GUIDe: Generative and Uncertainty-Informed Inverse Design for On-Demand Nonlinear Functional Responses

Inverse design is a common yet challenging engineering problem, particularly for nonlinear functional responses such as mechanical behavior or spectral analysis. Deep generative models are motivated by intractability, non-existence or non-uniqueness of solutions, and the need for rapid solution-space exploration. In this study, we show that deep generative model-based and optimization-based approaches can provide incomplete solutions or hallucinate given out-of-distribution targets. To address this, we propose the Generative and Uncertainty-informed Inverse Design (GUIDe) framework, which leverages probabilistic machine learning, statistical inference, and Markov chain Monte Carlo to generate designs with targeted nonlinear behaviors. Instead of inverse mappings, i.e., response mapsto design, GUIDe adopts design mapsto response: a forward model predicts each design's nonlinear functional response and evaluates the confidence under a user-specified tolerance. Sampling the solution space by this confidence yields diverse feasible designs. Our validation on nacre-inspired materials finds solutions beyond the training range, even under out-of-distribution targets.