Physics-based machine learning for inverse design of porous metamaterials

Emerging as a paradigmatic material system, porous metamaterials have the potential to deliver highly adaptable and unique properties across a wide range of applications. This project focuses on establishing a physics-based machine learning framework to design porous metamaterials based on desired properties. The aims to address challenges such as the high-dimensional topological design space, the presence of multiple local optima, and the high computational cost associated with inverse design. The proposed method generalizes to establish the structure-property mapping, with porous metamaterials represented in diverse forms of data. The initial plan involved building and testing the framework by combining synthetic 3D porous microstructures with CT-scan-based representative volume elements (RVEs) of porous open-foam specimens. The framework will leverage a property-variational autoencoder (pVAE) to establish robust mappings between 3D microstructures and their corresponding effective properties. The pVAE integrates a variational autoencoder (VAE) with a regression network, creating a compact latent space that facilitates efficient interpolation and optimization. The VAE utilizes a convolutional encoder to compress input structures into a low-dimensional latent space modeled as a Gaussian distribution and a decoder to reconstruct the corresponding 3D geometries. Training is guided by a composite loss function that combines reconstruction loss, KL divergence for latent space regularization, and regression loss to align the latent space with the target effective properties. To enhance the interpretability and structure of the latent space, a physical constraints approach will be incorporated into the bottleneck of the model. By aligning latent representations with underlying physical principles, this method facilitates the development of a robust and efficient structure-property mapping framework. In addition to reducing data dependency, it improves the model's ability to capture essential physical relationships, thereby enhancing overall performance and applicability.

The pVAE, with its capability to learn probabilistic mappings, establishes a relationship between input 3D structures and desired effective properties. Its latent space, constrained by physical principles and guided by effective properties, encapsulates microstructural features in a compact, interpretable form, enabling efficient interpolation and novel structure generation. The framework supports both direct encoding of microstructures and latent space sampling for generating realizations. Furthermore, an optimization framework facilitates inverse design, enabling scalable, data-driven creation of porous metamaterials tailored to specific properties, advancing multiscale structure-property mapping methodologies.

Doctoral Researcher: Phu Thien Nguyen

Scientific Advisors: Fadi Aldakheel, Ludovic Chamoin