Data-Driven Topology Optimization with Multiclass Microstructures using Latent Variable Gaussian Process

TL;DR

This paper introduces a novel multi-response latent-variable Gaussian process model to enable data-driven topology optimization across multiple microstructure classes, improving design flexibility and structural performance.

Contribution

It extends LVGP models to handle multiclass microstructures with mixed variables, facilitating continuous transitions and gradient-based optimization in multiscale design.

Findings

Multiclass microstructure modeling improves structural performance.

The MR-LVGP model captures interactions between microstructure classes and parameters.

Gradient-based topology optimization benefits from continuous microstructure transitions.

Abstract

The data-driven approach is emerging as a promising method for the topological design of multiscale structures with greater efficiency. However, existing data-driven methods mostly focus on a single class of microstructures without considering multiple classes to accommodate spatially varying desired properties. The key challenge is the lack of an inherent ordering or distance measure between different classes of microstructures in meeting a range of properties. To overcome this hurdle, we extend the newly developed latent-variable Gaussian process (LVGP) models to create multi-response LVGP (MR-LVGP) models for the microstructure libraries of metamaterials, taking both qualitative microstructure concepts and quantitative microstructure design variables as mixed-variable inputs. The MR-LVGP model embeds the mixed variables into a continuous design space based on their collective effects on the responses, providing substantial insights into the interplay between different geometrical classes and material parameters of microstructures. With this model, we can easily obtain a continuous and differentiable transition between different microstructure concepts that can render gradient information for multiscale topology optimization. We demonstrate its benefits through multiscale topology optimization with aperiodic microstructures. Design examples reveal that considering multiclass microstructures can lead to improved performance due to the consistent load-transfer paths for micro- and macro-structures.