A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. An interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for the optimal training samples on the fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, a k-nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 17 to 2,658x speed-up with 1 to 5% relative errors.

翻译：本文提出了一种参数化自适应物理驱动贪心潜在空间动力学识别（gLaSDI）方法，用于对高维非线性动力系统进行准确、高效且鲁棒的数据驱动降阶建模。在提出的gLaSDI框架中，自编码器发现高维数据的内在非线性潜在表示，而动力学识别（DI）模型捕获局部潜在空间动力学。采用交互式训练算法训练自编码器和局部DI模型，能够识别简单的潜在空间动力学，并提高数据驱动降阶建模的准确性和效率。为了最大化并加速探索参数空间以实现最优模型性能，引入了一种结合物理信息残差误差指标和随机子集评估的自适应贪心采样算法，动态搜索最优训练样本。此外，为了利用局部DI模型捕获的局部潜在空间动力学，在参数空间中以最少数量的局部DI模型提高建模精度，采用了k近邻凸插值方案。通过建模各种非线性动力学问题（包括Burgers方程、非线性热传导和径向对流），验证了所提出框架的有效性。所提出的自适应贪心采样在精度上优于传统的预定义均匀采样。与高保真模型相比，gLaSDI实现了17到2,658倍的加速，相对误差仅为1%到5%。