We are currently looking for Ph.D. students in the general area of geometric computing with a focus on smart materials, complex assemblies, computational caustics, 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.
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
The geometry of specular objects (e.g. those made from glass or mirror materials) determines how light hitting the object is refracted or reflected. The object can be seen as a mapping function that transforms an incoming light distribution into an outgoing distribution. The goal of this project is to solve the inverse problem of finding the geometry of a specular object such that a desired light distribution is achieved for a fixed given input light. A specific instance of this problem has been studied in our lab, where light images are drawn as illustrated here. The goal of the project is to lift the limitations of the specific and rather restrictive setup of current computational caustic methods to generalize the approach to arbitrary target light distributions. This requires a new formulation of the inverse optimization problem and new effective algorithms for its solution, leveraging recent advances in optimal transport theory and optimization methods in machine learning.
Keywords: raytracing, optics, optimal transport, finite element methods, inverse algorithms, shape optimization, machine learning
LGG is part of the National Centre of Competence in Research (NCCR) Digital Fabrication (DFAB) that conducts collaborative research at the Doctoral and Postdoctoral levels in the disciplines of computer science architecture, civil and structural engineering, material science, mechanical engineering and mechatronics, and control systems engineering. The methodology of the NCCR is highly collaborative and cross-disciplinary, and is oriented toward training scholars and developing advanced practitioners in the fields of engineering, science and architecture.