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

Abstract: Inverse design problems are pervasive in engineering, particularly when dealing with nonlinear system responses, such as in mechanical behavior or spectral analysis. The inherent intractability, non-existence, or non-uniqueness of their solutions, and the need for swift exploration of the solution space necessitate the adoption of machine learning and data-driven approaches, such as deep generative models. Here, we show that both deep generative model-based and optimization-based methods can yield unreliable solutions or incomplete coverage of the solution space. To address this, we propose the Generative and Uncertainty-informed Inverse Design (GUIDe) framework, leveraging probabilistic machine learning, statistical inference, and Markov chain Monte Carlo sampling to generate designs with targeted nonlinear behaviors. Unlike inverse models that directly map response to design, i.e., response $\mapsto$ design, we employ a design $\mapsto$ response strategy: a forward model that predicts each design's nonlinear functional response allows GUIDe to evaluate the confidence that a design will meet the target, conditioned on a target response with a user-specified tolerance level. Then, solutions are generated by sampling the solution space based on the confidence. We validate the method by designing the interface properties for nacre-inspired composites to achieve target stress-strain responses. Results show that GUIDe enables the discovery of diverse feasible solutions, including those outside the training data range, even for out-of-distribution targets.