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

2025-09-06

AI Summary

Inverse design of nonlinear system responses—such as mechanical behavior or spectral properties—is challenging due to potential nonexistence, nonuniqueness, and computational intractability of solutions. Method: We propose a generative and uncertainty-aware framework that abandons conventional inverse mapping and instead adopts a forward “design ↦ response” modeling paradigm. It integrates deep generative models, probabilistic machine learning, and Markov Chain Monte Carlo sampling to reliably generate diverse, physically feasible designs conditioned on target responses—including out-of-distribution targets. Contribution/Results: To our knowledge, this is the first approach to embed rigorous uncertainty quantification directly into the generative inverse design pipeline, ensuring physical plausibility, statistical reliability, and comprehensive solution-space coverage. Evaluated on bioinspired composite interface design, the framework successfully generates multiple valid microstructures matching prescribed stress–strain responses, substantially outperforming existing data-driven methods in generalization and robustness.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Web Mining and Content Analysis: Web data generation and simulation

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.

Problem

• Inverse design for nonlinear functional responses
• Unreliable solutions from existing machine learning methods
• Generating designs with targeted nonlinear behaviors

Innovation

• Probabilistic machine learning with statistical inference
• Forward model predicting design's nonlinear response
• Markov chain Monte Carlo sampling solution space