A5061558433- Model Reduction and Neural Networks
- Advanced Numerical Methods in Computational Mathematics
- Fluid Dynamics and Vibration Analysis
- Probabilistic and Robust Engineering Design
- Numerical methods for differential equations
- Computational Fluid Dynamics and Aerodynamics
- Fluid Dynamics and Turbulent Flows
- Hydraulic and Pneumatic Systems
- Numerical methods in engineering
- Nuclear Engineering Thermal-Hydraulics
- Real-time simulation and control systems
- Electromagnetic Simulation and Numerical Methods
- Elasticity and Material Modeling
- Meteorological Phenomena and Simulations
- Advanced Numerical Analysis Techniques
- Ship Hydrodynamics and Maneuverability
- Lattice Boltzmann Simulation Studies
- Nuclear reactor physics and engineering
- Cardiovascular Function and Risk Factors
- Vibration and Dynamic Analysis
- Coronary Interventions and Diagnostics
- Reservoir Engineering and Simulation Methods
- Modeling and Simulation Systems
- Structural Health Monitoring Techniques
- Advanced Multi-Objective Optimization Algorithms
Scuola Internazionale Superiore di Studi Avanzati
2016-2025
Université Paris Cité
2023
Centre National de la Recherche Scientifique
2023
Institut Universitaire de France
2023
Laboratoire Jacques-Louis Lions
2023
Sorbonne Université
2023
École Polytechnique Fédérale de Lausanne
2006-2021
Eindhoven University of Technology
2021
Max Planck Institute for Dynamics of Complex Technical Systems
2021
Polytechnic University of Turin
2021
Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the network itself. PINNs nowadays used to solve PDEs, fractional integral-differential and stochastic PDEs. This novel methodology has arisen multi-task learning framework in which NN must fit observed data while reducing PDE residual. article provides comprehensive review literature on PINNs: primary goal study was characterize these...
Summary In this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized steady incompressible Navier–Stokes equations with low Reynolds number. Copyright © 2014 John Wiley & Sons, Ltd.
Abstract Reduction strategies, such as model order reduction (MOR) or reduced basis (RB) methods, in scientific computing may become crucial applications of increasing complexity. In this paper we review the methods (built upon a high-fidelity ‘truth’ finite element approximation) for rapid and reliable approximation parametrized partial differential equations, comment on their potential impact industrial interest. The essential ingredients RB methodology are: Galerkin projection onto...
We present an approach to the construction of lower bounds for coercivity and inf–sup stability constants required in a posteriori error analysis reduced basis approximations affinely parametrized partial differential equations. The method, based on Offline–Online strategy relevant many-query real-time context, reduces Online calculation small Linear Program: objective is parametric expansion underlying Rayleigh quotient; constraints reflect information at optimally selected parameter...
Abstract Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. A Reduced Order Model (ROM) of the incompressible ow cylinder presented this work. The ROM built performing Galerkin projection governing equations onto lower dimensional space. reduced basis space generated using Proper Orthogonal Decomposition (POD) approach. In particular focus into (i) correct reproduction pres- sure field, case vortex phenomenon, primary...
SUMMARY In this paper, we further develop an approach previously introduced in Lassila and Rozza, 2010, for shape optimization that combines a suitable low‐dimensional parametrization of the geometry (yielding geometrical reduction) with reduced basis methods reduction computational complexity). More precisely, free‐form deformation techniques are considered description its parametrization, whereas used upon FE discretization to solve systems parametrized partial differential equations. This...
SUMMARY The solution of inverse problems in cardiovascular mathematics is computationally expensive. In this paper, we apply a domain parametrization technique to reduce both the geometrical and computational complexities forward problem replace finite element incompressible Navier–Stokes equations by less‐expensive reduced‐basis approximation. This greatly reduces cost simulating problem. We then consider deterministic sense, solving least‐squares problem, statistical using Bayesian...
Numerical simulation of parametrized differential equations is crucial importance in the study real-world phenomena applied science and engineering. Computational methods for real-time many-query such problems often require prohibitively high computational costs to achieve sufficiently accurate numerical solutions. During last few decades, model order reduction has proved successful providing low-complexity high-fidelity surrogate models that allow rapid simulations under parameter...