标题： 动态系统的可扩展非线性流形降阶模型 显示英文标题

标题： Scalable nonlinear manifold reduced order model for dynamical systems

摘要： 域分解（DD）非线性流形降阶模型（NM-ROM）是一种计算高效的将底层物理原理整合到基于神经网络的数据驱动方法中的方法。 与线性子空间方法相比，NM-ROM具有更高的表达能力和增强的重构能力，而DD通过将域划分为代数子域，实现了成本效益高、并行训练自编码器。 在本工作中，我们通过实施一种“自下而上”的策略来研究该方法的可扩展性：在较小的域上训练NM-ROM，然后将其部署到更大的、可组合的域上。 该方法应用于二维时间依赖的Burgers方程表明，从较小的域外推到较大的域是稳定且有效的。 该方法在相对误差方面达到了1%的精度，并提供了近700倍的显著加速。 显示英文摘要

摘要： The domain decomposition (DD) nonlinear-manifold reduced-order model (NM-ROM) represents a computationally efficient method for integrating underlying physics principles into a neural network-based, data-driven approach. Compared to linear subspace methods, NM-ROMs offer superior expressivity and enhanced reconstruction capabilities, while DD enables cost-effective, parallel training of autoencoders by partitioning the domain into algebraic subdomains. In this work, we investigate the scalability of this approach by implementing a "bottom-up" strategy: training NM-ROMs on smaller domains and subsequently deploying them on larger, composable ones. The application of this method to the two-dimensional time-dependent Burgers' equation shows that extrapolating from smaller to larger domains is both stable and effective. This approach achieves an accuracy of 1% in relative error and provides a remarkable speedup of nearly 700 times.