RI:Small:Constrained Generative Models for Scientific and Engineering Applications

Generative artificial intelligence (AI) has recently attracted significant attention for its potential to revolutionize a broad range of scientific and engineering domains, including the design of novel materials and chemical compounds, advanced manufacturing, and robotics. However, while these models produce statistically plausible outputs, they often fail to adhere to physical principles, conservation laws, or safety constraints. Such violations result in suggested designs that may be impractical, unstable, or even hazardous. Additionally, many scientific domains have limited data available for model training, exacerbating these issues. This project addresses these challenges by developing AI tools explicitly informed by physical principles and safety constraints integrated directly into the generative process. If successful, these advances will provide scientists and engineers with practical methods to reliably generate designs that respect physical laws and safety limitations, significantly reducing costly trial-and-error experimentation and accelerating the development of new materials, devices, and processes. From a scientific standpoint, the project advances machine learning by introducing a new class of training-free, constraint-aware diffusion models that integrate differentiable optimization techniques with generative modeling. The project consists of three primary contributions. First, it establishes mathematical foundations for incorporating constraints into diffusion models by reformulating reverse diffusion as a sequence of optimization steps. This approach enables the enforcement of geometric, physical, or user-defined constraints without retraining. Second, it extends these models to handle dynamic constraints, ensuring adherence to time-dependent and physics-based rules throughout the generative process. Finally, it adapts this framework to discrete generative models, guaranteeing end-to-end consistency in tasks such as molecular design or natural language generation. On the education front, the project supports preparing students and the next generation of professionals in AI, equipping them with the skills and knowledge needed to contribute effectively to the evolving AI workforce and advance innovation across industries. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.