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 (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.

Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review

“…The learned mapping function was then used as the transformation operator in an EnKF for DA. Similar ideas can be found in [306], [238], [66], [236]. As mentioned in Section IV-B, [66], [236] compute the surrogate operator in some reduced latent space can further enhance the computational efficiency.…”

“…Similar ideas can be found in [306], [238], [66], [236]. As mentioned in Section IV-B, [66], [236] compute the surrogate operator in some reduced latent space can further enhance the computational efficiency. On the other hand, [307] aimed to learn directly the inverse (i.e., observation-to-state) transformation operator to speed-up the convergence of DA algorithms.…”

“…Building efficient forward surrogate models is an alternative solution to reduce the computational burden of inverse modellings [175], including parameter estimation [176]. The very recent work of [67] proposed the use of Generalised Latent Assimilation (GLA) (see [66] or our Section IV-B) to integrate real-time observations for model parameter adjustment that can yield more accurate future predictions. Learning from a high-fidelity mechanistic model, the authors first constructed a ROM-and ML-based surrogate for predicting wildfire dynamics.…”

“…Therefore, separate AE are often required for the states and the observations, leading to heterogeneous latent spaces. [227] LA [233], [234] LA+ [75], [73], [232] GLA [66] LSDA [236] DDA [237], [238] To tackle this bottleneck, GLA and Latent Space data assimilation (LSDA) were proposed in the very recent works of [66] and [236] which make use of local surrogate functions (i.e., polynomial functions [66] and Multi layer percepton (MLP) [236]) to connect multiple latent spaces. Afterward, variational DA can then be performed by solving a local optimisation problem using smooth surrogate functions as shown in Figure 8.…”

Structure Learning and Hyperparameter Optimization Using an Automated Machine Learning (AutoML) Pipeline

“…In the framework of AutoML, the model's creation becomes easier, in the sense that it requires a minimal (or at the best scenario not at all) designer's manual correction. As a result, it can be viewed as an alternative to more traditional considerations [5,6], operating as a vehicle, to alleviate the high demands for experts in building ML applications [7]; this is a fact that appears to be very appealing in commercial software production [8]. In addition, under the umbrella of AutoML, the ML approaches become accessible to non-expert users [9], thus enabling the organizations to leverage the power of ML in effectively solving a variety of real-world problems [1].…”