Related papers: MeshODE: A Robust and Scalable Framework for Mesh …
Solving Partial Differential Equation (PDE) interface problems on varying domains is a critical task in design and optimization, yet it remains computationally prohibitive for traditional solvers. Although operator learning has shown…
In this paper, we propose a novel learning-based framework for 3D shape registration, which overcomes the challenges of significant non-rigid deformation and partiality undergoing among input shapes, and, remarkably, requires no…
Meshing is a critical, but user-intensive process necessary for stable and accurate simulations in computational fluid dynamics (CFD). Mesh generation is often a bottleneck in CFD pipelines. Adaptive meshing techniques allow the mesh to be…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
Modern mesh generation pipelines whether learning-based or classical often produce outputs requiring post-processing to achieve production-quality geometry. This work introduces MeshCone, a convex optimization framework for guided mesh…
Recently, learning frameworks have shown the capability of inferring the accurate shape, pose, and texture of an object from a single RGB image. However, current methods are trained on image collections of a single category in order to…
We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…
Unstructured meshes are among the most versatile approaches for capturing non-canonical geometries in fluid dynamics simulations. Despite this, most high-fidelity first-principles phase-change models are developed and applied on structured…
A Computer-Aided Design (CAD) model encodes an object in two coupled forms: a parametric construction sequence and its resulting visible geometric shape. During iterative design, adjustments to the geometric shape inevitably require…
We present a discrete theory for modeling developable surfaces as quadrilateral meshes satisfying simple angle constraints. The basis of our model is a lesser known characterization of developable surfaces as manifolds that can be…
The current dominant paradigm for robotic manipulation involves two separate stages: manipulator design and control. Because the robot's morphology and how it can be controlled are intimately linked, joint optimization of design and control…
De-homogenization is becoming an effective method to significantly expedite the design of high-resolution multiscale structures, but existing methods have thus far been confined to simple static compliance minimization. There are two…
Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computational domains, etc.…
This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field, an increasingly common paradigm in applications including photogrammetry,…
Reconstructing the 3D shape of a deformable environment from the information captured by a moving depth camera is highly relevant to surgery. The underlying challenge is the fact that simultaneously estimating camera motion and tissue…
We present CortexODE, a deep learning framework for cortical surface reconstruction. CortexODE leverages neural ordinary differential equations (ODEs) to deform an input surface into a target shape by learning a diffeomorphic flow. The…
This paper addresses the problem of controlling a continuum manipulator (CM) in free or obstructed environments with no prior knowledge about the deformation behavior of the CM and the stiffness and geometry of the interacting obstructed…
We propose a neural network-based approach for collision detection with deformable objects. Unlike previous approaches based on bounding volume hierarchies, our neural approach does not require an update of the spatial data structure when…
The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
Mesh simplification is the process of reducing the number of vertices, edges and triangles in a three-dimensional (3D) mesh while preserving the overall shape and salient features of the mesh. A popular strategy for this is edge collapse,…