Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction such as Proper Orthogonal Decomposition, however, such methods can become inefficient or fail in the case of parameteric or strongly nonlinear models. Such limitations are usually tackled via a library of local reduction bases each of which being valid for a given parameter vector. The success of such methods, however, is strongly reliant upon the method used to relate the parameter vectors to the local bases, this is typically achieved using clustering or interpolation methods. We propose the replacement of these methods with a Variational Autoencoder (VAE) to be used as a generative model which can infer the local basis corresponding to a given parameter vector in a probabilistic manner. The resulting VAE-boosted parametric ROM \emph{VpROM} still retains the physical insights of a projection-based method but also allows for better treatment of problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty.

翻译：降阶模型在计算时间存在困难的众多工程领域中具有重要意义。既定方法采用基于投影的降阶技术，如本征正交分解，然而此类方法在处理参数化或强非线性模型时可能效率低下甚至失效。此类局限性通常通过构建局部降阶基库来应对，每个基向量适用于特定参数向量。然而，这类方法的成功强烈依赖于将参数向量与局部基关联的方法，通常采用聚类或插值技术实现。我们提出以变分自编码器替代这些方法，将其作为生成模型，能够以概率方式推断给定参数向量对应的局部基。由此产生的VAE增强参数化降阶模型VpROM既保留了投影方法的物理洞察力，又能更好地处理模型依赖性或激励特征导致动态行为跨越多个响应区域的问题。此外，VAE表示的概率性处理允许对降阶基进行不确定性量化，并可进一步传播至降阶模型响应。该方法的性能通过一个包含迟滞和多参数依赖性的开源仿真基准测试，以及一个具有非线性材料行为与模型不确定性的大型风力发电机塔筒实例得到验证。