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An agglomerative hierarchical clustering (AHC) framework and algorithm named HOSil based on a new linkage metric optimized by the average silhouette width (ASW) index is proposed. A conscientious investigation of various clustering methods…
We consider the numerical approximations of the Cahn-Hilliard equation with dynamic boundary conditions (C. Liu et. al., Arch. Rational Mech. Anal., 2019). We propose a first-order in time, linear and energy stable numerical scheme, which…
Hoist scheduling has become a bottleneck in electroplating industry applications with the development of autonomous devices. Although there are a few approaches proposed to target at the challenging problem, they generally cannot scale to…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
Hybrid dynamical systems are prevalent in science and engineering to express complex systems with continuous and discrete states. To learn the laws of systems, all previous methods for equation discovery in hybrid systems follow a two-stage…
This paper summarises a numerical investigation of phase mixing in time-independent Hamiltonian systems that admit a coexistence of regular and chaotic phase space regions, allowing also for low amplitude perturbations idealised as periodic…
In this work, we study a system of coupled Cahn-Hilliard equations describing the phase separation of a copolymer and a homopolymer blend. The numerical methods we propose are based on suitable combinations of existing schemes for the…
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…
Deep neural networks often produce miscalibrated probability estimates, leading to overconfident predictions. A common approach for calibration is fitting a post-hoc calibration map on unseen validation data that transforms predicted…
B* is a novel optimization framework that addresses a critical challenge in fixed-base manipulator robotics: optimal base placement. Current methods rely on pre-computed kinematics databases generated through sampling to search for…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
The use of the hyperspherical harmonic (HH) basis in the description of bound states in an $A$-body system composed by identical particles is normally preceded by a symmetrization procedure in which the statistic of the system is taken into…
The partitioned approach for the numerical integration of power system differential algebraic equations faces inherent numerical stability challenges due to delays between the computation of state and algebraic variables. Such delays can…
This paper considers the approximation of partial differential equations with a point collocation framework based on high-order local maximum-entropy schemes (HOLMES). In this approach, smooth basis functions are computed through an…
Hierarchical Multi-Label Classification (HMC) faces critical challenges in maintaining structural consistency and balancing loss weighting in Multi-Task Learning (MTL). In order to address these issues, we propose a classifier called HCAL…
The dynamic behavior of jointed assemblies exhibiting friction nonlinearities features amplitude-dependent dissipation and stiffness. To develop numerical simulations for predictive and design purposes, macro-scale High Fidelity Models…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Context: The Circular Restricted Three-Body Problem provides a fundamental framework for understanding resonant dynamics in binary star systems. Aims: We develop a unified Hamiltonian formulation for mean-motion resonances that encompasses…
This article proposes a hybrid adaptive numerical method based on the Dual Reciprocity Method (DRM) to solve problems with non-linear boundary conditions and large-scale problems, named Hybrid Adaptive Dual Reciprocity Method (H-DRM). The…
This paper establishes a continuous time approximation, a piece-wise continuous differential equation, for the discrete Heavy-Ball (HB) momentum method with explicit discretization error. Investigating continuous differential equations has…