用神经伽辽金方法高效传播初始条件不确定性，速度提升超10倍。
Filtered Neural Galerkin model reduction schemes for efficient propagation of initial condition uncertainties in digital twins
- 基于预训练神经网络构建滤波型神经伽辽金动态，直接演化均值与协方差。
- 相比传统集合方法，计算速度提升超过一个数量级。
- 适合需快速不确定性量化数字孪生系统，如实时控制与数据融合场景。
数字孪生中的不确定性量化对实现超越已有数据的可靠预测至关重要。关键挑战在于，即使使用降维模型，基于集合的方法在嵌入控制与数据同化循环时仍可能变得极其昂贵。本文提出一种降维建模方法，通过推进由初始条件不确定性引起的降维解分布的均值与协方差来演化时间，从而无需维护和传播代价高昂的降维解集合。均值与协方差的动态由预训练神经网络上的神经伽辽金方案获得，可被解释为类似高斯滤波与扩展卡尔曼滤波的滤波型神经伽辽金动力学。数值实验表明，该方法相较于基于集合的不确定性传播实现了超过一个数量级的速度提升。
原文摘要 · Abstract (English)
Uncertainty quantification in digital twins is critical to enable reliable and credible predictions beyond available data. A key challenge is that ensemble-based approaches can become prohibitively expensive when embedded in control and data assimilation loops in digital twins, even when reduced models are used. We introduce a reduced modeling approach that advances in time the mean and covariance of the reduced solution distribution induced by the initial condition uncertainties, which eliminates the need to maintain and propagate a costly ensemble of reduced solutions. The mean and covariance dynamics are obtained as a moment closure from Neural Galerkin schemes on pre-trained neural networks, which can be interpreted as filtered Neural Galerkin dynamics analogous to Gaussian filtering and the extended Kalman filter. Numerical experiments demonstrate that filtered Neural Galerkin schemes achieve more than one order of magnitude speedup compared to ensemble-based uncertainty propagation.
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