A surrogate model for topology optimisation of elastic structures via parametric autoencoders
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| Format: | Preprint |
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2025
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| author | Giacomini, Matteo Huerta, Antonio |
| author_facet | Giacomini, Matteo Huerta, Antonio |
| contents | A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation trajectory as a function of the iterations, the proposed approach devises a surrogate version of the entire optimisation pipeline. First, the method predicts a quasi-optimal topology for a given problem configuration as a surrogate model of high-fidelity topologies optimised with the homogenisation method. This is achieved by means of a feed-forward net learning the mapping between the input parameters characterising the system setup and a latent space determined by encoder/decoder blocks reducing the dimensionality of the parametric topology optimisation problem and reconstructing a high-dimensional representation of the topology. Then, the predicted topology is used as an educated initial guess for a computationally efficient algorithm penalising the intermediate values of the design variable, while enforcing the governing equations of the system. This step allows the method to correct potential errors introduced by the surrogate model, eliminate artifacts, and refine the design in order to produce topologies consistent with the underlying physics. Different architectures are proposed and the approximation and generalisation capabilities of the resulting models are numerically evaluated. The quasi-optimal topologies allow to outperform the high-fidelity optimiser by reducing the average number of optimisation iterations by $53\%$ while achieving discrepancies below $4\%$ in the optimal value of the objective functional, even in the challenging scenario of testing the model to extrapolate beyond the training and validation domain. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_22539 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A surrogate model for topology optimisation of elastic structures via parametric autoencoders Giacomini, Matteo Huerta, Antonio Numerical Analysis Artificial Intelligence Computational Engineering, Finance, and Science Machine Learning Optimization and Control 49M41, 74P05, 74P15, 74S05, 65M60, 65M30 A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation trajectory as a function of the iterations, the proposed approach devises a surrogate version of the entire optimisation pipeline. First, the method predicts a quasi-optimal topology for a given problem configuration as a surrogate model of high-fidelity topologies optimised with the homogenisation method. This is achieved by means of a feed-forward net learning the mapping between the input parameters characterising the system setup and a latent space determined by encoder/decoder blocks reducing the dimensionality of the parametric topology optimisation problem and reconstructing a high-dimensional representation of the topology. Then, the predicted topology is used as an educated initial guess for a computationally efficient algorithm penalising the intermediate values of the design variable, while enforcing the governing equations of the system. This step allows the method to correct potential errors introduced by the surrogate model, eliminate artifacts, and refine the design in order to produce topologies consistent with the underlying physics. Different architectures are proposed and the approximation and generalisation capabilities of the resulting models are numerically evaluated. The quasi-optimal topologies allow to outperform the high-fidelity optimiser by reducing the average number of optimisation iterations by $53\%$ while achieving discrepancies below $4\%$ in the optimal value of the objective functional, even in the challenging scenario of testing the model to extrapolate beyond the training and validation domain. |
| title | A surrogate model for topology optimisation of elastic structures via parametric autoencoders |
| topic | Numerical Analysis Artificial Intelligence Computational Engineering, Finance, and Science Machine Learning Optimization and Control 49M41, 74P05, 74P15, 74S05, 65M60, 65M30 |
| url | https://arxiv.org/abs/2507.22539 |