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Topology Optimization (TO) provides a systematic approach for obtaining structure design with optimum performance of interest. However, the process requires numerical evaluation of objective function and constraints at each iteration, which…
Point discretization of curved surfaces is required in many applications ranging from object rendering to the solution of surface partial differential equations (PDEs). These applications often impose that surfaces are sampled with local…
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…
Shape matching has been a long-studied problem for the computer graphics and vision community. The objective is to predict a dense correspondence between meshes that have a certain degree of deformation. Existing methods either consider the…
Topology optimization (TopOpt) is a mathematical-driven design procedure to realize optimal material architectures. This procedure is often used to automate the design of devices involving flow through porous media, such as micro-fluidic…
Problems in differentiable rendering often involve optimizing scene parameters that cause motion in image space. The gradients for such parameters tend to be sparse, leading to poor convergence. While existing methods address this sparsity…
The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by…
We present a new framework for the simultaneous optimiziation of both the topology as well as the relative density grading of cellular structures and materials, also known as lattices. Due to manufacturing constraints, the optimization…
The paper surveys topological problems relevant to the motion planning problem of robotics and includes some new results and constructions. First we analyse the notion of topological complexity of configuration spaces which is responsible…
Data-driven decision-making has drawn scrutiny from policy makers due to fears of potential discrimination, and a growing literature has begun to develop fair statistical techniques. However, these techniques are often specialized to one…
Topology optimization has matured to become a powerful engineering design tool that is capable of designing extraordinary structures and materials taking into account various physical phenomena. Despite the method's great advancements in…
This article combines shape optimization and homogenization techniques by looking for the optimal design of the microstructure in composite materials and of scaffolds. The development of materials with specific properties is of huge…
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…
We propose an algorithm for distributed optimization over time-varying communication networks. Our algorithm uses an optimized ratio between the number of rounds of communication and gradient evaluations to achieve fast convergence. The…
This paper deals with shape optimization for elastic materials under stochastic loads. It transfers the paradigm of stochastic dominance, which allows for flexible risk aversion via comparison with benchmark random variables, from…
Topology optimization (TO) in two dimensions often presents a trade-off between structural performance and manufacturability, with unpenalized (variable-thickness) methods yielding superior but complex designs, and penalized (SIMP) methods…
Additive manufacturing is a free-form manufacturing technique in which parts are built in a layer-by-layer manner. Laser powder bed fusion is one of the popular techniques used to fabricate metal parts. However, it induces residual stress…
Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
The locality of a graph problem is the smallest distance $T$ such that each node can choose its own part of the solution based on its radius-$T$ neighborhood. In many settings, a graph problem can be solved efficiently with a distributed or…
In the present work we introduce a novel graded-material design based on phase-field and topology optimization. The main novelty of this work comes from the introduction of an additional phase-field variable in the classical single-material…