University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > POD-DL-ROM: a comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs

POD-DL-ROM: a comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs

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MDLW03 - Deep learning and partial differential equations

Conventional reduced order models (ROMs) anchored to the assumption of modal linear superimposition, such as proper orthogonal decomposition (POD), may reveal inefficient when dealing with nonlinear time-dependent parametrized PDEs, especially for problems featuring coherent structures propagating over time. To enhance ROM efficiency, we propose a nonlinear approach to set ROMs by exploiting deep learning (DL) algorithms, such as convolutional neural networks. In the resulting DL-ROM, both the nonlinear trial manifold and the nonlinear reduced dynamics are learned in a non-intrusive way by relying on DL algorithms trained on a set of full order model (FOM) snapshots, obtained for different parameter values. Performing then a former dimensionality reduction on FOM snapshots through POD enables, when dealing with large-scale FOMs, to speedup training times, and decrease the network complexity, substantially. Accuracy and efficiency of the resulting POD -DL-ROM technique are assessed on different parametrized PDE problems in cardiac electrophysiology, computational mechanics and fluid dynamics, possibly accounting for fluid-structure interaction (FSI) effects, where new queries to the POD -DL-ROM can be computed in real-time.

This talk is part of the Isaac Newton Institute Seminar Series series.

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