Session: 36-03 Deep Learning based applications

Paper Number: 153107

Engineering Generative Adversarial Networks for Constrained and Multiobjective Problems 

In a previous publication [1] we have discussed a method for training a conditional Generative Adversarial Network (cGAN) on images of thermo-mechanical simulation results for an aero engine secondary air system seal, demonstrating the predictability of the Deep Learning models for key outputs of interest and assessing the ability of these models to generate designs in specific categories. The work was focused on the intricacies of training the ENGAN (Engineering cGAN) with data being categorised for a single output variable. A network trained for a single output is not aware of the other outputs and constraints and could generate solutions that are infeasible or not Pareto optimal.
In this article we present the notion of Multi-objective (MO) ENGANs. We have borrowed an idea from the Non-dominated Sorting Genetic Algorithm (NSGA2) [2] where a Genetic algorithm is used to minimize an amalgamation of the Pareto rank and the crowding distance, driving the designs towards the Pareto front (Pareto front rank of 1).
By definition all designs that have rank of 1 are part of the Pareto front. Adding a normalized crowding distance [0-0.9999] to each rank converts it to a real number and allows the Genetic algorithm in NSGA to ‘prefer’ solutions that are spaced away from each other in the objective space to improve diversity and avoid clustering.
For this study we are using a training data set of 86431 designs accompanied by training images. All infeasible designs were assigned a rank of 99999 and removed from the population. After applying the Pareto front ranking to the remaining designs, we obtained a vector of ranks varying from 1 to 62.
An ENGAN was trained using the same images as in the Single-Objective ENGAN study but using the categorization based on Pareto front labels. The network was trained to discriminate between feasible and non-feasible designs (Category 1-5 vs Category 6). It is also trained to discriminate between designs with low and high Pareto front ranking.
The trained ENGAN was successfully able to generate 100% feasible designs which were also close to Pareto optimal. The network can be used to generate large quantities of feasible designs which can be used for design space exploration purposes, saving a considerable amount of time from laborious design search and optimization practices. Furthermore, the network can be used to create an initial population of feasible and optimal designs, which can be used in various applications such as building surrogate models in the region of optimality or initializing a Genetic algorithm or using the points for multi-start gradient methods to perform a more aggressive optimization study.
The study shows that the images can be categorized for training using arbitrary rules that are mutually inclusive or exclusive. The multi-mode labelling ENGAN combines the targeting capability of the Single Objective ENGANs with the awareness of Pareto optimality and global feasibility. We were able to also target individually each of the objective functions at their optimal values, i.e., the corners of the Pareto front and separately its interior using a single network, as well as any other feasible design. This can eliminate the need of training of separate networks for each objective function, which can save considerable amount of time and GPU related costs, especially when training is performed on a subscription type of services such as the Microsoft Azure.
REFERENCES
[1] Nasti A., Voutchkov I., Keane A., “Generative deep learning on images of thermo-mechanical simulation results”, Proceedings of ASME Turbo Expo 2024, London UK, June 2024, Volume 10A, ISBN: 978-0-7918-8802-5. https://doi.org/10.1115/GT2024-126867 [2] K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II," in IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182-197, April 2002, https://doi:10.1109/4235.996017

Presenting Author: Ivan Voutchkov Rolls-Royce Plc

Presenting Author Biography: 24 years of experience in Machine Learning, AI, Optimisation and Surrogate modelling

Authors:

Ivan Voutchkov Rolls-Royce Plc
Adele Nasti Rolls-Royce Deutschland Ltd & Co KG
Andy Keane University of Southampton