Niccolo' Discacciati

After receiving my Bachelor’s degree in Mathematical Engineering from Polytechnic University of Milan (PoliMi) in 2015, I took part in the double degree Master program between EPFL and PoliMi in Computational Science and Engineering. After an internship at the Swiss National Supercomputing Center, I joined the MCSS chair as a Master student in 2018 to write my thesis. Following graduation in 2018, I am currently pursuing my doctoral studies under the supervision of Prof. Hesthaven.

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Neural network

A neural network can refer to a neural circuit of biological neurons (sometimes also called a biological neural network), a network of artificial neurons or nodes in the case of an artificial neur

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathema

Viscosity

The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity

Localized model order reduction and domain decomposition methods for coupled heterogeneous systems

Niccolo' Discacciati, Jan Sickmann Hesthaven

We propose a model order reduction technique to accurately approximate the behavior of multi-component systems without any a-priori knowledge of the coupled model. In the offline phase, we construct independent surrogate models by solving the local problems with parametrized interface boundary conditions, while we combine them using domain decomposition techniques during the online phase. We show the potential of the proposed approach in terms of accuracy, computational performance and robustness in a series of test cases, including nonlinear and multi-physics problems.

WILEY2023

Modeling synchronization in globally coupled oscillatory systems using model order reduction

Niccolo' Discacciati, Jan Sickmann Hesthaven

We construct reduced order models for two classes of globally coupled multi-component oscillatory systems, selected as prototype models that exhibit synchronization. These are the Kuramoto model, considered both in its original formulation and with a suitable change of coordinates, and a model for the circadian clock. The systems of interest possess strong reduction properties, as their dynamics can be efficiently described with a low-dimensional set of coordinates. Specifically, the solution and selected quantities of interest are well approximated at the reduced level, and the reduced models recover the expected transition to synchronized states as the coupling strengths vary. Assuming that the interactions depend only on the averages of the system variables, the surrogate models ensure a significant computational speedup for large systems.

AIP Publishing2021

Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neural networks

Niccolo' Discacciati, Jan Sickmann Hesthaven, Deep Ray

High-order numerical solvers for conservation laws suffer from Gibbs phenomenon close to discontinuities, leading to spurious oscillations and a detrimental effect on the solution accuracy. A possible strategy to reduce it comprises adding a suitable amount of artificial dissipation. Although several viscosity models have been proposed in the literature, their dependence on problem-dependent parameters often limits their performances. Motivated by the objective to construct a universal artificial viscosity method, we propose a new technique based on neural networks, integrated into a Runge-Kutta Discontinuous Galerkin solver. Numerical results are presented to demonstrate the performance of this network-based technique. We show that it is able both to guarantee optimal accuracy for smooth problems, and to accurately detect discontinuities, where dissipation has to be injected. A comparison with some classical models is carried out, showing that the network-based model is always at par with the best among the traditional optimized models, independently of the selected problem and parameters. (C) 2020 Elsevier Inc. All rights reserved.

ACADEMIC PRESS INC ELSEVIER SCIENCE2020