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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…
This paper is concerned with using discontinuous Galerkin isogeometric analysis (dGIGA) as a numerical treatment of Diffusion problems on orientable surfaces $\Omega \subset \mathbb{R}^3$. The computational domain or surface considered…
Physics-Informed Neural Networks (PINNs) often suffer from slow convergence, training instability, and reduced accuracy on challenging partial differential equations due to the anisotropic and rapidly varying geometry of their loss…
The method of geometric harmonics is adapted to the situation of incomplete data by means of the iterated geometric harmonics (IGH) scheme. The method is tested on natural and synthetic data sets with 50--500 data points and dimensionality…
Feature-based image matching has extensive applications in computer vision. Keypoints detected in images can be naturally represented as graph structures, and Graph Neural Networks (GNNs) have been shown to outperform traditional deep…
Mesh adaptivity is a technique to provide detail in numerical solutions without the need to refine the mesh over the whole domain. Mesh adaptivity in isogeometric analysis can be driven by Truncated Hierarchical B-splines (THB-splines)…
The steered response power phase transform (SRP-PHAT) is a beamformer method very attractive in acoustic localization applications due to its robustness in reverberant environments. This paper presents a spatial grid design procedure,…
We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for…
In this paper we analyse the pathwise approximation of stochastic differential equations by polynomial splines with free knots. The pathwise distance between the solution and its approximation is measured globally on the unit interval in…
Quick simulations for iterative evaluations of multi-design variables and boundary conditions are essential to find the optimal acoustic conditions in building design. We propose to use the reduced basis method (RBM) for realistic room…
This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the…
Diffusion models are widely used for generative tasks across domains. Given a pre-trained diffusion model, it is often desirable to fine-tune it further either to correct for errors in learning or to align with downstream applications.…
This paper investigates whether reward matching is a viable alternative to reward maximization methods for on-policy RL of LLMs. Group-relative Implicit Fine-Tuning (GIFT) is proposed, combining GRPO-style group sampling, DPO-style implicit…
This study presents an aposteriori error analysis of adaptive finite element approximations of parabolic boundary control problems with bilateral box constraints that act on a Neumann boundary. The control problem is discretized using the…
We introduce an optimized physics-informed neural network (PINN) trained to solve the problem of identifying and characterizing a surface breaking crack in a metal plate. PINNs are neural networks that can combine data and physics in the…
In this paper the numerical solution of potential problems defined on 3D unbounded domains is addressed with Boundary Element Methods (BEMs), since in this way the problem is studied only on the boundary, and thus any finite approximation…
This letter introduces a novel unmanned aerial vehicle (UAV)-intelligent reflecting surface (IRS) structure into near-field localization systems to enhance the design flexibility of IRS, thereby obtaining additional performance gains.…
We apply an unfitted HDG discretization to a model problem in shape optimization. The method proposed uses a fixed, shape regular, non-geometry conforming mesh and a high order transfer technique to deal with the curved boundaries arising…
An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…
The spatial impulse response (SIR) method is a well-known approach to calculate transient acoustic fields of arbitrary-shape transducers. It involves the evaluation of a time-dependent surface integral. Although analytic expressions of the…