Related papers: Neural Level Set Topology Optimization Using Unfit…
Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again…
In this research, we propose a deep learning based approach for speeding up the topology optimization methods. The problem we seek to solve is the layout problem. The main novelty of this work is to state the problem as an image…
We propose a new algorithm for the design of topologically optimized lightweight structures, under a minimum compliance requirement. The new process enhances a standard level set formulation in terms of computational efficiency, thanks to…
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…
We propose a method to modify a polygonal mesh in order to fit the zero-isoline of a level set function by extending a standard body-fitted strategy to a tessellation with arbitrarily-shaped elements. The novel level set-fitted approach, in…
We present a methodical procedure for topology optimization under uncertainty with multi-resolution finite element models. We use our framework in a bi-fidelity setting where a coarse and a fine mesh corresponding to low- and…
In this paper, we present a novel framework for deriving the evolution equation of the level set function in topology optimization, departing from conventional Hamilton-Jacobi based formulations. The key idea is the introduction of an…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
This paper proposes a variational framework for multi-objective level set topology optimization. The approach interprets the level set function as a generalized coordinate of a fictitious material and derives its equation of motion from…
Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
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…
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…
The objective of this paper is to introduce and demonstrate a robust methodology for solving multi-constrained 3D topology optimization problems. The proposed methodology is a combination of the topological level-set formulation, augmented…
Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is…
Level set-based immersed boundary techniques operate on nonconforming meshes while providing a crisp definition of interface and external boundaries. In such techniques, an isocontour of a level set field interpolated from nodal level set…
We propose in this paper a multilevel correction method to solve optimal control problems constrained by elliptic equations with the finite element method. In this scheme, solving optimization problem on the finest finite element space is…
Neural networks have recently been employed as material discretizations within adjoint optimization frameworks for inverse problems and topology optimization. While advantageous regularization effects and better optima have been found for…
Various topological techniques and tools have been applied to neural networks in terms of network complexity, explainability, and performance. One fundamental assumption of this line of research is the existence of a global (Euclidean)…