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

2025-07-30

AI Summary

For linear elastic structural topology optimization under parametric loads and boundary conditions, this paper proposes an end-to-end surrogate model based on a parametric autoencoder. The model employs a feedforward network combined with an encoder–decoder architecture to learn the mapping from the parameter space to a latent topological representation space, and incorporates physical constraints—such as equilibrium equations—and penalty-based posterior correction to achieve high-fidelity approximation of the full optimization pipeline. Its key innovation lies in formulating the entire optimization process as a learnable parametric mapping for the first time, yielding both strong generalization across unseen parameter configurations and robust extrapolation stability. Experimental results demonstrate a 53% average reduction in optimization iterations and a target objective error below 4%, significantly improving computational efficiency without compromising accuracy.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Deep Generative Models & Autoencoders
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Develops surrogate model for elastic structure topology optimization
• Predicts quasi-optimal topologies using parametric autoencoders
• Reduces computational cost while maintaining accuracy

Innovation

• Parametric autoencoders for topology optimisation
• Feed-forward net mapping system parameters
• Quasi-optimal topologies reduce iterations significantly