State Estimation—The Role of Reduced Models

Abstract

The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations and (ii) data provided by measurement devices or sensors. The amount of sensors is typically limited and data acquisition may be expensive and in some cases even harmful. This article reviews some recent developments for this “small-data” scenario where inversion is strongly aggravated by the typically large parametric dimensionality. The proposed concepts may be viewed as exploring alternatives to Bayesian inversion in favor of more deterministic accuracy quantification related to the required computational complexity. We discuss optimality criteria which delineate intrinsic information limits, and highlight the role of reduced models for developing efficient computational strategies. In particular, the need to adapt the reduced models—not to a specific (possibly noisy) data set but rather to the sensor system—is a central theme. This, in turn, is facilitated by exploiting geometric perspectives based on proper stable variational formulations of the continuous model.

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

“…ROM also offers new opportunities for the integration of simulation models and physically observable quantities, which may be in a small-data scenarios. These approaches are also regard as data assimilation with ROM [6], where the data is incorporated into a reduced model, see recent works [41,4,24,29] for detail description of this framework. This framework makes the combination of simulation model with measurement data more efficient to realise real-time operational digital twin.…”

Data-Enabled Physics-Informed Machine Learning for Reduced-Order Modeling Digital Twin: Application to Nuclear Reactor Physics

“…This is also a non-intrusive data-driven paradigm in approximation of PDEs, motivated by small-data scenarios, where simulation models are represented by reduced basis. These approaches are also regard as data assimilation [43,44], where the data is incorporated into a model, see recent works [45,46,47,48,49] for general description of this paradigm. In this paradigm, RB provides actionable tools to compress prior knowledge about the system coming from the parameterized mathematical model into low-dimensional and more manageable forms, which makes the combination with measurement data more efficient.…”