Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models

Abstract

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 computational fluid dynamics (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.

An efficient digital twin based on machine learning SVD autoencoder and generalised latent assimilation for nuclear reactor physics

“…Recently, latent assimilation techniques are introduced in the work of [1,61,27] where the DA is performed after having compressed the state and the observation data into the same latent space. However, as noted in the work [25], it is almost infeasible to compress the full state space and observations into a same latent space in a wide range of DA applications, where only a part of the state are observable. Thus in this work, the Generalised Latent Assimilation (GLA) is used, in which we split the observations and the background field into two parts, that only the background field stays in the latent space.…”

“…where B and R denote the prior errors in the state and the observation space, respectively [22]. However, as pointed out by the recent works of [25,26], the minimisation of equation ( 12) can be challenging due to the complexity and the non-differentiability of ML functions. Following their ideas, we make use of the GLA algorithms by computing a local polynomial surrogate functions that links 𝝁 and 𝒚.…”

Reduced Order Surrogate Modelling and Latent Assimilation for Dynamical Systems

“…The latent assimilation (LA) approach was first introduced in the work of [2] for CO 2 spread modeling. A generalised Latent Assimilation algorithm was proposed in the recent work of [9]. The observation quantities v t are first preprocessed to fit the space of the state variables u t , i.e.,…”

Reduced order digital twin and latent data assimilation for global wildfire prediction

“…However, predictive models trained using large amounts of data do not necessarily guarantee long-term prediction accuracy. In fact, iterative applications of Sequence-to-Sequence (Seq2seq) forecasting models can lead to error accumulation, resulting in incorrect long-term predictions (Cheng et al, 2022a;Cheng et al, 2022b). Researchers have applied data assimilation (DA) methods to address this challenge.…”

“…Latent data Assimilation (LA), which combines ROM, ML surrogated models, and DA was recently proposed (Peyron et al, 2021) and applied to a wide range of engineering problems, including air pollution modelling (Amendola et al, 2021), multiphase fluid dynamics (Cheng et al, 2022a) and regional wildfire predictions (Cheng et al, 2022b). In LA, data compression happens before the DA operation (Peyron et al, 2021), significantly reducing the computational cost.…”