使用自适应采样投影的混沌多尺度问题预测降阶建模
Predictive Reduced Order Modeling of Chaotic Multi-scale Problems Using Adaptively Sampled Projections
AI总结：
本文提出一种基于自适应采样投影的降阶模型，通过在线逐时间步调整基函数并引入非局部信息，实现对混沌、多尺度及对流主导问题的高效准确预测。
摘要：
本文提出了一种基于自适应投影的降阶模型（ROM）公式，用于对具有混沌和对流主导物理特性的问题进行模型降阶。我们构建了一种高效方法，在在线执行的每个时间步上自适应地调整基函数，以考虑未解析的动力学。该自适应ROM在最小二乘框架下建立，并采用变量变换以提升稳定性和鲁棒性。我们开发了一种高效策略，将非局部信息纳入基函数自适应中，显著增强了所得ROM的预测能力。文中给出了计算复杂度的详细分析并进行了验证。研究表明，该自适应ROM公式所需的离线训练可以忽略不计，并且天然支持未来状态预测和参数化预测。该公式在代表性的反应流基准问题上进行了评估，结果表明这些ROM能够提供高效且准确的预测，包括涉及因参数变化和瞬态现象而导致动力学发生显著变化的情况。本工作的一个关键贡献是开发并展示了一种全面的ROM公式，该公式以混沌、多尺度和输运主导问题中的预测能力为目标。
英文摘要：
An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step of the on-line execution to account for the unresolved dynamics. The adaptive ROM is formulated in a Least-Squares setting using a variable transformation to promote stability and robustness. An efficient strategy is developed to incorporate non-local information in the basis adaptation, significantly enhancing the predictive capabilities of the resulting ROMs. A detailed analysis of the computational complexity is presented, and validated. The adaptive ROM formulation is shown to require negligible offline training and naturally enables both future-state and parametric predictions. The formulation is evaluated on representative reacting flow benchmark problems, demonstrating that the ROMs are capable of providing efficient and accurate predictions including those involving significant changes in dynamics due to parametric variations, and transient phenomena. A key contribution of this work is the development and demonstration of a comprehensive ROM formulation that targets predictive capability in chaotic, multi-scale, and transport-dominated problems.
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