We introduce a denoising diffusion algorithm to discover microstructures with nonlinear fine-tuned properties. Denoising diffusion probabilistic models are generative models that use diffusion-based dynamics to gradually denoise images and generate realistic synthetic samples. By learning the reverse of a Markov diffusion process, we design an artificial intelligence to efficiently manipulate the topology of microstructures to generate a massive number of prototypes that exhibit constitutive responses sufficiently close to designated nonlinear constitutive behaviors. To identify the subset of microcstructures with sufficiently precise fine-tuned properties, a convolutional neural network surrogate is trained to replace high-fidelity finite element simulations to filter out prototypes outside the admissible range. Results of this study indicate that the denoising diffusion process is capable of creating microstructures of fine-tuned nonlinear material properties within the latent space of the training data. More importantly, this denoising diffusion algorithm can be easily extended to incorporate additional topological and geometric modifications by introducing high-dimensional structures embedded in the latent space. Numerical experiments are conducted on the open-source mechanical MNIST data set (Lejeune, 2020). Consequently, this algorithm is not only capable of performing inverse design of nonlinear effective media, but also learns the nonlinear structure–property map to quantitatively understand the multiscale interplay among the geometry, topology, and their effective macroscopic properties.

我们引入了一种去噪扩散算法来发现具有非线性微调特性的微结构。去噪扩散概率模型是生成模型，它使用基于扩散的动力学来逐渐对图像进行去噪并生成逼真的合成样本。通过学习马尔可夫扩散过程的逆过程，我们设计了一种人工智能来有效地操纵微结构的拓扑结构，以生成大量原型，这些原型表现出足够接近指定非线性本构行为的本构响应。为了识别具有足够精确的微调特性的微结构子集，训练了一个卷积神经网络代理来代替高保真有限元模拟，以过滤掉允许范围之外的原型。这项研究的结果表明，去噪扩散过程能够在训练数据的潜在空间内创建微调非线性材料特性的微观结构。更重要的是，这种去噪扩散算法可以很容易地扩展，通过引入嵌入潜在空间的高维结构来合并额外的拓扑和几何修改。在开源机械 MNIST 数据集（Lejeune，2020）上进行了数值实验。因此，该算法不仅能够进行非线性有效介质的逆向设计，还能学习非线性结构-特性图，以定量理解几何、拓扑及其有效宏观特性之间的多尺度相互作用。