An efficient goal‐based reduced order model approach for targeted adaptive observations

Abstract

SUMMARYAn efficient adjoint sensitivity technique for optimally collecting targeted observations is presented. The targeting technique incorporates dynamical information from the numerical model predictions to identify when, where, and what types of observations would provide the greatest improvement to specific model forecasts at a future time. A functional (goal) is defined to measure what is considered important in modelling problems. The adjoint sensitivity technique is used to identify the impact of observations on the predictive accuracy of the functional, then placing the sensors at the locations with high impacts. The adaptive (goal) observation technique developed here has the following features: (1) over existing targeted observation techniques, its novelty lies in that the interpolation error of numerical results is introduced to the functional (goal) which ensures the measurements are a distance apart; (2) the use of proper orthogonal decomposition (POD) and reduced order modeling (ROM) for both the forward and backward simulations, thus reducing the computational cost; and (3) the use of unstructured meshes. The targeted adaptive observation technique, is developed here within an unstructured mesh finite element model (Fluidity). In this work, a POD ROM is used to form the reduced order forward model by projecting the original complex model from a high dimensional space onto a reduced order space. The reduced order adjoint model is then constructed directly from the reduced order forward model. This efficient adaptive observation technique has been validated with two test cases: a model of an ocean Gyre and a model of 2D urban street canyon flows.

Model identification of reduced order fluid dynamics systems using deep learning

“…The ROM is expected to play a major role in facilitating real-time turnaround of computational results. It has been applied into a number of fields, for example, nonlinear large-scale systems, 13 ocean modelling, 14,15 sensor location optimisation, 16 air pollution modelling, 17 shape optimisation, 18 porous media problems, 19 aerospace, 20,21 optimal control, 22,23 multiscale fracture, 24 shallow water, [25][26][27] and neutron problems. 28 Reduced order models can be broadly divided into 2 types: intrusive ROMs and non-intrusive ROMs (NIROMs).…”

Reduced order framework for convection dominant and pure diffusive problems based on combination of deep long short‐term memory and proper orthogonal decomposition/dynamic mode decomposition methods

“…Model order reduction (MOR) is a useful method to obtain a reasonable approximation by significantly reducing the computational cost of such problems. MOR is applied to various fields, for example, large scale nonlinear systems, 1 ocean modeling, 2 sensor position optimization, 3 air pollution modeling, 4 shape optimization, 5 aerospace, 6 optimal control, 7 and neutron problems 8 . MOR methods are developed to capture the main dynamics of the process, through which a computationally efficient approximation solution can be obtained 9 .…”

An advanced hybrid deep adversarial autoencoder for parameterized nonlinear fluid flow modelling

“…• The proposed method exploits spatial features by use of convolutional neural networks. It will be advantageous over the traditional reduced order models (ROMs) (Fang et al, 2017;Xiao et al, 2019) since the high-dimensional datasets are compressed into the low-dimensional representations by nonlinearity functions in a convolutional encoder. In this way, the predictive fluid flows containing high nonlinearity and chaotic nature can be represented by a convolutional decoder.…”