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.
Highlights
Computational simulations are playing an increasingly important role in engineering design, reducing the quantity of physical testing required by using simulations to model the performance of new designs
An alternative formulation for Knowledge Based Neural Network (KBaNN) was later introduced in Wang and Zhang (1997) in which prior knowledge is embedded in a neural network in the form of a “knowledge layer” consisting of empirical functions[14]
The general architecture for a KBaNN capable of bi-fidelity modelling is illustrated in Fig. 1, in the figure Fc(x) refers to an evaluation of the coarse model, which is modified at the output layer by the neural network
Summary
Computational simulations are playing an increasingly important role in engineering design, reducing the quantity of physical testing required by using simulations to model the performance of new designs. Reliability based design optimisation (RBDO) algorithms seek to find the design which minimises a cost function subject to probabilistic c onstraints[2]. An attractive strategy for mitigating the computational cost of these algorithms is to supplement the results of the most accurate models of a system, referred to as high-fidelity models, with models that are computationally less expensive. These low-fidelity models may have simplified physics, a coarser meshing or less detailed geometries and as a consequence are not as accurate. The general architecture for a KBaNN capable of bi-fidelity modelling is illustrated in Fig. 1, in the figure Fc(x) refers to an evaluation of the coarse model, which is modified at the output layer by the neural network
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
