InvDesFlow-AL: active learning-based workflow for inverse design of functional materials

Developing inverse design methods for functional materials with specific properties is critical to advancing fields like renewable energy, catalysis, energy storage, and carbon capture. Generative models based on diffusion principles can directly produce new materials that meet performance constraints, thereby significantly accelerating the material design process. However, existing methods for generating and predicting crystal structures often remain limited by low success rates. In this work, we propose a novel inverse material design generative framework called InvDesFlow-AL, which is based on active learning strategies. This framework can iteratively optimize the material generation process to gradually guide it towards desired performance characteristics. In terms of crystal structure prediction, the InvDesFlow-AL model achieves an RMSE of 0.0423 Å, representing an 32.96% improvement in performance compared to existing generative models. Additionally, InvDesFlow-AL has been successfully validated in the design of low-formation-energy and low-Ehull materials. It can systematically generate materials with progressively lower formation energies while continuously expanding the exploration across diverse chemical spaces. Notably, through DFT structural relaxation validation, we identified 1,598,551 materials with Ehull < 50 meV, indicating their thermodynamic stability and atomic forces below 1e-4 eV/Å. These results fully demonstrate the effectiveness of the proposed active learning-driven generative model in accelerating material discovery and inverse design. To further prove the effectiveness of this method, we took the search for BCS superconductors under ambient pressure as an example explored by InvDesFlow-AL. As a result, we successfully identified Li2AuH6 as a conventional BCS superconductor with an ultra-high transition temperature of 140 K, and also discovered several other superconducting materials that surpass the theoretical McMillan limit and have transition temperatures within the liquid nitrogen temperature range. This discovery provides strong empirical support for the application of inverse design in materials science.