{
  "id": "2011.11327",
  "version": "v1",
  "published": "2020-11-23T11:08:05.000Z",
  "updated": "2020-11-23T11:08:05.000Z",
  "title": "Reduced Order Modeling for Parameterized Time-Dependent PDEs using Spatially and Memory Aware Deep Learning",
  "authors": [
    "Nikolaj T. Mücke",
    "Sander M. Bohté",
    "Cornelis W. Oosterlee"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We present a novel reduced order model (ROM) approach for parameterized time-dependent PDEs based on modern learning. The ROM is suitable for multi-query problems and is nonintrusive. It is divided into two distinct stages: A nonlinear dimensionality reduction stage that handles the spatially distributed degrees of freedom based on convolutional autoencoders, and a parameterized time-stepping stage based on memory aware neural networks (NNs), specifically causal convolutional and long short-term memory NNs. Strategies to ensure generalization and stability are discussed. The methodology is tested on the heat equation, advection equation, and the incompressible Navier-Stokes equations, to show the variety of problems the ROM can handle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-23T11:08:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reduced order model",
      "parameterized time-dependent pdes",
      "memory aware deep learning",
      "nonlinear dimensionality reduction stage",
      "long short-term memory nns"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}