Physics‐Informed Active Learning With Simultaneous Weak‐Form Latent Space Dynamics Identification

Abstract

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 with 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 1779 speed‐up.