Deep learning-driven intelligent mesoscopic model (DeepMeso): a case study on ferroelectrics

Integrating artificial intelligence with computational methods has emerged as a transformative force in materials research, exemplified by breakthroughs such as DeepH and DeepMD. However, a critical gap persists in multiscale intelligent design: the lack of mesoscopic models capable of bridging microstructural features with macroscopic properties. Here, we develop DeepMeso, a generative deep learning-enabled mesoscopic model, for the intelligent design of complex heterogeneous materials. To exemplify the framework, we instantiate it in ferroelectrics (DeepFerro), where our workflow first integrates a data-driven surrogate model to predict key ferroelectric properties with an accuracy exceeding 99.6%. Then, we implement a 3D generative network to achieve inverse design across both composition and microstructure spaces, directly targeting predefined polarization objectives. When tasked with multi-objective on-demand generation, DeepFerro yields a mean squared error of 0.0497 and an R2 value of 95.44% against simulation benchmarks. Critically, it also exhibits robust transferability and extrapolation capability across 63 distinct ferroelectric systems, demonstrating its generalizability in end-to-end optimization. In parallel, model interpretability translates the learned relations into explicit, hierarchical guidelines. This generalizable intelligent design framework DeepMeso could be further extended to diverse heterogeneous materials, which will deepen the understanding of composition–microstructure–property relationships and facilitate the on-demand inverse design at the mesoscopic scale.