Artificial neural network for bifurcating phenomena modelled by nonlinear parametrized PDEs
session 2 (Zoom) (15:00–16:30 GMT)
This work aims to develop and investigate a computational framework to study parametrized partial differential equations (PDEs) which model nonlinear systems undergoing bifurcations. Bifurcation analysis, ie following the coexisting branches due to the non-uniqueness of the solution, as well as determining the bifurcation points themselves, are complex computational tasks   . The combination of reduced basis (RB) model reduction and artificial neural network (ANN) can potentially reduce the computational burden by several orders of magnitude and shed light on new strategies. Following the POD-NN approach , we analyzed two CFD applications where both physical and geometrical parameters were considered. We studied the Navier–Stokes equations for a viscous, steady, and incompressible flow: (i) in a planar straight channel with a narrow inlet of varying width, and (ii) in a triangular parametrized cavity . All the simulations were performed within the open source software FEniCS and RBniCS  for the RB framework, integrated with PyTorch to construct the neural network.
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-  RBniCS - reduced order modelling in FEniCS. www.rbnicsproject.org