Optimality-Informed Operator Learning for Generalizable Topology Optimization

Topology optimization is a powerful computational technology that enables engineers to design lightweight, high-performance structures for applications ranging from aerospace and energy systems to advanced manufacturing and sustainable infrastructure. Despite its success, today's topology optimization methods are computationally expensive and must be solved from scratch whenever design requirements, loading conditions, or geometries change, limiting their use in rapid design exploration and real-time engineering applications. Recent advances in artificial intelligence (AI) have shown promise for accelerating this process, but current AI approaches often produce physically inconsistent or suboptimal designs because they learn only from examples without understanding the fundamental principles of engineering optimization. This project will develop a new generation of trustworthy AI that learns the underlying principles governing optimal engineering designs rather than simply mimicking existing solutions. By combining engineering optimization theory with scientific machine learning, this research will transform topology optimization into a reusable and generalizable design capability that can rapidly generate high-quality designs across a wide range of engineering problems. The project will broaden access to advanced design technologies, accelerate innovation in aerospace, energy, advanced manufacturing, and resilient infrastructure, and provide interdisciplinary training for students at the intersection of engineering design, optimization, and artificial intelligence. Open-source software, benchmark datasets, and reproducible workflows will be released to promote broad community adoption. This project aims to develop an optimality-informed neural operator framework for generalizable topology optimization. Unlike existing machine learning approaches that directly regress optimal topologies from training examples, the framework learns the infinite-dimensional optimization operator that maps problem specifications—including loading conditions, boundary conditions, and design domains—to verifiable optimal designs. The central innovation is to embed the Karush–Kuhn–Tucker (KKT) optimality conditions, including the state equations, adjoint equations, and stationarity conditions, directly into the neural operator to learn the governing laws of optimal design rather than merely fitting data. The research will investigate the theoretical foundations of optimality-informed operator learning, including the effects of strong and weak enforcement of physics and optimality constraints, the use of optimization trajectory and optimality data for improved generalization, and the development of scalable algorithms for multiphysics topology optimization. By unifying variational optimization theory, adjoint sensitivity analysis, and neural operator learning within a single computational framework, this research is expected to establish a new paradigm for trustworthy, interpretable, and transferable AI in engineering design. 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.