The parametric greedy latent space dynamics identification (gLaSDI) framework
has demonstrated promising potential for accurate and efficient modeling of
high-dimensional nonlinear physical systems. However, it remains challenging to
handle noisy data. To enhance robustness against noise, we incorporate the
weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed
weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained
simultaneously to discover intrinsic nonlinear latent-space dynamics of
high-dimensional data. Compared to the standard sparse identification of
nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction
and robust latent space discovery, therefore leading to more accurate and
efficient reduced-order modeling. Furthermore, the greedy physics-informed
active learning in WgLaSDI enables adaptive sampling of optimal training data
on the fly for enhanced modeling accuracy. The effectiveness of the proposed
framework is demonstrated by modeling various nonlinear dynamical problems,
including viscous and inviscid Burgers' equations, time-dependent radial
advection, and the Vlasov equation for plasma physics. With data that contains
5-10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude,
achieving 1-7% relative errors. Compared with the high-fidelity models, WgLaSDI
achieves 121 to 1,779x speed-up.

通过将弱形式非线性动力学（WENDy）引入 gLaSDI 的框架，我们提出了具有自适应采样特性的 WgLaSDI 框架，它能够更准确和高效地建模高维非线性物理系统，并且在处理噪声数据时具备稳健性。