Local bi-fidelity field approximation with Knowledge Based Neural Networks for Computational Fluid Dynamics

Abstract

This work presents a machine learning based method for bi-fidelity modelling. The method, a Knowledge Based Neural Network (KBaNN), performs a local, additive correction to the outputs of a coarse computational model and can be used to emulate either experimental data or the output of a more accurate, but expensive, computational model. An advantage of the method is that it can scale easily with the number of input and output features. This allows bi-fidelity modelling approaches to be applied to a wide variety of problems, for instance in the bi-fidelity modelling of fields. We demonstrate this aspect in this work through an application to Computational Fluid Dynamics, in which local corrections to a velocity field are performed by the KBaNN to account for mesh effects. KBaNNs were trained to make corrections to the free-stream velocity field and the boundary layer. They were trained on a limited data-set consisting of simple two-dimensional flows. The KBaNNs were then tested on a flow over a more complex geometry, a NACA 2412 airfoil. It was demonstrated that the KBaNNs were still able to provide a local correction to the velocity field which improved its accuracy. The ability of the KBaNNs to generalise to flows around new geometries that share similar physics is encouraging. Through knowledge based neural networks it may be possible to develop a system for bi-fidelity, computer based design which uses data from past simulations to inform its predictions.

Machine Learning Methods in CFD for Turbomachinery: A Review

“…Approaches based on Gaussian processes (co-kriging) [96,97], multi-fidelity Polynomial Chaos Expansions [98,99], multilevel Monte Carlo [100], and different forms of physics informed neural networks such as those by Wang and Zhang [101] and Yang et al [102] have all been proposed for the solution of the PDEs that govern fluid flows. More recently, Pepper et al [103] presented a Knowledge-Based Neural Network (KBaNN) capable of computing additive corrections to the output of a model based on a coarse computational mesh. The KBaNN was able to generalise to flows that share similar physics.…”

Multi-fidelity reduced-order surrogate modelling

“…A wide range of MF surrogate modelling techniques have been developed based on Gaussian processes [41][42][43] and neural networks (NNs) [44][45][46][47][48]. They have found recent applications in many areas of scientific computing, including uncertainty quantification, inference and optimization [49][50][51][52][53][54][55]. Nevertheless, MF techniques often become impractical when approximating high-dimensional systems, thereby limiting their ability to directly approximate the full solution fields of PDEs.…”

Bi-fidelity conditional value-at-risk estimation by dimensionally decomposed generalized polynomial chaos expansion

“…The novel method combines (1) the DD-GPCE approximation of a high-dimensional stochastic output function, (2) an innovative method using Fourier-polynomial expansions of the mapping between the stochastic low-fidelity and high-fidelity output data for efficiently calculating the DD-GPCE, and (3) a standard sampling-based CVaR estimation integrated with the DD-GPCE. In contrast to existing bi-or multi-fidelity methods, based on an additive and/or multiplicative correction to the low fidelity output [14,30,29], the proposed bi-fidelity method employs linear or higher-order orthonormal basis functions consistent with the probability measure of the low-fidelity output to approximate the high-fidelity output, thus achieving nearly exponential convergence rate for the output data. Such Fourier-polynomial approximations demand only a handful of high-fidelity output evaluations.…”