Advanced Computational Methods for Imperfect/Uncertain Geometries

Every manufactured object—from a turbine blade to a hip implant—carries tiny geometric flaws from production or wear, and current computer models cannot handle these imperfections efficiently. This project tackles a fundamental gap in engineering simulation: existing digital models assume perfect, smooth shapes, but real-world parts have random dents, scratches, or warps that degrade performance. The researchers at Cambridge and Duke will combine two mathematical techniques—immersed boundary methods (which handle complex shapes without rebuilding the entire simulation mesh) and probabilistic subdivision surfaces (which represent uncertain geometries mathematically)—to create a new class of computational tools that can model imperfect parts as they actually exist. If successful, the work will accelerate digital product development and, more importantly, enable practical digital twins—virtual replicas that track a physical product from design through manufacturing, operation, and maintenance. Currently, training these digital twins for parts with uncertain geometries is slow and expensive. The new methods would make it feasible to simulate how a corroded pipe or a slightly misaligned gear will behave over its lifetime, without needing to rebuild the model from scratch each time. This is fundamental computational science with clear engineering applications, particularly for industries where safety and longevity depend on understanding how real-world imperfections affect performance.