同步进行弱形式潜在空间动力学辨识的物理信息主动学习
Physics-informed active learning with simultaneous weak-form latent space dynamics identification
AI总结：
提出 WgLaSDI 框架，将 WENDy 与自编码器同步训练并结合物理信息主动采样，提升含噪高维非线性动力学的降阶建模精度与效率。
摘要：
参数化贪婪潜在空间动力学辨识（gLaSDI）框架已在高维非线性物理系统的准确高效建模方面展现出良好潜力。然而，处理含噪数据仍具挑战性。为增强抗噪鲁棒性，我们将非线性动力学弱形式估计（WENDy）引入 gLaSDI。在所提出的弱形式 gLaSDI（WgLaSDI）框架中，autoencoder（自编码器）与 WENDy 被同步训练，以发现高维数据内在的非线性潜在空间动力学。与 gLaSDI 中采用的标准非线性动力学稀疏辨识（SINDy）相比，WENDy 能够实现方差缩减和鲁棒的潜在空间发现，从而带来更准确、更高效的降阶建模。此外，WgLaSDI 中的贪婪物理信息主动学习支持在运行过程中自适应采样最优训练数据，以提高建模精度。通过对多种非线性动力学问题建模，验证了所提框架的有效性，包括黏性和无黏 Burgers 方程、时间相关径向平流以及等离子体物理中的 Vlasov 方程。在含有 5–10% 高斯白噪声的数据上，WgLaSDI 比 gLaSDI 优数个数量级，相对误差达到 1–7%。与高保真模型相比，WgLaSDI 实现了 121 至 1,779 倍的加速。
英文摘要：
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.
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