Weak formulation-based GENERIC formalism neural networks for learning dynamical systems from noisy measurements

  • Park, Jun Sur (Korea University Sejong)
  • Hashim, Auroni (North Carolina State University)
  • Cheung, Siu Wun (Lawrence Livermore National Laboratory)
  • Choi, Youngsoo (Lawrence Livermore National Laboratory)
  • Shin, Yeonjong (North Carolina State University)

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We propose the weak formulation-based GENERIC formalism informed neural networks (WGFINNs), which effectively handle noisy measurement data for data-driven approximation of dynamical systems. WGFINNs are based on GFINNs so that the first and second laws of thermodynamics are exactly met, yet offer a robust learning framework against noise in data. In theoretical sides, we prove that the noise level and the time-step size of data are critical factors that have significantly impacts on the accuracy of the solutions. In particular, the analysis suggests that the weak formulation-based approach produces solutions that are less sensitive to the noise level and the time-step size than those from the strong formulation. Numerical experiments confirm these findings and demonstrate the effectiveness of WGFINNs in handling noisy data.