Mattia Manucci with talks at several conferences

Mattia Manucci, PostDoc at the SimTech Cluster of Excellence, focuses in his research on the development of Model Order Reduction (MOR) strategies for dynamical systems. Specifically, he is investigating the use of Contour Integral Methods based on Laplace transform as a reduction tool to efficiently and reliably deal with the control of dynamical stems used to model heat supply through local, climate-neutral feeds. With this, he is funded within the framework of the BMBF-fundes project ElAN which was acquired by Junior Research Group Leader Benjamin Unger. He will now present his research on the occasion of several conferences.

The 10th edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2023) will take place on 5-7 June 2023 in Chania, Greece.

The objectives of COUPLED PROBLEMS 2023 are to present and discuss state of the art, mathematical models, numerical methods and computational techniques for solving coupling problems of multidisciplinary character in science and engineering. The conference goal is to make step forward in the formulation and solution of real-life problems with a multidisciplinary vision, accounting for all the complex couplings involved in the physical description of the problem.

In Session “IS16 - II  - Nonlinear and deepl learning based model reduction for coupled problems”, chaired by Silke Glas (University of Twente), Mattia Manucci will talk about “Model order reduction in contour integration method for parametric linear evolution equations.”

In this talk on Monday, 5 June, from 2:30 to 4:30 pm, the problem of numerical approximation of evolution PDEs is considered. A peculiarity of the considered equations is their dependence on a few parameters, which is associated with the need to calculate multiple solutions as the parameters vary, possibly real-time. The proposed method approximates a complex contour integral in order to invert numerically the Laplace transform of the solution \cite{GLM}. The considered contours are constructed in such a way as to approximate certain curves, so-called pseudospectral, which characterize the space operator of the equation. The proposed approach is particularly well-suited to parabolic equations, where the contour can be essentially bounded. When the operator is hyperbolic the application of the method becomes critical, as the inversion of the Laplace transform on the continuous problem cannot be limited to a bounded contour. However, many numerical approaches introduce an artificial diffusion, which makes the proposed approach feasible. For the purpose of real-time computations for several instances of the parameters, various methodologies based on reduced bases or on model reduction methods have been proposed in the literature, which allow to solve small dimensional problems, maintaining a control of the accuracy. However, when the operator is hyperbolic, reduced basis methods and model order reduction based on classical time stepping schemes fail to provide the desired performances due to a critical decay of the Kolmogorov n-width. The use of reduction methods based on the Laplace transform on pseudospectral contours is new and seems to have several advantages (see \cite{GM}) with respect to those considered in the literature. The communication is inspired by collaborations with M. Lopez Fernandez (Malaga) and C. Lubich (Tuebingen).

Only a week later, Mattia Manucci will give a contributed talk in Madrid on “Approximation of the smallest eigenvalue of large hermitian matrices dependent on parameters” during this year’s Conference of the International Linear Algebra Society ILAS(2023) that will take place from 12 to 16 June in Madrid (Spain).

Again a week later, the University of Porto will be the next stop on his itinerary where Mattia Manucci will talk about “Sparse Data-Driven Quadrature Rules via ℓp-Quasi-Norm Minimization” at the ECCOMAS Young Investigators Conference (YIC2023). The ECCOMAS Young Investigators Conference YIC2023 is the 7^th in the series of International Conferences, organized since 2012 with the main purpose of bringing together, within a relaxed environment, students and young researchers developing their work on all areas related with computational science and engineering.

In this talk he and the other authors will present the focal underdetermined system solver as numerical tool to recover sparse empirical quadrature rules for parametrized integrals from existing data. This algorithm, originally proposed for image and signal reconstruction, relies on an approximated ℓp-quasi-norm minimization. Compared to ℓ1-norm minimization, the choice of 0 < p < 1 provides a natural framework to accommodate usual constraints which quadrature rules must fulfil. We also extend an a priori error estimate available for the ℓ1-norm formulation by considering the error resulting from data compression. Finally, we present numerical examples to investigate the numerical performance of our method and compare our results to both ℓ1-norm minimization and nonnegative least squares method.

Mattia Manucci is a numerical analyst. He defended his PhD in mathematics in February 2023 at the Gran Sasso Science Institute of L'Aquila. He conducted his research under the supervision of Prof. Dr. Nicola Guglielmi. Prior to his doctoral studies, he earned a bachelor's degree in mathematics for engineering in 2016 at Politecnico di Torino. In 2018, he obtained a master's degree in mathematical engineering from Politecnico di Torino and a Master's degree in Computational Mechanics from Ecole Centrale de Nantes. His research focuses on the numerical discretization of time-dependent partial differential equations (PDEs) and the application of Model Order Reduction (MOR) techniques to accelerate numerical simulations. During his PhD, he specifically worked on the combination of Contour Integral Methods (CIMs) for time integration and projection MOR techniques in the contest of linear parametric PDEs.