2023/04/17 by Hubert Baty, Baty, Hubert
Physics and Astronomy · Engineering · #Model Reduction and Neural Networks #Fluid Dynamics and Turbulent Flows #Nuclear Engineering Thermal-Hydraulics
paper · pdf · doi:10.48550/arxiv.2304.08289
Physics informed neural networks (PINNs) are nowadays used as efficient\nmachine learning methods for solving differential equations. However,\nvanilla-PINNs fail to learn complex problems as ones involving stiff ordinary\ndifferential equations (ODEs). This is the case of some initial value problems\n(IVPs) when the amount of training data is too small and/or the integration\ninterval (for the variable like the time) is too large. We propose very simple\nrecipes to improve the training process in cases where only prior knowledge at\ninitial time of training data is known for IVPs. For example, more physics can\nbe easily embedded in the loss function in problems for which the total energy\nis conserved. A better definition of the training data loss taking into account\nall the initial conditions can be done. In a progressive learning approach, it\nis also possible to use a growing time interval with a moving grid (of\ncollocation points) where the differential equation residual is minimized.\nThese improvements are also shown to be efficient in PINNs modeling for solving\nboundary value problems (BVPs) as for the high Reynolds steady-state solution\nof advection-diffusion equation.\n