Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations

  title={Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations},
  author={Hassan Arbabi and J. E. Bunder and Giovanni Samaey and Anthony J. Roberts and Ioannis G. Kevrekidis},
The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential operators requires extensive spatiotemporal data. For learning coarse-scale PDEs from computational fine-scale simulation data, the training data collection process can be prohibitively expensive. We propose to transformatively facilitate this training data… 

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