Related papers: First-Order Bilevel Topology Optimization for Fast…
Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…
In the current industry, the development of optimized mechanical components able to satisfy the customer requirements evolves quickly. Therefore, companies are asked for efficient solutions to improve their products in terms of stiffness…
The traditional element-based topology optimization based on material penalization typically aims at a 0/1 design. Our numerical experiments reveal that the compliance of a smooth design is overestimated when material properties of boundary…
This paper studies the complexity of finding an $\epsilon$-stationary point for stochastic bilevel optimization when the upper-level problem is nonconvex and the lower-level problem is strongly convex. Recent work proposed the first-order…
To solve large-scale or high-resolution topology optimization problem, a novel algorithm is developed based on modified bi-directional evolutionary structure optimization (BESO) and extended finite element method (XFEM). Within XFEM, a set…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
We present in this paper novel accelerated fully first-order methods in \emph{Bilevel Optimization} (BLO). Firstly, for BLO under the assumption that the lower-level functions admit the typical strong convexity assumption, the…
In this paper we present a new GPU-oriented mesh optimization method based on high-order finite elements. Our approach relies on node movement with fixed topology, through the Target-Matrix Optimization Paradigm (TMOP) and uses a global…
Topology optimization (TO) is a family of computational methods that derive near-optimal geometries from formal problem descriptions. Despite their success, established TO methods are limited to generating single solutions, restricting the…
Topology optimization (TO) is a well-established methodology for structural design under user-defined constraints, e.g. minimum volume and maximum stiffness. However, such methods have traditionally been applied to static, deterministic…
In recent years, topology optimization (TO) has gained widespread attention as a powerful structural design method. However, its application remains challenging due to the deep expertise and extensive development effort required.…
We consider stochastic unconstrained bilevel optimization problems when only the first-order gradient oracles are available. While numerous optimization methods have been proposed for tackling bilevel problems, existing methods either tend…
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
Structural topology optimization (TO) is central to engineering design but remains computationally intensive due to complex physics and hard constraints. Existing deep-learning methods are limited to fixed square grids, a few hand-coded…
In this work, we present an efficiently computational approach for designing material micro-structures by means of topology optimization. The central idea relies on using the isogeometric analysis integrated with the parameterized level set…
Wide variety of engineering design tasks can be formulated as constrained optimization problems where the shape and topology of the domain are optimized to reduce costs while satisfying certain constraints. Several mathematical approaches…
Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…
We develop and apply a novel shape optimization exemplified for a two-blade rotor with respect to the figure of merit ($FM$). This topologically assisted optimization (TAO) contains two steps. First a global evolutionary optimization is…
Topology Optimization seeks to find the best design that satisfies a set of constraints while maximizing system performance. Traditional iterative optimization methods like SIMP can be computationally expensive and get stuck in local…
In this work, we study nonconvex-strongly convex online bilevel optimization (OBO) using only first-order oracle. Existing OBO algorithms are mainly based on hypergradient descent, which requires access to a Hessian-vector product (HVP)…