Rank Reduction AutoEncoders Shows Efficient Topology Optimization of Mechanical Designs with QoI

Researchers are tackling the computational cost of topology optimisation, a crucial technique in mechanical design, with a novel data-driven approach. Ismael Ben-Yeluna (E.T.S. de Ingenierıa Aeron autica y del Espacio, Universidad Polit ecnica de Madrid), Mohammed El Fallaki Idrissi, and Jad Mounayer (both from ENSAM Institute of Technology PIMM) et al. demonstrate a framework utilising Rank Reduction AutoEncoders (RRAEs) to rapidly predict structural responses and even generate new designs. This work significantly advances the field by compressing complex, high-dimensional data into a low-rank format, enabling both forward and inverse analysis with improved efficiency and accuracy, as shown through benchmark testing on a half MBB beam. The methodology promises to unlock faster, more robust optimisation cycles and facilitate innovative generative design possibilities.

Reducing computational cost in topology optimisation using rank reduction and latent space mapping offers significant efficiency gains

Scientists have developed a data-driven framework for accelerating topology optimization (TO) through a novel combination of Rank Reduction Autoencoders (RRAEs) and neural latent-space mappings. This methodology efficiently approximates the relationship between optimized structural geometries and their mechanical responses, specifically focusing on compliance-minimized linear elastic structures.
The research addresses the computational demands of TO, particularly when numerous analyses are needed for design exploration, uncertainty quantification, or inverse design challenges. High-dimensional TO results are initially compressed using RRAEs, which encode data into a low-rank approximation via Singular Value Decomposition (SVD).

This process identifies and retains the most important features within the data, effectively reducing dimensionality. Separate RRAE models are trained for both geometry and various types of Quantity of Interest (QoI), encompassing scalar metrics, one-dimensional stress fields, and complete two-dimensional von Mises stress distributions.

The resulting low-dimensional latent coefficients are then interconnected using multilayer perceptrons to solve both direct and inverse problems. The team achieved accurate and computationally efficient surrogate models capable of predicting structural responses from geometry and, crucially, recovering geometries from prescribed performance targets.

Numerical results, demonstrated on a benchmark half MBB beam problem generated using Solid Isotropic Material with Penalization (SIMP) optimization, reveal increasing robustness and fidelity with richer QoI considerations. This work also establishes a foundation for generative mechanical design, allowing for the synthesis of novel geometries and responses through exploration within the latent space.

Experiments show that the proposed framework enables fast forward and inverse analysis, offering a significant improvement over traditional TO methods. The methodology’s ability to handle diverse QoIs, from simple scalar values to complex stress distributions, enhances its versatility and applicability to a wider range of engineering problems. This research opens new avenues for automated structural design and optimization, potentially revolutionizing the process of creating high-performance, lightweight structures.

Rank Reduction Autoencoder and Neural Network Integration for Topology Optimisation Analysis presents a novel approach

Scientists developed a data-driven framework for fast forward and inverse analysis in topology optimization by integrating Rank Reduction Autoencoders with neural latent-space mappings. The research targeted efficient approximation of the relationship between optimized geometries and their mechanical responses, specifically compliance-minimized linear elastic structures.

High-dimensional topology optimization results were initially compressed using Rank Reduction Autoencoders, which encoded data into a low-rank approximation via Singular Value Decomposition. Separate RRAE models were trained for both geometry and various types of Quantity of Interest, including scalar metrics, one-dimensional stress fields, and complete two-dimensional von Mises stress distributions.

This ensured comprehensive capture of structural behaviour across different performance indicators. The resulting low-dimensional latent coefficients were then mapped using multilayer perceptrons to solve both direct and inverse problems. Direct problems involved predicting structural responses from given geometries, while inverse problems focused on recovering geometries from prescribed performance targets.

Experiments employed a benchmark topology optimization problem centred on a half MBB beam, utilising datasets generated through density-based Solid Isotropic Material with Penalization optimization. The study pioneered a method for generating surrogate models, demonstrating increased robustness and fidelity with richer Quantity of Interest considerations.

Numerical results confirmed the framework’s ability to deliver accurate and computationally efficient surrogates. This methodology also provides a foundation for generative mechanical design, enabling the synthesis of novel geometries and responses through exploration of the latent space. The approach achieves significant computational savings by reducing the dimensionality of the design space while preserving critical performance characteristics.

Rank Reduction Autoencoders enable rapid forward and inverse topology optimisation for complex designs

Scientists have developed a data-driven framework for fast forward and inverse analysis in topology optimization (TO) by integrating Rank Reduction Autoencoders (RRAEs) with neural latent-space mappings. The research focuses on efficiently approximating the relationship between optimized geometries and their corresponding mechanical responses, specifically compliance-minimized linear elastic structures.

High-dimensional TO data was compressed using RRAEs, encoding it into a low-rank approximation via Singular Value Decomposition (SVD) to identify key features. Separate RRAE models were trained for geometry and various types of Quantity of Interest (QoI), including scalar metrics, one-dimensional stress fields, and complete two-dimensional von Mises stress distributions.

The resulting low-dimensional latent coefficients were then mapped using multilayer perceptrons to solve both direct and inverse problems. Experiments were conducted on a benchmark TO problem involving a half MBB beam, utilising datasets generated through density-based Solid Isotropic Material with Penalization (SIMP) optimization.

Numerical results demonstrate the framework’s ability to create accurate and computationally efficient surrogate models. Increasing the richness of the QoIs considered led to improved robustness and fidelity of the surrogate. The team measured performance gains through reduced computational cost while maintaining accuracy in predicting structural responses from given geometries.

The methodology also facilitates generative mechanical design by enabling the synthesis of novel geometries and responses through exploration of the latent space. This work provides a foundation for creating new designs by navigating the latent space and generating corresponding structural responses. The study confirms that the proposed approach enables accurate prediction of structural behaviour from geometry and reconstruction of geometry from desired performance targets.

The framework’s ability to handle diverse QoIs, from scalar values to full stress distributions, demonstrates its versatility and potential for complex engineering applications. This breakthrough delivers a powerful tool for accelerating the design process and exploring a wider range of structural possibilities.

Latent space mapping predicts structural behaviour from optimised designs with remarkable accuracy

Scientists have developed a data-driven framework to accelerate both forward and inverse analysis within topology optimization, utilising Rank Reduction Autoencoders (RRAEs) and neural latent-space mappings. This methodology efficiently approximates the relationship between optimized structural geometries and their mechanical responses, specifically focusing on compliance-minimized linear elastic structures.

The approach compresses high-dimensional topology optimization data using RRAEs, which employ Singular Value Decomposition to identify and retain the most important features representing the data. Separate RRAEs are trained for geometry and various types of Quantity of Interest (QoI), including scalar metrics, one-dimensional stress fields, and two-dimensional von Mises stress distributions.

The resulting low-dimensional latent coefficients are then mapped using multilayer perceptrons, enabling predictions of structural responses from geometry and the recovery of geometries from desired performance targets. Demonstrations on a half MBB beam benchmark problem, generated using Solid Isotropic Material with Penalization (SIMP) optimization, show the framework achieves accurate and computationally efficient surrogate models, with performance improving as more complex QoIs are incorporated.

Furthermore, the methodology facilitates generative mechanical design through exploration of the latent space, allowing for the synthesis of novel geometries and corresponding responses. The authors acknowledge limitations related to the specific benchmark problem and optimization algorithm used, potentially restricting the direct applicability of the framework to different scenarios.

Future research directions include extending the methodology to more complex loading conditions, material models, and geometric domains. This work establishes a promising pathway for accelerating topology optimization and enabling efficient exploration of design spaces, potentially reducing the computational cost associated with creating high-performance, lightweight structures.