driving physics of the dynamical system by imposing physics-driven restrictions on the side of the latent space. We demonstrate the benefits of such a fusion in terms of achieving improved performance on illustrative simulation examples and experimental case studies of nonlinear systems. Our results indicate that the physics-based models involved in the employed transition and emission functions essentially enforce a more structured and physically interpretable latent space, which is essential to generalization and prediction capabilities.
翻译:在本文中,我们提出了一个概率物理指导框架,称为物理引导深马可夫模型(PgDMM),这一框架特别着眼于从测量数据中推断非线性动态系统的特点和潜在结构,从测量数据中推断出非线性动态系统的特点和潜在结构,通常很难对潜在变量进行精确的推断。最近浮现的一个备选办法是利用变异推论来进行近似推导。在这样一个办法中,该系统的过渡和排放功能通过进料前神经网络(深基因模型)进行参数化。然而,由于神经网络功能的通用和高度灵活配置,所学的潜伏空间往往容易缺乏物理解释和结构代表。为了解决这一问题,我们把基于物理的状态空间模型与深马可夫模型联系起来,从而为非线性动态动态动态系统提供一种混合模型框架,利用深层学习的明示力量,同时保留动态系统的驱动物理学,同时对潜伏空间的侧面施加物理驱动限制。我们展示了这种以物理驱动力为基础的潜在网络空间模型的优点,从本质上将基于物理的预测性模型的模型和结构性模型的模型转化为分析结果,并用更精确的模型来说明我们所采用的实验性模型在改进的物理模型中应用中应用了一种实验性模型,在改进了一种实验性模型的模拟性模型的模型中,在改进了一种实验性模型的模型,并用来进行了一种基础的模型的模型的模拟的模型的模拟性分析。