A physics-constrained deep generative framework for the intelligent inverse design of terahertz metamaterials

Designing advanced terahertz (THz) metamaterials is severely hampered by a critical workflow bottleneck, such as the design of toroidal dipoles metamaterials for sensing and communication. Traditional design is hindered by slow, computationally expensive simulations. Deep learning accelerates this process, but is undermined by two issues: the ‘non-uniqueness’ problem and a more critical data-centric bottleneck—the statistical rarity of training samples capturing key physical phenomena (e.g., high-frequency oscillations), which we address here. To overcome these hurdles, we developed a physics-constrained generative framework. This framework is anchored by a high-fidelity forward physical engine—a deep residual network (ResNet) achieving a predictive accuracy (R2) of 0.9977. We then embed this engine directly into the training loop of a conditional variational autoencoder (cVAE), using a cycle-consistency loss to impose a strong physical constraint. Crucially, a novel ‘spectral oscillation score’ metric first allows us to quantitatively diagnose this data rarity as the root cause of poor performance. The resulting physics-constrained cVAE then successfully overcomes this limitation, showing significant accuracy improvements for complex spectra and demonstrating the unique ability to generate diverse, valid solutions for a single design target. The research not only provides a powerful new paradigm for intelligent THz metamaterial design from diagnosis to solution, but also its underlying strategy—first diagnosing the data bottleneck and then imposing physical constraints to guide solution generation—also offers a transferable blueprint for tackling other inverse problems in the data-driven physical sciences.