Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models
Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models
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DOI：
10.1007/s10915-022-02059-4
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发表时间：
2023-01-01
影响因子：
2.5
通讯作者：
Arcucci, Rossella
中科院分区：
文献类型：
--
作者：
Cheng, Sibo;Chen, Jianhua;Arcucci, Rossella
利用机器学习算法生成的降维模型和低维代理模型已被广泛应用于高维动力系统中，以提高算法效率。在本文中，我们开发了一个系统，它结合了降阶代理模型和一种新的数据同化(DA)技术，用于合并来自不同物理空间的实时观测。我们利用局部光滑代理函数将编码的系统变量空间与当前观测值的空间联系起来，以较低的计算代价实现变分DA。这种新的系统，称为广义潜同化，既能提高降阶模式的效率，又能提高资料同化的精度。文中还对替代代价函数和原始同化代价函数的差异进行了理论分析，给出了依赖于局部训练集大小的上界。新方法在一个两相液体流动的高维(CFD)应用上进行了测试，其中含有非线性观测算子，这是目前的潜同化方法所不能处理的。数值结果表明，本文提出的同化方法可以显着提高深度学习代理模型的重构和预测精度，比CFD模拟快近1000倍。
Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a system which combines reduced-order surrogate models with a novel data assimilation (DA) technique used to incorporate real-time observations from different physical spaces. We make use of local smooth surrogate functions which link the space of encoded system variables and the one of current observations to perform variational DA with a low computational cost. The new system, named generalised latent assimilation can benefit both the efficiency provided by the reduced-order modelling and the accuracy of data assimilation. A theoretical analysis of the difference between surrogate and original assimilation cost function is also provided in this paper where an upper bound, depending on the size of the local training set, is given. The new approach is tested on a high-dimensional (CFD) application of a two-phase liquid flow with non-linear observation operators that current Latent Assimilation methods can not handle. Numerical results demonstrate that the proposed assimilation approach can significantly improve the reconstruction and prediction accuracy of the deep learning surrogate model which is nearly 1000 times faster than the CFD simulation.