Active learning in latent spaces enables rapid inverse design of ferroelectric ceramics for energy storage

Ferroelectric ceramics are promising energy-storage candidates for miniaturizing high-power electronic systems, yet synergistically enhancing energy density and efficiency remains constrained by intricate coupling between chemical compositions and polarization configurations. Achieving high-throughput compositional exploration while solving real-time polarization dynamics is nearly impossible with traditional simulations due to prohibitive computational costs. Here, we propose an inverse design framework integrating a variational generative model with active learning optimization to accelerate the development of ferroelectrics with enhanced energy-storage performance under limited electric fields. By formulating the time-dependent Ginzburg-Landau equation governing domain structure evolution as conditional sampling within model latent space, achieving synergistic optimization of chemistry and polarization configurations. Through four-round closed-loop synthesis, we successfully obtain Bi_0.5Na_0.5TiO₃-based relaxor-ferroelectrics exhibiting exceptional energy density of ~2.3 J cm^-3 and ~80% efficiency at a low field of 200 kV cm^-1. This work establishes an efficient, generalizable route for the inverse design of next-generation energy-storage dielectric materials.