Related papers: Variable offsets and processing of implicit forms …
Shape priors have long been known to be effective when reconstructing 3D shapes from noisy or incomplete data. When using a deep-learning based shape representation, this often involves learning a latent representation, which can be either…
Sampling from distributions of implicitly defined shapes enables analysis of various energy functionals used for image segmentation. Recent work describes a computationally efficient Metropolis-Hastings method for accomplishing this task.…
We introduce a computational framework for the topology optimization of cellular structures with spatially varying architecture, which is applied to functionally graded truss lattices under quasistatic loading. We make use of a first-order…
Concepts from quantum topological states of matter have been extensively utilized in the past decade in creating mechanical metamaterials with topologically protected features, such as one-way edge states and topologically polarized…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
Randomly crumpled sheets have shape memory. In order to understand the basis of this form of memory, we simulate triangular lattices of springs whose lengths are altered to create a topography with multiple potential energy minima. We then…
The pseudopotential model within the Lattice Boltzmann Method (LBM) framework has emerged as a prominent approach in computational fluid dynamics due to its dual strengths in physical intuitiveness and computational tractability. However,…
We present a practical algorithm for partially relaxing multiwell energy densities such as pertain to materials undergoing martensitic phase transitions. The algorithm is based on sequential lamination, but the evolution of the…
Digital terrain models (DTMs) are created using elevation data collected in geological surveys using varied sampling techniques like airborne lidar and depth soundings. This often leads to large data sets with different distribution…
A modification of the implicit algorithm for particle-in-cell simulations proposed by Petrov and Davis [2011] is presented. The original lattice arrangement is not inherently divergence-free, possibly leading to unphysical results. This…
This is the third in a series of papers studying the vertex-algebraic structure of principal subspaces of twisted modules for lattice vertex operator algebras. We focus primarily on lattices $L$ whose Gram matrix contains only non-negative…
We propose an optimization proxy in terms of iterative implicit gradient methods for solving constrained optimization problems with nonconvex loss functions. This framework can be applied to a broad range of machine learning settings,…
The inverse design of microstructures plays a pivotal role in optimizing metamaterials with specific, targeted physical properties. While traditional forward design methods are constrained by their inability to explore the vast…
The Finite element method (FEM) has long served as the computational backbone for topology optimization (TO). However, for designing structures undergoing large deformations, conventional FEM-based TO often exhibits numerical instabilities…
We propose a new approach for controlling the characteristics of certain mesh faces during optimization of high-order curved meshes. The practical goals are tangential relaxation along initially aligned curved boundaries and internal…
Grids are a general representation for capturing regularly-spaced information, but since they are uniform in space, they cannot dynamically allocate resolution to regions with varying levels of detail. There has been some exploration of…
The collective dynamics of topological structures have been of great interest from both fundamental and applied perspectives. For example, the studies of dynamical properties of magnetic vortices and skyrmions not only deepened the…
Accurate structural relaxation is critical for advanced materials design. Traditional approaches built on physics-derived first-principles calculations are computationally expensive, motivating the creation of machine-learning interatomic…
We introduce Topological Offsets, a novel approach to generate manifold and self-intersection-free offset surfaces that are topologically equivalent to an offset infinitesimally close to the surface. Our approach, by construction, creates a…
Interatomic potentials are essential to go beyond ab initio size limitations, but simulation results depend sensitively on potential parameters. Forward propagation of parameter variation is key for uncertainty quantification, whilst…