We are currently looking for interns, Ph.D. students, and post-doctoral scholars in the general area of geometric computing and digitial fabrication with a focus on smart materials, deployable structures, complex assemblies, and computational design. Please visit the links to find out more about our research efforts in these areas. LGG and EPFL offer a world-class, highly collaborative international research environment with competitive salaries and a beautiful setting on the shores of Lake Geneva.
Below are several examples of potential PhD research topics. This list is not exhaustive and other topics in the general domains of geometry processing, physics-based simulation, numerical optimization, computational design, or digital fabrication are possible.
3D assemblies refer to objects that combine multiple component parts into a structure with a specific form and/or functionality. Due to the ability to make complex and/or large objects from simple and small parts, 3D assemblies are widely used, e.g., in toys, mechanisms, furniture, and architecture. Designing complex assemblies is a challenging problem since we need to consider not only the geometry of parts and their local joining but also the functional and aesthetic performance of the whole assembly. The goal of this project is to develop computational methods and tools to assist the design, fabrication, and construction of complex assemblies. To achieve this goal, we investigate novel high-level assembly representations, combinatorial optimization algorithms, construction-aware design principles, and suitable design exploration methods.
Keywords: combinatorial optimization, graph algorithms, geometry optimization, joining technology, robotic assembly
Using insights from geometry and physical simulation, we can alter the behavior of materials to meet functional goals. For instance, we can cut slits into a solid, inextensible sheet of material to allow it to expand, and then by carefully designing these cuts, we can ensure the sheet pops into the curved surface of our choice when it is stretched. Or, we can design fine-scale microstructure geometry to create a 3D printed object that deforms in useful or surprising ways when forces are applied. This project seeks to develop computational techniques and tools such as efficient PDE solvers and shape optimization algorithms for designing and applying metamaterials in settings ranging from 3D printing to architecture.
Keywords: (discrete) differential geometry, shape optimization, partial differential equations, physics-based simulation
In this project we will explore the latest advances in machine learning to develop effective algorithms for geometric design space exploration. The core idea is to leverage forward simulation methods to train generative models such as variational auto encoders or generative adversarial networks to facilitate user- and performance-driven design of advanced geometric structures. This requires designing new learning architectures that are suitable for 3D geometric data with complex physical behavior that is directly linked to the object's performance. Another aspect of the research is to learn from user behavior to discover specific design preferences linked to a designer’s unique style in order to more effectively explore design alternatives.
Keywords: machine learning, generative adversarial networks, deep learning, optimization
Shape-morphing structures are physical systems that can transition (morph) from one geometric state to another. They find applications in diverse fields, for example as deployable solar panels for satellites, medical implants such as heart stents, morphable air foils, smart textiles, soft robotics, or architectural facade systems. In this project we focus on deployable surfaces that can be fabricated in a planar state and then be actuated to a programmed 3D target state. This means that the deployed state is encoded in the 2D material through locally prescribed deformation behavior. The goal is to develop novel computational tools for inverse design of such shape-morphing surfaces, that is, to find a suitable flat 2D material state that can be automatically deployed to a functional 3D target shape. This requires careful design of physics-based simulation and geometric optimization algorithms to handle the intricate coupling of geometry, material, and physical actuation.
Keywords: physics-based simulation, geometric optimization, computational design, finite element methods, inverse algorithms