Working Paper Article Version 2 This version is not peer-reviewed

# Non-parametric Surrogate Model Method based on Machine Learning

Version 1 : Received: 26 April 2021 / Approved: 28 April 2021 / Online: 28 April 2021 (17:27:43 CEST)
Version 2 : Received: 23 June 2021 / Approved: 25 June 2021 / Online: 25 June 2021 (11:58:24 CEST)
Version 3 : Received: 22 January 2022 / Approved: 24 January 2022 / Online: 24 January 2022 (10:39:52 CET)

How to cite: Cao, J.; Li, Q.; Xu, L.; Yang, R.; Dai, Y. Non-parametric Surrogate Model Method based on Machine Learning. Preprints 2021, 2021040762 Cao, J.; Li, Q.; Xu, L.; Yang, R.; Dai, Y. Non-parametric Surrogate Model Method based on Machine Learning. Preprints 2021, 2021040762

## Abstract

In this paper, a novel "non-parametric" surrogate model method is introduced. The method extracts geometric information from surface mesh of fluid domain using Graph Neural Network (GNN) and predicts the two-dimensional distributions of flow variables (in forms of contours) using Convolutional Neural Network (CNN). This method can extract relevant geometric information from surface mesh automatically, while existing data-driven surrogate model methods need manual parameterisation, which may generates a lot of uncertainties. Existing methods can only process geometries defined by their own parameterisation methods because the inputs of existing surrogate models are human-defined geometric parameters, while new methods can process any geometries with the same topology because its input is the surface mesh, which could potentially access more designs from different sources to create a larger database. In addition, this novel surrogate model is able to predict the contour of variables, not only several performance metrics. Predicting contours can also prevent over-fitting problem by balancing the data size of input and output. In this paper, this novel surrogate model method will be demonstrated with an example: low pressure steam turbine exhaust system. The new surrogate model uses 10 surface meshes of the system as input and predicts the power flux contour at the outlet of the last rotor. To build the surrogate model, altogether 582 numerical simulations have been created, which contains two types of geometries defined by different methods. Among them, 550 cases are used for training, and 32 cases are used for testing. The power output of the last two stages predicted by the surrogate model has 0.86 $\%$ difference compared with those of numerical simulations. The similarity score that measures the differences between the simulated and predicted contours is 0.9594 (1.0 being identical).

## Keywords

surrogate model method; optimisation; graph neural network; parameterisation

## Subject

ENGINEERING, Mechanical Engineering

Comment 1
Commenter: Jiajun Cao
Commenter's Conflict of Interests: Author
Comment: Some content, the presentation of results and the structure of the article
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