A. Russo

L. Beirão da Veiga, F. Dassi, A. Russo et al.

The Virtual Element Method (VEM) is a well-established framework for solving partial differential equations on polygonal and polyhedral meshes. In this paper, we introduce a novel hybrid VEM that integrates both conforming and nonconforming virtual spaces. We apply this formulation to a three-dimensional linear elasticity problem, providing rigorous theoretical analysis to demonstrate optimal convergence rates. Furthermore, we explore the extension of this approach to domains with curved boundaries.

L. Beirão da Veiga, F. Brezzi, F. Dassi et al.

We consider, as a simple model problem, the application of Virtual Element Methods (VEM) to the linear Magnetostatic three-dimensional problem in the formulation of F. Kikuchi. In doing so, we also introduce new serendipity VEM spaces, where the serendipity reduction is made only on the faces of a general polyhedral decomposition (assuming that internal degrees of freedom could be more easily eliminated by static condensation). These new spaces are meant, more generally, for the combined approximation of $H^1$-conforming ($0$-forms), $H({\rm {\bf curl}})$-conforming ($1$-forms), and $H({\rm div})$-conforming ($2$-forms) functional spaces in three dimensions, and they would surely be useful for other problems and in more general contexts.

L. Beirão da Veiga, F. Brezzi, F. Dassi et al.

We give here a simplified presentation of the lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in three dimensions. The method can be applied to very general decompositions of the computational domain (as is natural for Virtual Element Methods) and uses as unknowns the (constant) tangential component of the magnetic field $\mathbf{H}$ on each edge, and the vertex values of the Lagrange multiplier $p$ (used to enforce the solenoidality of the magnetic induction $\mathbf{B}=μ\mathbf{H}$). In this respect the method can be seen as the natural generalization of the lowest order Edge Finite Element Method (the so-called "first kind Nédélec" elements) to polyhedra of almost arbitrary shape, and as we show on some numerical examples it exhibits very good accuracy (for being a lowest order element) and excellent robustness with respect to distortions.

L. Beirao da Veiga, F. Brezzi, L. D. Marini et al.

We extend the basic idea of Serendipity Virtual Elements from the previous case (by the same authors) of nodal ($H^1$-conforming) elements, to a more general framework. Then we apply the general strategy to the case of $H(div)$ and $H(curl)$ conforming Virtual Element Methods, in two and three dimensions.

F. D. Amaro, R. Antonietti, E. Baracchini et al.

Optical-readout Time Projection Chambers (TPCs) produce megapixel-scale images whose fine-grained topological information is essential for rare-event searches, but whose size challenges real-time data selection. We present an unsupervised, reconstruction-based anomaly-detection strategy for fast Region-of-Interest (ROI) extraction that operates directly on minimally processed camera frames. A convolutional autoencoder trained exclusively on pedestal images learns the detector noise morphology without labels, simulation, or fine-grained calibration. Applied to standard data-taking frames, localized reconstruction residuals identify particle-induced structures, from which compact ROIs are extracted via thresholding and spatial clustering. Using real data from the CYGNO optical TPC prototype, we compare two pedestal-trained autoencoder configurations that differ only in their training objective, enabling a controlled study of its impact. The best configuration retains (93.0 +/- 0.2)% of reconstructed signal intensity while discarding (97.8 +/- 0.1)% of the image area, with an inference time of approximately 25 ms per frame on a consumer GPU. The results demonstrate that careful design of the training objective is critical for effective reconstruction-based anomaly detection and that pedestal-trained autoencoders provide a transparent and detector-agnostic baseline for online data reduction in optical TPCs.

F. D. Amaro, R. Antonietti, E. Baracchini et al.

The CYGNO experiment employs an optical-readout Time Projection Chamber (TPC) to search for rare low-energy interactions using finely resolved scintillation images. While the optical readout provides rich topological information, it produces large, sparse megapixel images that challenge real-time triggering, data reduction, and background discrimination. We summarize two complementary machine-learning approaches developed within CYGNO. First, we present a fast and fully unsupervised strategy for online data reduction based on reconstruction-based anomaly detection. A convolutional autoencoder trained exclusively on pedestal images (i.e. frames acquired with GEM amplification disabled) learns the detector noise morphology and highlights particle-induced structures through localized reconstruction residuals, from which compact Regions of Interest (ROIs) are extracted. On real prototype data, the selected configuration retains (93.0 +/- 0.2)% of reconstructed signal intensity while discarding (97.8 +/- 0.1)% of the image area, with ~25 ms per-frame inference time on a consumer GPU. Second, we report a weakly supervised application of the Classification Without Labels (CWoLa) framework to data acquired with an Americium--Beryllium neutron source. Using only mixed AmBe and standard datasets (no event-level labels), a convolutional classifier learns to identify nuclear-recoil-like topologies. The achieved performance approaches the theoretical limit imposed by the mixture composition and isolates a high-score population with compact, approximately circular morphologies consistent with nuclear recoils.

L. Beirão da Veiga, A. Russo, G. Vacca

In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approximation of problems posed on a curved domain or with a curved interface. While an approximation of the domain with polygons leads, for degree of accuracy $k \geq 2$, to a sub-optimal rate of convergence, we show (both theoretically and numerically) that the proposed curved VEM lead to an optimal rate of convergence.

L. Beirão da Veiga, F. Dassi, A. Russo

We develop a numerical assessment of the Virtual Element Method for the discretization of a diffusion-reaction model problem, for higher "polynomial" order k and three space dimensions. Although the main focus of the present study is to illustrate some h-convergence tests for different orders k, we also hint on other interesting aspects such as structured polyhedral Voronoi meshing, robustness in the presence of irregular grids, sensibility to the stabilization parameter and convergence with respect to the order k.