Related papers: Mesh quality preserving shape optimization using n…

Generative models have attracted considerable attention for their ability to produce novel shapes. However, their application in mechanical design remains constrained due to the limited size and variability of available datasets. This study…

This paper proposes an arc-search interior-point algorithm for the nonlinear constrained optimization problem. The proposed algorithm uses the second-order derivatives to construct a search arc that approaches the optimizer. Because the arc…

This work studies shape filtering techniques, namely the convolution-based (explicit) and the PDE-based (implicit), and introduces an implicit bulk-surface filtering method to control the boundary smoothness and preserve the internal mesh…

Within this work, we present a novel approach to fracture simulations based on shape optimization techniques. Contrary to widely-used phase-field approaches in literature the proposed method does not require a specified 'length-scale'…

Nonlinearity plays a crucial role in deep neural networks. In this paper, we investigate the degree to which the nonlinearity of the neural network is essential. For this purpose, we employ the Koopman operator, extended dynamic mode…

We present an enhanced version of the parametric nonlinear reduced order model for shape imperfections in structural dynamics we studied in a previous work [1]. The model is computed intrusively and with no training using information about…

In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…

Topology optimization (TO) has experienced a dramatic development over the last decades aided by the arising of metamaterials and additive manufacturing (AM) techniques, and it is intended to achieve the current and future challenges. In…

We introduce a novel solver to significantly reduce the size of a geometric operator while preserving its spectral properties at the lowest frequencies. We use chordal decomposition to formulate a convex optimization problem which allows…

We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…

We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…

Facing the physical limitations and energy consumption bottlenecks of traditional electronic devices, we propose an innovative design framework integrating evolutionary algorithms and metasurface technology, aiming to achieve intelligent…

In this paper, we propose a meshfree approximation method for the implicit filter developed in [2], which is a novel numerical algorithm for nonlinear filtering problems. The implicit filter approximates conditional distributions in the…

We propose a method that morphs high-orger meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero…

Nonsmoothness is often a curse for optimization; but it is sometimes a blessing, in particular for applications in machine learning. In this paper, we present the specific structure of nonsmooth optimization problems appearing in machine…

This work is concerned with the micro-architecture of multi-layer material that globally exhibits desired mechanical properties, for instance a negative apparent Poisson ratio. We use inverse homogenization, the level set method, and the…

Many chemical and biological experiments involve multiple treatment factors and often it is convenient to fit a nonlinear model in these factors. This nonlinear model can be mechanistic, empirical or a hybrid of the two. Motivated by…

We consider the problem of matching two shapes assuming these shapes are related by an elastic deformation. Using linearized elasticity theory and the finite element method we seek an elastic deformation that is caused by simple external…

3D shape analysis is an important research topic in computer vision and graphics. While existing methods have generalized image-based deep learning to meshes using graph-based convolutions, the lack of an effective pooling operation…

We consider minimizing a function consisting of a quadratic term and a proximable term which is possibly nonconvex and nonsmooth. This problem is also known as scaled proximal operator. Despite its simple form, existing methods suffer from…