论文信息 - Artificial neural network for bifurcating phenomena modelled by nonlinear parametrized PDEs

Artificial neural network for bifurcating phenomena modelled by nonlinear parametrized PDEs

bifurcating nonlinear PDEs, overcoming intrusive EIM/DEIM strategies. How: POD-NN approach which combines ROMs and non-intrusive learning of reduced coefficients. Why: Investigate efficiently complex bifurcating behaviour in a real-time context. Artificial neural network for bifurcating phenomena modelled by nonlinear parametrized PDEs Federico Pichi1, Francesco Ballarin1, Gianluigi Rozza1 and Jan Hesthaven2 1 mathLab, Mathematics Area, SISSA International School for Advanced Studies, Trieste, Italy 2EPFL, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

[1] Jan S. Hesthaven,et al. Non-intrusive reduced order modeling of nonlinear problems using neural networks , 2018, J. Comput. Phys..

[2] Gianluigi Rozza,et al. Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier-Stokes equations with model order reduction , 2020, ArXiv.

[3] Gianluigi Rozza,et al. Reduced Basis Approaches for Parametrized Bifurcation Problems held by Non-linear Von Kármán Equations , 2018, Journal of Scientific Computing.

[4] Annalisa Quaini,et al. A Reduced Order Modeling Technique to Study Bifurcating Phenomena: Application to the Gross-Pitaevskii Equation , 2020, SIAM J. Sci. Comput..