A two stages Deep Learning Architecture for Model Reduction of Parametric Time-Dependent Problems

• URL: http://arxiv.org/abs/2301.09926v2
• Date: Wed, 25 Jan 2023 07:36:14 GMT
• Title: A two stages Deep Learning Architecture for Model Reduction of Parametric Time-Dependent Problems
• Authors: Isabella Carla Gonnella, Martin W. Hess, Giovanni Stabile, Gianluigi Rozza
• Abstract summary: Parametric time-dependent systems are of crucial importance in modeling real phenomena. We present a general two-stages deep learning framework able to perform that generalization with low computational effort in time. Results are obtained applying the framework to incompressible Navier-Stokes equations in a cavity.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Parametric time-dependent systems are of a crucial importance in modeling real phenomena, often characterized by non-linear behaviors too. Those solutions are typically difficult to generalize in a sufficiently wide parameter space while counting on limited computational resources available. As such, we present a general two-stages deep learning framework able to perform that generalization with low computational effort in time. It consists in a separated training of two pipe-lined predictive models. At first, a certain number of independent neural networks are trained with data-sets taken from different subsets of the parameter space. Successively, a second predictive model is specialized to properly combine the first-stage guesses and compute the right predictions. Promising results are obtained applying the framework to incompressible Navier-Stokes equations in a cavity (Rayleigh-Bernard cavity), obtaining a 97% reduction in the computational time comparing with its numerical resolution for a new value of the Grashof number.

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