arXiv subjects

Andrea Angino

Publications and source records attributed to Andrea Angino.

5 recordsLinked to original sources

arXiv2026

A Non-Monotone Preconditioned Trust-Region Method for Neural Network Training

Training deep neural networks at scale can benefit from domain decomposition, where the network is split into subdomains trained in parallel and coupled by a global trust-region mechanism. Building on the Additively Preconditioned Trust-Region Strategy (APTS), we propose a non-monotone variant with a nonlinear additive Schwarz preconditioner that combines parallel subdomain corrections with global coarse-space directions. A windowed acceptance criterion allows controlled objective increases, avoiding needless rejection of effective coarse steps. The resulting non-monotone APTS (NAPTS) preserves accuracy while reducing CPU time by 30\% and cutting rejected steps to one third of those in APTS.

math.OC↗

arXiv2026

Protect the Brain When Treating the Heart: Feasibility of 2.5D U-Net for Real-Time Gaseous Microemboli Detection

Gaseous microemboli (GME) represent a common complication of cardiac structural interventions across both surgical and transcatheter approaches. Intraoperative transesophageal echocardiography (TEE) represents a convenient methodology to monitor and visualize the presence of circulating GME. However, their detection and quantification are far from trivial due to operator-dependent view, high velocity, and objects with similar structure in the background. Here, we propose a feasibility study based on a 2.5D U-Net architecture to detect GME in space-time connected data. We applied and tested such an architecture on a pilot dataset of eight TEE recordings ($60$ fps, $600\times 800$ pixels) from eight different patients undergoing cardiac surgery, resulting in improved detection of moving GMEs against the background with respect to classical spot detection algorithms and 2D U-Net, yet retaining real-time execution speed with respect to more complex deep-learning architectures. Under leave-one-patient-out cross-validation, the selected model achieved strong detection performance under a three-pixel radius-tolerant grace-zone evaluation, with a precision of 92.55\% and recall of 80.54\%, corresponding to radius-tolerant Intersection over Union (IoU) and Dice coefficients of 73.95\% and 84.13\%, respectively. Complementarily, strict pixel-based segmentation metrics were also computed, yielding an IoU of 41.74\% and a Dice coefficient of 57.98\%. The selected model achieved an average inference time of $0.12 s$ per batch on the tested hardware. To assess specificity on unseen data, we additionally evaluated the model on an external GME-negative TEE dataset, where it produced predominantly empty or near-empty masks, indicating a low rate of spurious detections. These results support the technical feasibility of real-time GME segmentation.

cs.LG↗

arXiv2026

Adaptive Kernel Methods

Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel Hilbert space (RKHS), determined solely by the chosen kernel and the dataset, whose elements identify the basis elements. Consequently, the projection operator underlying the kernel method depends on the loss function, the dataset, and the choice of ambient RKHS. In this study, we consider kernel methods whose solution spaces also depend on learnable parameters that are independent of the dataset. The resulting methods can be viewed as variable projection operators that depend on the loss function, the dataset, and the new learnable parameters instead of a fixed RKHS. This work has two main contributions. First, we propose an efficient approximation of kernels associated with infinite-dimensional RKHSs, commonly used to reduce the solution-space dimension for large datasets. Second, we construct fixed-dimensional, parameter-dependent solution spaces that enable highly efficient kernel models suitable for large-scale problems without the need to approximate kernels of infinite-dimensional RKHSs. Our novel family of adaptive kernel methods generalizes earlier approaches, including Random Fourier Features, and we demonstrate their effectiveness through several numerical experiments.

math.NA↗

arXiv2025

Trust-Region Methods with Low-Fidelity Objective Models

We introduce two multifidelity trust-region methods based on the Magical Trust Region (MTR) framework. MTR augments the classical trust-region step with a secondary, informative direction. In our approaches, the secondary ``magical'' directions are determined by solving coarse trust-region subproblems based on low-fidelity objective models. The first proposed method, Sketched Trust-Region (STR), constructs this secondary direction using a sketched matrix to reduce the dimensionality of the trust-region subproblem. The second method, SVD Trust-Region (SVDTR), defines the magical direction via a truncated singular value decomposition of the dataset, capturing the leading directions of variability. Several numerical examples illustrate the potential gain in efficiency.

math.NA↗

arXiv2024

Two-level trust-region method with random subspaces

We introduce a two-level trust-region method (TLTR) for solving unconstrained nonlinear optimization problems. Our method uses a composite iteration step, which is based on two distinct search directions. The first search direction is obtained through minimization in the full/high-resolution space, ensuring global convergence to a critical point. The second search direction is obtained through minimization in the randomly generated subspace, which, in turn, allows for convergence acceleration. The efficiency of the proposed TLTR method is demonstrated through numerical experiments in the field of machine learning

math.NA↗