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.

Xiaolong He

April Tran

David M. Bortz

Youngsoo Choi

International Journal for Numerical Methods in Engineering

《国际工程数值方法杂志》发表了原创论文，描述了适用于工程问题的数值方法的重大、新颖的发展。该杂志以欢迎在计算工程广泛领域的贡献而闻名，包括模型简化中的计算问题，不确定性量化、验证和确认、逆分析和随机方法、优化、元素技术、求解技术和并行计算、损伤和断裂、微观和纳米尺度力学、低速流体动力学、流固耦合、电磁学、耦合扩散现象，以及误差估计和网格生成。需要强调的是，这绝不是一份详尽的清单，尤其欢迎有关多尺度、多物理或多学科问题以及新兴主题的论文。

The International Journal for Numerical Methods in Engineering publishes original papers that describe significant and novel developments in numerical methods applicable to engineering problems. The journal is known for welcoming contributions across a wide range of computational engineering fields, including computational issues in model simplification, uncertainty quantification, validation and verification, inverse analysis and stochastic methods, optimization, element techniques, solution techniques and parallel computing, damage and fracture, micromechanics and nanomechanics, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, as well as error estimation and mesh generation. It is important to emphasize that this is by no means an exhaustive list, and papers on multiscale, multiphysics, or interdisciplinary issues, as well as emerging topics, are especially encouraged.

《International Journal for Numerical Methods in Engineering》发表原创论文，介绍适用于工程问题的数值方法的重大和新颖发展。该杂志以欢迎计算工程广泛领域的贡献而闻名，包括模型简化中的计算问题、不确定性量化、验证与确认、逆分析和随机方法、优化、元素技术、求解技术与并行计算、损伤与断裂、微观和纳米尺度力学、低速流体动力学、流固耦合、电磁学、耦合扩散现象，以及误差估计和网格生成。需要强调的是，这并不是一份详尽的清单，尤其欢迎有关多尺度、多物理或多学科问题以及新兴主题的论文。

Category	Quartile
工程技术	3
工程技术, 工程综合	3
工程技术, 数学跨学科应用	3

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

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Category	Quartile
MATHEMATICS, INTERDISCIPLINARY APPLICATIONS	1