标题： 基于随机Koopman正交分解和可解释深度学习的非线性PDE降阶数据驱动双模型 显示英文标题

标题： Reduced Order Data-driven Twin Models for Nonlinear PDEs by Randomized Koopman Orthogonal Decomposition and Explainable Deep Learning

摘要： 本研究引入了一种基于现代Koopman算子理论的数据驱动孪生建模框架，通过以较低的复杂度准确捕捉非线性动力学而无需手动参数调整，相较于经典模态分解有了显著进步。 该方法结合了一种新算法与Pareto前沿分析，构建了一个紧凑且高保真的降阶模型，平衡了准确性与效率。 一个可解释的NLARX深度学习框架实现了实时、自适应的校准与预测，而一个关键创新——通过随机正交投影计算正交Koopman模式——确保了最优的数据表示。 这种数据驱动的孪生建模方法是完全自洽的，避免了启发式选择，并通过集成可解释的学习技术增强了可解释性。 所提出的方法在冲击波现象中进行了验证，包括三个复杂度逐渐增加的实验，并对生成的数据驱动孪生模型进行了定性分析。 显示英文摘要

摘要： This study introduces a data-driven twin modeling framework based on modern Koopman operator theory, offering a significant advancement over classical modal decomposition by accurately capturing nonlinear dynamics with reduced complexity and no manual parameter adjustment. The method integrates a novel algorithm with Pareto front analysis to construct a compact, high-fidelity reduced-order model that balances accuracy and efficiency. An explainable NLARX deep learning framework enables real-time, adaptive calibration and prediction, while a key innovation-computing orthogonal Koopman modes via randomized orthogonal projections-ensures optimal data representation. This approach for data-driven twin modeling is fully self-consistent, avoiding heuristic choices and enhancing interpretability through integrated explainable learning techniques. The proposed method is demonstrated on shock wave phenomena using three experiments of increasing complexity, accompanied by a qualitative analysis of the resulting data-driven twin models.