INVERSE DESIGN OF NONLINEAR MATERIAL MICROSTRUCTURES VIA DEEP-GENERATIVE-PRIOR BAYESIAN INFERENCE

Inverse design of microstructures for heterogeneous materials with nonlinear mechanical behaviors commonly suffers from the ill-posed “one-to-many” mapping problem and the curse of dimensionality caused by ultra-high-dimensional data. Most existing methods fail to balance the accuracy, diversity, and scalability of microstructure inverse design, so they cannot satisfy the requirements of tailored design in practical engineering fields. This study proposes a novel approach for inverse design of nonlinear heterogeneous material microstructures based on Deep-Generative-Prior Bayesian Inference (DGP-BI). A Variational Autoencoder (VAE) is employed to conduct probabilistic dimensionality reduction on ultra-high-dimensional microstructure data and build a probabilistically regularized prior distribution in the low-dimensional latent space. A forward prediction surrogate model based on convolutional neural networks is constructed to realize the likelihood evaluation of nonlinear mechanical response curves. Combined with the Markov Chain Monte Carlo (MCMC) algorithm, Bayesian posterior sampling is implemented, which converts the ill-posed inverse problem unsolvable in traditional high-dimensional space into a tractable probabilistic inference problem in the low-dimensional latent space. Furthermore, the DGP-BI method features outstanding modularity and multi-property scalability. When a new physical property is introduced as design constraints, the whole framework does not need to be rebuilt. Only a likelihood evaluation module corresponding to the new property need to be added to achieve multi-physical knowledge fusion in the posterior sampling process, while the existing models can be fully reused. In this paper, MNIST heterogeneous materials are selected. The applicability and effectiveness of the DGP-BI method are systematically analyzed in the inverse design scenarios of single and multiple tailored mechanical properties. The research results prove that the proposed method can effectively overcome the ill-posed challenges and the curse of dimensionality in the inverse design of nonlinear heterogeneous material microstructures, with the remarkable merits of accuracy, efficiency and robustness. It supplies critical theoretical support and technical routes for the customized inverse design of material microstructures guided by nonlinear mechanical properties and multi-property collaborative design, and thus possesses extensive engineering application prospects.