![]() All these aspects are avoided when employing DL-ROMs, which learn in a non-intrusive way both the nonlinear trial manifold and the reduced dynamics, by relying on deep (e.g., feedforward, convolutional, autoencoder) neural networks. These might be related to (i) the need to deal with projections onto high dimensional linear approximating trial manifolds, (ii) expensive hyper-reduction strategies, or (iii) the intrinsic difficulty to handle physical complexity with a linear superimposition of modes. Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) – built, e.g., through proper orthogonal decomposition (POD) – when applied to nonlinear time-dependent parametrized partial differential equations (PDEs).
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