A. A. 2024-2025

Past events:

• 14/03/2024, Guan Haoran, visiting PhD student from the Hong Kong Polytechnic University

Time&Location: 14:30 - Aula Levi (Laboratorio Primo Piano), Dipartimento di Matematica, Università di Bologna

Title: Some recent developments of deterministic CholeskyQR

Abstract: CholeskyQR is a popular algorithm for QR factorization in both academia and industry. In order to have good orthogonality, CholeskyQR2 is developed by repeating CholeskyQR twice. Shifted CholeskyQR3 introduces a shifted item in order to deal with ill-conditioned matrices with good orthogonality. This talk primarily focuses on deterministric methods. We define a new matrix norm and make improvements to the shifted item and error estimations in CholeskyQR algorithms. We use such a technique and provide an analysis to some sparse matrices in the industry for CholeskyQR. Moreover, we combine CholeskyQR and our new matrix norm with randomized models for probabilistic error analysis and make amelioration to CholeskyQR. A new 3-step algorithm without CholeskyQR2 is also developed with good orthogonality.

• 27/03/2024, Guillaume Le Gall, visiting PhD student from Université Savoie Mont Blanc.

Time&Location: 14:30 - Seminario I, Dipartimento di Matematica, Università di Bologna

Title: Spatiotemporal variability of solar radiations within an urban context: a characterisation by means of Principal Component Analysis

Abtract: Sunlight constitutes an abundant and endless natural fuel, available worldwide. In a society where a substantial part of the global energy yield is being directly expended at the city scale, urban areas appear as serious candidates for the production of solar energy. Their intrinsic complexity yet makes it challenging. The morphological heterogeneity between urban geometries and intricacy of their materials optical properties especially contribute together to causing important spatiotemporal variations in the distribution of incident solar radiations. The field of irradiance received by a specific urban region (e.g. façade, building, district) may thus rapidely become the result of complex miscellaneous interactions between many degrees of freedom. Besides, Principal Component Analysis (PCA) has been widely validated as an efficient algorithm to identify the principal behavioural features, or modes of variability, of a high-dimensional phenomenon. An approach is proposed here for analysing the variations in space and time of the solar resource within an urban context by means of PCA. A parametric investigation is conducted on a set of theoretical 100×100 m² urban districts, defined as arrangements of cuboid-like buildings, with various typological indicators (Total Site Coverage, Average Building Height) and surface materials (Lambertian, highly-specular) at three different latitudes. For each configuration, the distribution of irradiance incident on the facets of the central building is modelled via backwards Monte-Carlo ray tracing over a full year and under clear sky conditions, with a 15 min timestep and 1 m spatial resolution. PCA is subsequently applied to the simulated radiative fields to extract dominant modes of variation. First results validate energy-based orthogonal decompositions like PCA as efficient tools for characterising the variability distribution of multivariate phenomena in this context, allowing for the identification of district areas subjected to important spatial and temporal variations of the solar resource. Characteristic time scales are clearly represented across successive orders of decomposition. Information about the district morphology is also obtained, with the contribution of surrounding geometries being portrayed by specific spatial modes. Similar prevalent variables are further repetitively encountered across multiple evaluated surfaces, but at different modal ranks.

• 10/04/2024, Martina Iannacito, PostDoc @ UniBO

Time&Location: 14:30 - Seminario II, Dipartimento di Matematica, Università di Bologna

Title: Potential and applications of tensor-based algorithms

Abstract: Tensors have become widely used in various domains due to their practicality. Tensor factorization techniques are used to solve computationally demanding problems, analyze large datasets, and refine descriptions of complex phenomena. This presentation outlines the development of my research on tensors, including an overview of commonly used tensor methods and their applications in various fields such as remote sensing, multilinear algebra, numerical simulation, and signal processing. Criteria for selecting the most appropriate tensor technique depending on the problem under consideration will be emphasized. The presentation aims to outline the advantages and limitations inherent in these techniques. It explores the challenges and offers insights into current research directions driven by real-world, computational, and applied problems.

• 24/04/2024, Lorenzo Piccinini, PhD student @ UniBO

Time&Location: 14:30 - Aula Arzelà, Dipartimento di Matematica, Università di Bologna

Title: Truncated LSQR for Matrix Least Squares Problems and Application to Dictionary Learning

Abstract: We are interested in the numerical solution of the matrix least squares problem min_X ∥AXB + CXD-F ∥_F , with A and C full column rank, B, D full row rank, F an n×n matrix of low rank, and ∥•∥_F the Frobenius norm. We derive a matrix-oriented implementation of LSQR, and devise an implementation of the truncation step that exploits the properties of the method. Experimental comparisons with the Conjugate Gradient method applied to the normal matrix equation and with a (new) sketched implementation of matrix LSQR illustrate the competitiveness  of the proposed algorithm. We also explore the applicability of our method in the context of Kronecker-based Dictionary Learning, and devise a representation of the data that seems to be promising for classification purposes.

• 07/05/2024, Luca Ratti, (Junior) Assistant Professor @ UniBO

Time&Location: 16:00 - Seminario II, Dipartimento di Matematica, Università di Bologna

Title: Learned regularization for linear inverse problems

Abstract: An inverse problem is the task of retrieving an unknown quantity from indirect observations. When the model describing the measurement acquisition is linear, this results in the inversion of a linear operator (a matrix, in a discrete formulation) which is usually ill-posed or ill-conditioned. A common strategy to tackle ill-posedness in inverse problems is to use regularizers, which are (families of) operators providing a stable approximation of the inverse map. Model-based regularization techniques often leverage prior knowledge of the exact solution, such as smoothness or sparsity with respect to a suitable representation; on the other side, in recent years many data-driven methods have been developed in the context of machine learning. Those techniques tackle the approximation of the inverse operator in suitable spaces of parametric functions (i.e., neural networks) and rely on large datasets of paired measurements and ground-truth objects. In this talk, I will focus on hybrid strategies, which aim at blending model-based and data-driven approaches, providing both satisfying numerical results and sound theoretical guarantees. I will describe a general framework to comprise many existing techniques in the theory of statistical learning, also reporting some recent theoretical advances (in the direction of generalization guarantees). I will help the discussion by presenting some relevant examples in the context of medical imaging and, specifically, in computed tomography.

• 23/05/2024, Sascha Portaro, PhD student @ UniBO

Time&Location: 14:30 - Seminario I, Dipartimento di Matematica, Università di Bologna

Title: Row-aware Randomized SVD with applications

Abstract: We introduce a novel procedure for computing an SVD-type approximation of a tall matrix A. Specifically, we propose a randomization-based algorithm that improves the standard Randomized Singular Value Decomposition (RSVD). Most significantly, our approach, the Row-aware RSVD (R-RSVD), explicitly constructs information from the row space of A. This leads to better approximations to Range(A) while maintaining the same computational cost. The efficacy of the R-RSVD is supported by both robust theoretical results and extensive numerical experiments. Furthermore, we present an alternative algorithm inspired by the R-RSVD, capable of achieving comparable accuracy despite utilizing only a subsample of the rows of A, resulting in a significantly reduced computational cost. This method, that we name the Subsample Row-aware RSVD (Rsub-RSVD), is supported by a weaker error bound compared to the ones we derived for the R-RSVD, but still meaningful as it ensures that the error remains under control. Additionally, numerous experiments demonstrate that the Rsub-RSVD trend is akin to the one attained by the R-RSVD when the subsampling parameter is on the order of n, for a m×n A, with m >> n. Finally, we consider the application of our schemes in two very diverse settings which share the need for the computation of singular vectors as an intermediate step: the computation of CUR decompositions by the discrete empirical interpolation method (DEIM) and the construction of reduced-order models in the Loewner framework, a data-driven technique for model reduction of dynamical systems.

• 05/06/2024, Francesco Gravili, PhD student @ UniBO

Time&Location: 11:00 - Aula B. Levi, Dipartimento di Matematica, Università di Bologna

Title: Computation  of centralities in temporal multilayer networks

Abstract: Multilayer networks are a type of complex network that consist of multiple layers, where each layer represents a different type of connection or interaction between the same set of nodes. These networks are used to model systems where entities are connected in multiple ways simultaneously, capturing the complexity of real-world relationships better than traditional single-layer networks. Through a particular interlayer structure, the dynamical evolution of a complex system over time can be represented. Computing the centrality of a temporal network can improve our understanding of how the most important nodes in a network change over time. Our focus is centered on the computation of the centralities of a multilayer temporal network whose modifications over time consist of low-rank updates of the edge adjacency matrix of a transport network. Using  Krylov subspace methods for matrix function approximations, we will exploit the particular structure of the problem to gain some computational advantages and modeling insights.

• 18/06/2024, Silvia Tozza, (Senior) Assistant Professor @ UniBO

Time&Location: 15:45 - Aula B. Levi, Dipartimento di Matematica, Università di Bologna

Title: Image segmentation via an adaptive “filtered” scheme based on a modified level-set method 

Abstract: This seminar addresses the problem of image segmentation through an accurate high-order scheme based on the level-set method. In this approach, the curve evolution is described as the 0-level set of a representation function, but the velocity that drives the curve to the boundary of the object has been modified in order to obtain a new velocity with additional properties that are extremely useful to develop a more stable high-order approximation with a small additional cost. The approximation scheme proposed here is the 2D version of an adaptive “filtered” scheme, which combines two building blocks (a monotone scheme and a high-order scheme) via a filter function and smoothness indicators that allow one to detect the regularity of the approximate solution adapting the scheme in an automatic way. Some numerical tests on synthetic and real images confirm the accuracy of the proposed method and the advantages given by the new velocity. 

• 12/09/2024, Marco Verani, Politecnico di Milano

Time&Location: 15:45 - Aula Arzelà, Dipartimento di Matematica, Università di Bologna

Title: A Virtual Element method for non-Newtonian fluid flows

Abstract: In this talk, we present a Virtual Element discretization for the steady motion of non-Newtonian, incompressible fluids. A specific stabilization, tailored to mimic the monotonicity and boundedness properties of the continuous operator, is introduced and theoretically investigated. The proposed method has several appealing features, including the exact enforcement of the divergence free condition and the possibility of making use of fully general polygonal meshes. A complete well-posedness and convergence analysis of the proposed method is presented under mild assumptions on the non-linear laws, encompassing common examples such as the Carreau--Yasuda model. Numerical experiments validating the theoretical bounds as well as demonstrating the practical capabilities of the proposed formulation are presented.  

• 10/10/2024, Kai Bergermann, Math Dept, TU-Chemnitz, Germany

Time&Location: 11:00 - Seminario II, Dipartimento di Matematica, Università di Bologna

Title: Numerical linear algebra meets multiplex networks 

Abstract: Multiplex networks are used to model complex systems from myriad applications. They generalize classical complex networks by recording different types of relationships, different interactions, or changing interactions over time between the same entities in different layers. They possess natural linear algebraic representations in terms of structured matrices, which makes efficient numerical linear algebra techniques a valuable tool for their analysis. In this talk, we give an overview over several network science problems that can be formulated in terms of matrix function expressions, which we approximate by polynomial and rational Krylov methods. We discuss centrality measures, the solution of stiff systems of non-linear differential equations with exponential Runge--Kutta integrators, as well as un- and semi-supervised community detection. Additionally, we present a nonlinear spectral method for core-periphery detection in multiplex networks. All presented methods have a linear runtime scaling, which allows the treatment of large-scale multiplex networks and we present numerical experiments for all considered problems. 

•  26/11/2024, Paolo Zuzolo, PhD student @ UniBO

Time&Location: 11:00 - Seminario II, Dipartimento di Matematica, Università di Bologna

Title: Deep spectral features for 3D shape analysis 

Abstract: 3D shape analysis tasks often involve characterizing a 3D object by an invariant, computationally efficient, and discriminative numerical representation, called shape descriptors. Among those, spectral-based shape descriptors have become increasingly widespread, since the spectrum is an isometry invariant, and thus is independent of the object’s representation including parametrization and spatial position[1]. However, large spectral decompositions and the choice of the most significant eigen-couples become computationally expensive for large set of data-points. We introduce a concise learning-based shape descriptor, computed through a Generalized Graph Neural Network (G-GNN) [2]. The G-GNN is an unsupervised graph neural network, leveraging spectral-based convolutional operators, derived from a learnable, energy-driven evolution process. Applied to a 3D polygonal mesh, the G-GNN allows to learn features acting as global shape descriptor of the 3D object. Using a 3D mesh related Dirichlet-like energy leads to a spectral and intrinsic shape descriptor, tied to the isometry invariant Laplace-Beltrami operator. Finally, by equipping the G-GNN with a suitable shape retrieval loss, the spectral shape descriptor can be employed in non-linear dimensionality reduction problems since it can define an optimal embedding, squeezing the latent information of a 3D model into a compact low-dimensional shape representation of the 3D object [1] Martin Reuter, Franz-Erich Wolter, Niklas Peinecke, Laplace–Beltrami spectra as ‘Shape-DNA’ of surfaces and solids, Computer-Aided Design, Volume 38, Issue 4, 2006, Pages 342-366, ISSN 0010-4485, https://doi.org/10.1016/j.cad.2005.10.011. [2] D. Lazzaro, S. Morigi, P. Zuzolo, Learning intrinsic shape representations via spectral mesh convolutions, Neurocomputing, Volume 598, 2024, 128152, ISSN 0925-2312, https://doi.org/10.1016/j.neucom.2024.128152. 

•  16/12/2024, Li Yang, Hunan Normal University (China)

Time&Location: 10:00 - Aula Bombelli, Dipartimento di Matematica, Università di Bologna

Title: Advances in Sparse Signal Recovery and Inverse Problems: Robust Models and Adaptive Techniques 

Abstract: This seminar presents two recent works focused on sparse signal recovery and inverse problems. The first part introduces the truncated Huber penalty, a non-convex penalty function designed for robust signal recovery. We explore its application in constrained and unconstrained models, proving theoretical properties of the optimal solutions. An efficient algorithm based on the block coordinate descent method is also discussed, along with applications in signal and image processing. The second part covers a generalized Tikhonov regularization framework with spatially varying weights estimated via a neural network. This end-to-end approach integrates adaptive parameter estimation, improving detail preservation. 

• 09/01/2025, Giovanni Seraghiti, University of Mons (Belgium) and Università di Firenze

Time&Location: 11:00 - Seminario II, Dipartimento di Matematica, Università di Bologna

Title: Adaptive gradient methods and parameter pruning

Abstract: In this seminar, I will talk about Objective Function Free Optimization (OFFO) in the context of pruning the parameter of a given model. OFFO algorithms are methods where the objective function is never computed; instead, they rely only on derivative information, thus on the gradient in the first-order case. I will give an overview of the main OFFO methods, focusing on adaptive algorithms such as Adagrad, Adam, RMSprop, ADADELTA, which are gradient methods that share the common characteristic of depending only on current and past gradient information to adaptively determine the step size at each iteration. Next, I will briefly discuss the most popular pruning approaches. As the name implies, pruning a model, typically a neural networks, refers to the process of reducing its size and complexity, typically by removing certain parameters that are considered unnecessary for its performance. Pruning emerges as an alternative compression technique for neural networks to matrix and tensor factorization or quantization. Mainly, I will focus on pruning-aware methods that uses specific rules to classify parameters as relevant or irrelevant at each iteration, enhancing convergence to a solution of the problem at hand, which is robust to pruning irrelevant parameters after training.Finally, I will introduce a novel deterministic algorithm which is both adaptive and pruning-aware, based on a modification Adagrad scheme that converges to a solution robust to pruning with complexity of $\log(k) \backslash k$. I will illustrate some preliminary results on different applications.

• 27/01/2025, Liwei Hu, PhD student @ UniBO

Time&Location: 14:30 - Aula Seminario II, Dipartimento di Matematica, Università di Bologna

Title: A regularization method for landslide thickness estimation

Abstract: Accurately estimating landslides’ failure surface depth is essential for hazard prediction. However, most of the classical methods rely on overly simplistic assumptions [1]. In this work, we will present the landslide thickness estimation problem as an inverse problem Aw = b, obtained from discretization of the thickness equation [2]:

∂(hf vx)/∂x + ∂(hf vy)/∂y = − ∂ζ/∂t ,  (1)

where the forward operator A contains information on the surface velocity (v_x, v_y), the right-hand side b corresponds to the surface elevation change ∂ζ/∂t, and w is the thickness hf . By employing a regularization approach, the inverse problem is reformulated as an optimization problem. In real-world scenarios, often no information on neither the noise type nor the noise level affecting data is available. In this context, the correct choice of the regularization parameter becomes a pressing issue. We propose a method to determine this parameter in a fully automatic way for the thickness inversion problem. Results obtained on both synthetic data generated by landslide simulation software and data measured from real-world landslides will be shown.

[1] Jaboyedoff M., Carrea D., Derron M.H., Oppikofer T., Penna I.M., Rudaz B. (2020): A review of methods used to estimate initial landslide failure surface depths and volumes. Engineering Geology, 267, 105478

[2] Booth A. M. ; Lamb M. P. ; Avouac J.P. ; Delacourt C. (2013): Landslide velocity, thickness, and rheology from remote sensing: La Clapière landslide, France. Geophysical Research Letters, Vol. 40, 4299 - 4304.

• 26/02/2025, Sabrina Pellegrino, Assistant Professor @ PoliBa

Time&Location: 15:30 - Aula Seminario I, Dipartimento di Matematica, Università di Bologna

Title: Spectral collocation methods for nonlocal perydynamic problems and applications

Abstract: Peridynamics is a nonlocal version of continuum mechanics theory able to incorporate singularities since it does not take into account spatial partial derivatives. As a consequence, it assumes long-range interactions among material particles and is able to describe the formation and the evolution of fractures. The discretization of such nonlocal model requires the use of raffinate numerical tools for approximating the solutions to the model. Due to the presence of a convolution product in the definition of the nonlocal operator, we propose a spectral collocation method based on the implementation of Fourier and Chebyshev polynomials to discretize the model. The choice can benefit of the FFT algorithm and allow us to deal efficiently with the imposition of non-periodic boundary conditions by a volume penalization technique. We prove the convergence of such methods in the framework of fractional Sobolev space and discuss numerically the stability of the scheme. We also investigate the qualitative aspects of the convolution kernel and of the nonlocality parameters by solving an inverse peridynamic problem by using a Physics-Informed Neural Network activated by suitable Radial Basis functions. Additionally, we propose a virtual element approach to obtain the solution of a nonlocal diffusion problem. The main feature of the proposed technique is that we are able to construct a nonlocal counterpart for the divergence operator in order to obtain a weak formulation of the peridynamic model and exploit the analogies with the known results in the context of Galerkin approximation. We prove the convergence of the proposed method and provide several simulations to validate our results.

References:

[1] Lopez, L., Pellegrino, S. F. (2021). A spectral method with volume penalization for a nonlinear peridynamic model International Journal for Numerical Methods in Engineering 122(3): 707–725. https://doi.org/10.1002/nme.6555

[2] Lopez, L., Pellegrino, S. F. (2022). A space-time discretization of a nonlinear peridynamic model on a 2D lamina Computers and Mathematics with Applications 116: 161–175. https://doi.org/10.1016/j.camwa.2021.07.0041

[3] Lopez, L., Pellegrino, S. F. (2022). A non-periodic Chebyshev spectral method avoiding penalization techniques for a class of nonlinear peridynamic models International Journal for Numerical Methods in Engineering 123(20): 4859–4876. https://doi.org/10.1002/nme.7058

[4] Difonzo, F. V., Lopez, L., Pellegrino, S. F. (2024). Physics informed neural networks for an inverse problem in peridynamic models Engineering with Computers. https://doi.org/10.1007/s00366-024-01957-5

[5] Difonzo, F. V., Lopez, L., Pellegrino, S. F. (2024). Physics informed neural networks for learning the horizon size in bond-based peridynamic models Computer Methods in Applied Mechanics and Engineering. https://doi.org/10.1016/j.cma.2024.117727

• 13/03/2025, Laura Galli, Associate Professor @ UniBO

Time&Location: 14:30 - Aula Seminario II, Dipartimento di Matematica, Università di Bologna

Title: Formulations and algorithms for the Delay Constrained Routing problem

Abstract: Given a telecommunication network represented by a directed graph, our problem is to route one single stream of packets on the IP network along a min-cost path with a constraint on the maximum delay that any packet may incur. From a mathematical point of view, this problem, known as Delay Constrained Routing (DCR), can be formulated as a Mixed-Integer Second-Order Cone Program (MISOCP), where one needs to simultaneously (and "optimally") compute paths and reserve resources along the paths of the network. The DCR problem presents an interesting mixture of combinatorial and continuous structures and naturally lends itself to decomposition methods. We will discuss formulations, algorithms and computational results on real/realistic network instances.

• 20/03/2025, Monica Pragliola, Assistant Professor @ UniNA

Time&Location: 15:30 - Aula Seminario II, Dipartimento di Matematica, Università di Bologna

Title: Sparsity Promoting Hierarchical Bayesian Model for EIT

Abstract: The aim of Electrical Impedance Tomography (EIT) is to determine the electrical conductivity distribution inside a domain by applying currents and measuring voltages on its boundary. Mathematically, the EIT reconstruction task can be formulated as a non-linear inverse problem. The Bayesian inverse problems framework has been applied expensively to solutions of the EIT inverse problem, in particular in the cases when the unknown conductivity is believed to be blocky. In this talk, we demonstrate that by exploiting linear algebraic considerations it is possible to organize the calculation for the Bayesian solution of the nonlinear EIT inverse problem via finite element methods with sparsity promoting priors in a computationally efficient manner. The proposed approach uses the Iterative Alternating Sequential (IAS) algorithm for the solution of the linearized problems. Within the IAS algorithm, a substantial reduction in computational complexity is attained by exploiting the low dimensionality of the data. Numerical tests on synthetic and real data illustrate the computational efficiency of the proposed algorithm.

• 14/05/2025, Karl Meerbergen, Professor @ KU Leuven

Time&Location: 11:30 - Aula Bombelli, Dipartimento di Matematica, Università di Bologna

Title: Rational Approximation and Linearization of Matrix Valued Functions: Algorithms and Application 

Abstract: A nonlinear matrix is a matrix whose entries are nonlinear functions of a parameter. Such problems arise from physics (Schroedinger equation) and mechanical engineering (porous materials, boundary element method, e.g.). The last 20 years, rational approximation methods and linearization were proposed to approximate such matrices by linear pencils of much higher dimensions. Applications are the nonlinear eigenvalue problem, parametric linear systems, frequency sweeping, model order reduction and the solution of time dependent problems with nonlinear frequency dependencies. We give an overview of approximation methods with focus on AAA and Krylov methods that exploit the structure of the linear pencil. 

• 10/06/2025, Ricardo Nochetto, Professor @ University of Maryland, College Park

Time&Location: 11:00 - Seminario II, Dipartimento di Matematica, Università di Bologna

Title: Liquid Crystal Networks: A Challenge in Computational Science

Abstract: Modeling, analysis and computation are three pillars of computational science. We discuss them within the context of liquid crystal networks (LCNs). These materials couple a nematic liquid crystal with a rubbery material. When actuated with heat or light, the interaction of the liquid crystal with the rubber creates complex shapes. Thin bodies of LCNs are natural candidates for soft robotics applications. We start from the classical 3D trace energy formula and derive a reduced 2D membrane energy as the formal asymptotic limit of vanishing thickness, including both stretching and bending energies, and characterize the zero energy deformations. We design a sound numerical method and discuss its Gamma convergence. We present computations showing the geometric effects that arise from liquid crystal defects as well as computations of nonisometric origami within and beyond theory. This work is joint with L. Bouck, G. Benavides, and S. Yang.