经过认证的数据驱动的物理信息贪婪自动编码器模拟器
Certified data-driven physics-informed greedy auto-encoder simulator
摘要：
一个参数自适应贪婪潜在空间动力学识别（gLaSDI）框架的准确，高效，和认证的数据驱动的物理通知贪婪自动编码器模拟器的高维非线性动力系统。在所提出的框架中，自动编码器和动态识别模型进行交互式训练，以发现内在的和简单的潜在空间动态。为了有效地探索最佳模型性能的参数空间，引入了一种自适应贪婪采样算法，该算法集成了物理信息误差指示器，以在飞行中搜索最佳训练样本，优于传统的预定义均匀采样。此外，一个有效的k-最近邻凸插值方案，利用本地潜在的空间动态提高可预测性。数值结果表明，该方法实现了121到2,658倍的速度，相对误差为1%到5%的径向平流和二维Burgers动力学问题。
英文摘要：
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.
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