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Feature selection is an important and active research area in statistics and machine learning. The Elastic Net is often used to perform selection when the features present non-negligible collinearity or practitioners wish to incorporate…
In this work, we address the implementation and performance of inexact Newton-Krylov and quasi-Newton algorithms, more specifically the BFGS method, for the solution of the nonlinear elasticity equations, and compare them to a standard…
From the mesoscopic point of view, a new concept of soft matching for mass points is proposed. Then a soft Lasso's approach to learn the soft dynamical equation for the physical mechanical relationship is proposed, too. Furthermore, a…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a…
The efficient optimization of actuated soft structures, particularly under complex nonlinear forces, remains a critical challenge in advancing robotics. Simulations of nonlinear structures, such as soft-bodied robots modeled using the…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…
In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…
This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The…
Quantum algorithms have been identified as a potential means to accelerate computational fluid dynamics (CFD) simulations, with the lattice Boltzmann method (LBM) being a promising candidate for realizing quantum speedups. Here, we extend…
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…
To date, the simulation of organ deformations for applications like therapy planning or image-guided interventions is calculated by solving the elastodynamics equations. While efficient solvers have been proposed for fast simulations,…
We develop a new algorithm for the Brownian dynamics of soft matter systems that evolves time by spatially correlated Monte Carlo moves. The algorithm uses vector wavelets as its basic moves and produces hydrodynamics in the low Reynolds…
This paper is devoted to the investigation of inertial dynamical systems with implicit Hessian-driven damping for strongly quasiconvex optimization which is a specific class of nonconvex optimization problems. We first establish exponential…
Soft robotic systems are known for their flexibility and adaptability, but traditional physics-based models struggle to capture their complex, nonlinear behaviors. This study explores a data-driven approach to modeling the…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
The precision, stability, and performance of lightweight high-strength steel structures in heavy machinery is affected by their highly nonlinear dynamics. This, in turn, makes control more difficult, simulation more computationally…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
Nonlinear unsteady vortex lattice-vortex particle methods (NL-UVLM-VPM) provide medium-fidelity predictions of rotorcraft aerodynamics with explicit three-dimensional wake representations at a moderate computational cost. This study…
This paper proposes a low order geometrically exact flexible beam formulation based on the utilisation of generic beam shape functions to approximate distributed kinematic properties of the deformed structure. The proposed nonlinear beam…