# A surrogate model for topology optimisation of elastic structures via parametric autoencoders

arXiv: https://arxiv.org/abs/2507.22539 · HTML: https://mlsanity.com/paper/2507.22539/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 60 references that are in the map.
- First posted on arXiv 30 Jul 2025.

## Builds on (most cited first, 17 of 17)

- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamics](https://mlsanity.com/paper/1912.11114/) (2019)
- [Deep learning for determining a near-optimal topological design without any iteration](https://mlsanity.com/paper/1801.05463/) (2018)
- [Deep learning of thermodynamics-aware reduced-order models from data](https://mlsanity.com/paper/2007.03758/) (2020)
- [On the use of Artificial Neural Networks in Topology Optimisation](https://mlsanity.com/paper/2208.02563/) (2022)
- [Topology Optimization via Machine Learning and Deep Learning: A Review](https://mlsanity.com/paper/2210.10782/) (2022)
- [Generative Design by Reinforcement Learning: Enhancing the Diversity of Topology Optimization Designs](https://mlsanity.com/paper/2008.07119/) (2020)
- [Progressive construction of a parametric reduced-order model for PDE-constrained optimization](https://mlsanity.com/paper/1407.7618/) (2014)
- [A Parametric Level Set Method for Topology Optimization based on Deep Neural Network (DNN)](https://mlsanity.com/paper/2101.03286/) (2021)
- [Data-scarce surrogate modeling of shock-induced pore collapse process](https://mlsanity.com/paper/2306.00184/) (2023)
- [Neural Networks for Generating Better Local Optima in Topology Optimization](https://mlsanity.com/paper/2407.17957/) (2024)
- [Separated response surfaces for flows in parametrised domains: comparison of a priori and a posteriori PGD algorithms](https://mlsanity.com/paper/2009.02176/) (2020)
- [Real-time topology optimization via learnable mappings](https://mlsanity.com/paper/2311.08473/) (2023)
- [Data augmentation for the POD formulation of the parametric laminar incompressible Navier-Stokes equations](https://mlsanity.com/paper/2312.14756/) (2023)
- [A super--convergent hybridisable discontinuous Galerkin method for linear elasticity](https://mlsanity.com/paper/1802.02123/) (2018)
- [A locking-free face-centred finite volume (FCFV) method for linear elasticity](https://mlsanity.com/paper/1806.07500/) (2018)
- [Hybridisable discontinuous Galerkin solution of geometrically parametrised Stokes flows](https://mlsanity.com/paper/2006.11846/) (2020)

## Built on by (most cited first, 3 of 3)

- [Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectives](https://mlsanity.com/paper/2603.12870/) (2026)
- [Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization](https://mlsanity.com/paper/2602.13513/) (2026)
- [Adversarial Agents on Topology Optimization: Understanding the Fragility and Robustness of Deep Learning-based and Physics-Based Design Models under Adversarial Perturbation](https://mlsanity.com/paper/2608.22606/) (2026)

## Abstract (arXiv)

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.