Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). This work focuses on the large class of physical systems that can be well described by models with quadratic nonlinear terms and proposes a regularizer for operator inference that induces a stability bias onto quadratic models. The proposed regularizer is physics informed in the sense that it penalizes quadratic terms with large norms and so explicitly leverages the quadratic model form that is given by the underlying physics. This means that the proposed approach judiciously learns from data and physical insights combined, rather than from either data or physics alone. Additionally, a formulation of operator inference is proposed that enforces model constraints for preserving structure such as symmetry and definiteness in the linear terms. Numerical results demonstrate that models learned with operator inference and the proposed regularizer and structure preservation are accurate and stable even in cases where using no regularization or Tikhonov regularization leads to models that are unstable.
翻译:操作员推断从高维物理系统的轨迹(非侵入性模型减少)中,以多维非线性术语学习低维动态系统模型。这项工作侧重于一大批物理系统,这些系统可以由带有二次非线性术语的模型很好地描述,并提议为操作员推断提供一个常规化器,使四端模型产生稳定性偏向。拟议的常规化器是物理学,因为它以大规范惩罚四方术语,从而明确利用基础物理学提供的四方模型形式。这意味着拟议方法明智地学习数据和物理洞察相结合,而不是仅仅从数据或物理中学习。此外,还提出了操作员推论的提法,以强制实施模型限制,以维护结构,如线性术语的对称和确定性。数字结果表明,即使没有使用正规化或Tikhonov的正规化导致模型不稳定,与操作员推断和拟议正规化和结构保持所学的模型也是准确和稳定的。