Enhancing Multi-Objective Optimization through Machine Learning-Supported Multiphysics Simulation

TL;DR

The paper addresses the high computational cost of multiobjective optimization in complex multiphysics systems by proposing a three-block pipeline that learns self-improving surrogate models from small, real-world datasets and uses explainable AI to guide data extension. It combines XGBoost baselines and deep networks (MLP/CNN) with NSGA-II to generate Pareto fronts, validating predictions against full simulations and leveraging xAI tools like feature importances and partial dependence plots. Two public use-case datasets (motor topology and U-bend CFD) demonstrate differing predictive challenges, revealing strong performance in the motor case ($MAPE$ < 5% in some conditions) and more difficulty under turbulent, high-dimensional regimes. The approach reduces the number of expensive simulations required to identify high-quality solution candidates, providing actionable insights into parameter relevance and design trade-offs, with practical impact on accelerated multiphysics design workflows.

Abstract

This paper presents a methodological framework for training, self-optimising, and self-organising surrogate models to approximate and speed up multiobjective optimisation of technical systems based on multiphysics simulations. At the hand of two real-world datasets, we illustrate that surrogate models can be trained on relatively small amounts of data to approximate the underlying simulations accurately. Including explainable AI techniques allow for highlighting feature relevancy or dependencies and supporting the possible extension of the used datasets. One of the datasets was created for this paper and is made publicly available for the broader scientific community. Extensive experiments combine four machine learning and deep learning algorithms with an evolutionary optimisation algorithm. The performance of the combined training and optimisation pipeline is evaluated by verifying the generated Pareto-optimal results using the ground truth simulations. The results from our pipeline and a comprehensive evaluation strategy show the potential for efficiently acquiring solution candidates in multiobjective optimisation tasks by reducing the number of simulations and conserving a higher prediction accuracy, i.e., with a MAPE score under 5% for one of the presented use cases.

Figures (10)

• Figure 1: Proposed strategy for training and self-optimising surrogate models using machine learning and deep learning techniques to tackle multiobjective optimisation problems in complex multiphysics simulations.
• Figure 2: Ilustration of our proposed Pipeline for self-optimising surrogate models, which can be seamlessly integrated into the optimisation process of multiphysics problems and comprises three main blocks: data acquisition, surrogate model training, and multiobjective optimisation.
• Figure 3: Parameterised 2D rotor segment of the baseline machine with black fields representing the magnet components and grey areas for the air cavities.
• Figure 4: Parameterised geometry with boundary points (green) and curve parameters (red). The Figure is adapted and rotated from DSB+22
• Figure 5: Assessment of surrogate model performance using MAPE scores and residual analysis on the test sets for each use case.