Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM construction, schemes that allow to retain a portion of the physics tend to enhance the interpretability and generalization of ROMs. However, physics-based techniques can adversely scale when dealing with nonlinear systems that feature parametric dependencies. This study introduces a generative physics-based ROM that is suited for nonlinear systems with parametric dependencies and is additionally able to quantify the confidence associated with the respective estimates. A main contribution of this work is the conditioning of these parametric ROMs to features that can be derived from monitoring measurements, feasibly in an online fashion. This is contrary to most existing ROM schemes, which remain restricted to the prescription of the physics-based, and usually a priori unknown, system parameters. Our work utilizes conditional Variational Autoencoders to continuously map the required reduction bases to a feature vector extracted from limited output measurements, while additionally allowing for a probabilistic assessment of the ROM-estimated Quantities of Interest. An auxiliary task using a neural network-based parametrization of suitable probability distributions is introduced to re-establish the link with physical model parameters. We verify the proposed scheme on a series of simulated case studies incorporating effects of geometric and material nonlinearity under parametric dependencies related to system properties and input load characteristics.

翻译：降阶模型（ROMs）作为计算密集型数字孪生模拟器的替代工具，在工程各领域发挥着重要作用。尽管存在纯数据驱动的ROM构建方法，但保留部分物理机制的方案往往能增强ROM的可解释性与泛化能力。然而，在处理具有参数依赖性的非线性系统时，基于物理的方法可能存在扩展性不足的问题。本研究提出一种适用于参数依赖非线性系统的生成式物理基ROM，该模型能够量化相关估计值的置信度。本工作的核心贡献在于将这些参数化ROM与可从监测测量中（通常以在线方式）提取的特征进行条件化关联，这与大多数现有ROM方案形成鲜明对比——后者通常局限于基于物理的系统参数设定（这些参数往往先验未知）。我们采用条件变分自编码器，将所需的降阶基连续映射到从有限输出测量中提取的特征向量，同时支持对ROM估计的关键量进行概率评估。通过引入基于神经网络的概率分布参数化辅助任务，重建了与物理模型参数的关联。我们在系列仿真案例中验证了所提方案，这些案例涵盖了系统特性与输入载荷特性相关参数依赖下的几何非线性和材料非线性效应。