Related papers: A variational-level-set based partitioning method …

We study numerically the cluster structure of random ensembles of two NP-hard optimization problems originating in computational complexity, the vertex-cover problem and the number partitioning problem. We use branch-and-bound type…

Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…

While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…

This paper proposes a new sequential model learning architecture to solve partially observable Markov decision problems. Rather than compressing sequential information at every timestep as in conventional recurrent neural network-based…

We propose a variational principle combining a phase-field functional for structural topology optimization with a mixed (three-field) Hu-Washizu functional, then including directly in the formulation equilibrium, constitutive, and…

The goal of this paper is to present a new efficient image segmentation method based on evolutionary computation which is a model inspired from human behavior. Based on this model, a four layer process for image segmentation is proposed…

We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…

It is a challenging task to accurately perform semantic segmentation due to the complexity of real picture scenes. Many semantic segmentation methods based on traditional deep learning insufficiently captured the semantic and appearance…

In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…

Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of…

We propose a method for high-performance semantic image segmentation (or semantic pixel labelling) based on very deep residual networks, which achieves the state-of-the-art performance. A few design factors are carefully considered to this…

Thesedays, Convolutional Neural Networks are widely used in semantic segmentation. However, since CNN-based segmentation networks produce low-resolution outputs with rich semantic information, it is inevitable that spatial details (e.g.,…

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…

In this paper, the problem of the minimal description of the structure of a vector function f(x) over an $N$-dimensional interval is studied. Methods adaptively subdividing the original interval in smaller subintervals and evaluating f(x)…

This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…

This paper addresses representational block named Hierarchical-Split Block, which can be taken as a plug-and-play block to upgrade existing convolutional neural networks, improves model performance significantly in a network.…

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…

We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies…

This paper presents a method for the optimization of multi-component structures comprised of two and three materials considering large motion sliding contact and separation along interfaces. The structural geometry is defined by an explicit…

In this paper, we propose the differentiable voxelization of 3D meshes via the winding number and solid angles. The proposed approach achieves fast, flexible, and accurate voxelization of 3D meshes, admitting the computation of gradients…