Dual-Constrained Diffusion Model for Nonlinear Microstructure Inverse Design with Direct Evaluation

Abstract

Diffusion models have emerged as powerful tools for inverse design, yet their stochastic nature typically requires surrogate models or additional numerical simulations to verify target-condition satisfaction. To address this bottleneck, we propose a dual-constrained diffusion framework that jointly generates structural designs and solution fields under both physical and conditional constraints. The framework combines a dual-constrained diffusion model (DCDM) for training-stage constraint enforcement with dual-guided diffusion sampling (DGS) for sampling-stage guidance, enabling direct evaluation without additional numerical simulations. We demonstrate the framework through the inverse design of hyperelastic microstructures conditioned on prescribed strain energy under uniaxial extension. Compared with a conventional diffusion model, DCDM with DGS reduces physics residual errors by more than an order of magnitude. In addition, 1,000 generated candidates can be screened directly in approximately 0.27 seconds. Importantly, because the dual constraints are incorporated during training, a single DCDM supports target-aligned unguided generation and can be combined with DGS for guided generation. For high-density in-distribution targets, unguided generation produces structurally diverse candidates with reliable direct evaluation at one-fifth the sampling time of guided generation. When higher target fidelity is desired or out-of-distribution targets are considered, DGS can be activated on the same trained model to increase the number of valid candidates and maintain reliable target satisfaction beyond the training distribution. The proposed framework provides a general and practical approach to inverse design for systems governed by physical laws, requiring only the definition of physics and condition residuals.