We create an data-efficient and accurate surrogate model for structure-property linkages of spinodoid metamaterials with only 75 data points -- far fewer than the several thousands used in prior works -- and demonstrate its use in multi-objective inverse design. The inverse problem of finding a material microstructure that leads to given bulk properties is of great interest in mechanics and materials science. These inverse design tasks often require a large dataset, which can become unaffordable when considering material behavior that requires more expensive simulations or experiments. We generate a data-efficient surrogate for the mapping between the characteristics of the local material structure and the effective elasticity tensor and use it to inversely design structures with multiple objectives simultaneously. The presented neural network-based surrogate model achieves its data efficiency by inherently satisfying certain requirements, such as equivariance with respect to permutations of structure parameters, which avoids having to learn them from data. The resulting surrogate of the forward model is differentiable, allowing its direct use in gradient-based optimization for the inverse design problem. We demonstrate in three inverse design tasks of varying complexity that this approach yields reliable results while requiring significantly less training data than previous approaches based on neural-network surrogates. This paves the way for inverse design involving nonlinear mechanical behavior, where data efficiency is currently the limiting factor.
Guided Diffusion for Fast Inverse Design of Density-based Mechanical Metamaterials
School of Mathematical Sciences, University of Science and Technology of China（中国科学技术大学数学科学学院）；Beijing Academy of Artificial Intelligence（北京人工智能研究院）；Hefei University of Technology（合肥工业大学）
Nonlinear Inverse Design of Mechanical Multi-Material Metamaterials Enabled by Video Denoising Diffusion and Structure Identifier
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；National Center for Supercomputing Applications（国家超级计算应用中心）；Kansas State University（堪萨斯州立大学）；New York University Abu Dhabi（纽约大学阿布扎比分校）
Algebraic Language Models for Inverse Design of Metamaterials via Diffusion Transformers
Mechanics & Materials Laboratory, Department of Mechanical and Process Engineering, ETH Zürich（机械与材料实验室，机械与过程工程系，苏黎世联邦理工学院）；Department of Materials Science and Engineering, Delft University of Technology（材料科学与工程系，代尔夫特理工大学）
