Non-intrusive model reduction for a 3D unstructured mesh control volume finite element reservoir model and its application to fluvial channels

Abstract

A non-intrusive model reduction computational method using hypersurfaces representation has been developed for reservoir simulation and further applied to 3D fluvial channel problems in this work. This is achieved by a combination of a radial basis function (RBF) interpolation and proper orthogonal decomposition (POD) method. The advantage of the method is that it is generic and non-intrusive, that is, it does not require modifications to the original complex source code, for example, a 3D unstructured mesh control volume finite element (CVFEM) reservoir model used here. The capability of this non-intrusive reduced order model (NIROM) based on hypersurfaces representation has been numerically illustrated in a horizontally layered porous media case, and then further applied to a 3D complex fluvial channel case. By comparing the results of the NIROM against the solutions obtained from the high fidelity full model, it is shown that this NIROM results in a large reduction in the CPU computation cost while much of the details are captured.

An autoencoder‐based reduced‐order model for eigenvalue problems with application to neutron diffusion

“…Reduced‐order modeling or model reduction 1 is a numerical technique that has made a significant impact across a broad range of fields, including aerodynamics, 2 hemodynamics, 3 fracture, 4,5 porous media, 6,7 and molecular dynamics 8 . Its aim is to produce a low‐dimensional model which is a good approximation of a high‐dimensional model (high‐fidelity model), but which can be solved in a fraction of the computational time required by the high‐fidelity model (HFM).…”

“…However, to find solutions for unseen parameter values, projection of the high-fidelity system onto the basis functions is replaced by interpolating between snapshots (or snapshots that have themselves been projected onto the basis functions). Although cubic interpolation 26 or radial basis functions 7 were originally used for the interpolation, NIROM methods have since embraced machine learning, using a variety of neural networks for this purpose, including autoencoders in combination with long short-term memory networks, 27,28 multilayer perceptrons, 29 and Gaussian process regression. 22,30 When using neural networks, the offline stage involves training a neural network to learn how the solutions depend on various model parameters, and the online stage involves evaluating the neural network for an unseen parameter value or values.…”

An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion

“…Reduced-order modelling or model reduction [52] is a numerical technique that has made a significant impact across a broad range of fields, including aerodynamics [65], haemodynamics [4], fracture [34,1], porous media [31,63] and molecular dynamics [29]. Its aim is to produce a low-dimensional model which is a good approximation of a highdimensional model (high-fidelity model), but which can be solved in a fraction of the computational time required by the high-fidelity model (HFM).…”

“…However, to find solutions for unseen parameter values, projection of the high-fidelity system onto the basis functions is replaced by interpolating between snapshots (or snapshots that have themselves been projected onto the basis functions). Although cubic interpolation [11] or radial basis functions [63] were originally used for the interpolation, NIROM methods have since embraced machine learning, using a variety of neural networks for this purpose, including autoencoders in combination with Long Short-Term Memory networks [22,61], multi-layer perceptrons [27] and Gaussian Process Regression [23,64]. When using neural networks, the offline stage involves training a neural network to learn how the solutions depend on various model parameters, and the online stage involves evaluating the neural network for an unseen parameter value or values.…”

A proper orthogonal decomposition variational multiscale meshless interpolating element‐free Galerkin method for incompressible magnetohydrodynamics flow

“…Reduced‐order models are derived in References and from low‐order bases computed by applying proper orthogonal decomposition (POD) on an a priori ensemble of data of the Navier‐Stokes model. A nonintrusive model reduction computational method is developed in Reference using hypersurfaces representation for reservoir simulation and further it was applied to 3D fluvial channel problems. Recently, authors of Reference presented a fantastic nonintrusive reduced‐order model based on machine learning, which is a great achievement for data‐driven modelling community.…”