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Topics in Continuum Mechanics

Reminders on linear algebra and tensor calculus
Kinematics of deformable bodies
Eulerian and Lagrangian descriptions of motion
Balance laws of continuum mechanics: conservation of mass, balance of linear and angular momentum, energy balance and dissipation inequality
Constitutive equations
Fluid dynamics: the Navier Stokes equations
Solid mechanics: nonlinear and linearized elasticity
Selected topics from the mechanics of biological systems

Books:

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Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier–Stokes equations with model order reduction

Pichi F, Strazzullo M, Ballarin F, Rozza G. Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier–Stokes equations with model order reduction. ESAIM: M2AN [Internet]. 2022 ;56(4):1361 - 1400. Available from: https://doi.org/10.1051/m2an/2022044

MicroROM: An Efficient and Accurate Reduced Order Method to Solve Many-Query Problems in Micro-Motility

Giuliani N, Hess MW, DeSimone A, Rozza G. MicroROM: An Efficient and Accurate Reduced Order Method to Solve Many-Query Problems in Micro-Motility. [Internet]. 2020 . Available from: https://arxiv.org/abs/2006.13836

The Neural Network shifted-proper orthogonal decomposition: A machine learning approach for non-linear reduction of hyperbolic equations

Papapicco D, Demo N, Girfoglio M, Stabile G, Rozza G. The Neural Network shifted-proper orthogonal decomposition: A machine learning approach for non-linear reduction of hyperbolic equations. Computer Methods in Applied Mechanics and Engineering [Internet]. 2022 ;392. Available from: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85124488633&doi=10.1016%2fj.cma.2022.114687&partnerID=40&md5=12f82dcaba04c4a7c44f8e5b20101997

Summer school on Reduced Order Methods in Computational Fluid Dynamics

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Non-linear MOR: non-linear manifold method

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Data Enhanced Reduced Order Models for Turbulent Flows

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Deep-learning based ROMs for fast transient dynamics

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Application of Neural Networks in the optimisation of a hybrid energy system

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Digital Twins: state of the art and future challenges

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