论文标题
经过认证的数据驱动物理知识的贪婪自动编码器模拟器
Certified data-driven physics-informed greedy auto-encoder simulator
论文作者
论文摘要
开发了一个参数自适应贪婪潜在空间动态标识（GLASDI）框架，以实现高维非线性动力学系统的准确，高效和经过数据驱动的数据驱动的物理学意识到的贪婪的自动编码器模拟器。在提出的框架中，对自动编码器和动态标识模型进行了交互训练，以发现内在和简单的潜在空间动力学。为了有效地探索最佳模型性能的参数空间，引入了与物理信息误差指示器集成的自适应贪婪采样算法，以搜索即时搜索最佳的训练样本，胜过传统预定义的均匀均匀采样。此外，采用了有效的K-Nearthen最邻居凸插值方案来利用局部潜在空间动力学，以提高可预测性。数值结果表明，所提出的方法在径向对流和2D汉堡动态问题的相对误差中达到了121至2,658倍的速度。
A parametric adaptive greedy Latent Space Dynamics Identification (gLaSDI) framework is developed for accurate, efficient, and certified data-driven physics-informed greedy auto-encoder simulators of high-dimensional nonlinear dynamical systems. In the proposed framework, an auto-encoder and dynamics identification models are trained interactively to discover intrinsic and simple latent-space dynamics. To effectively explore the parameter space for optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed error indicator is introduced to search for optimal training samples on the fly, outperforming the conventional predefined uniform sampling. Further, an efficient k-nearest neighbor convex interpolation scheme is employed to exploit local latent-space dynamics for improved predictability. Numerical results demonstrate that the proposed method achieves 121 to 2,658x speed-up with 1 to 5% relative errors for radial advection and 2D Burgers dynamical problems.
