A Unified, Extensible, and Differentiable Optimization Framework for Conceptual Design of Complex Engineered Systems

Nearly every complex engineered product, from automotive engine compartments and aircraft bays to medical devices and industrial energy systems, must pack many three-dimensional components into a tight space while routing the wires, cables, and pipes that connect them and ensuring that every part can be manufactured, assembled, and serviced over its lifetime. These decisions are made at the earliest stage of design, when they are hardest to reason about, yet they lock in most of the cost, reliability, and time-to-market of a product. Today this work is performed largely by hand by experienced designers, and its complexity exceeds what even experts can fully explore, so problems with manufacturability or maintenance access are often discovered late, after expensive commitments have already been made. This award supports the development of a computational design framework that allows engineers to explore layout, routing, and lifecycle trade-offs systematically and early, before architectural decisions become irreversible. By making manufacturability, serviceability, and lifecycle cost explicit during concept selection, the framework will reduce costly late-stage redesigns and accelerate innovation in industrial sectors critical to U.S. competitiveness. The project will release open software modules, benchmark problems, and documentation; integrate the resulting tools into graduate and senior undergraduate design courses as well as courses for practicing engineers; and train students in modern geometric computing, optimization, and AI-accelerated simulation. The technical objective of this research is a unified, extensible, and end-to-end differentiable optimization framework for the Spatial Packaging of Interconnected Systems with Physical Interactions (SPI2), in which layout, interconnect routing, multiphysics feasibility, and lifecycle constraints are optimized simultaneously at the conceptual design stage. The research combines hierarchical geometric representations with automatic differentiation to support expressive, physically meaningful objectives on complex three-dimensional geometry, and advances along three fronts: differentiable models of lifecycle requirements such as maintenance access, service motions, and assembly and disassembly feasibility; scalable geometry and physics computation, including AI-based surrogate models for the multiphysics governing SPI2 systems; and robust optimization strategies for the highly nonconvex problems that arise in this setting. The resulting framework will allow industrially relevant lifecycle and physics considerations to be introduced as plug-in objectives or constraints, and will be validated on benchmark families and industrially motivated test cases defined with the project's industrial collaborators. 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.